NorizanMohamedNawawiMFKE2008 DU

i
INVESTIGATION OF STIMULATED BRILLOUIN SCATTERING FOR
THE GENERATION OF MILLIMETER WAVE FOR
RADIO OVER FIBER SYSTEM
NORIZAN BINTI MOHAMED NAWAWI
A project report submitted in fulfillment of the
requirements for the award of the degree of
Master of Engineering (Electrical - Electronic & Telecommunication)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
MAY 2008
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To my beloved mother and father
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ACKNOWLEDGEMENT
Praise be to Allah s.w.t. to Whom we seek help and guidance and under His
benevolence we exist and without His help this project could not have been
accomplished.
My sincere gratitude goes first to my supervisor Dr. Sevia Mahdaliza Idrus for
her guidance and all the support. She is a very caring supervisor that cared a lot about
my progress and how much I learned from the project.
I would also like to thank all my friends for the numerous ideas and helpful
hands throughout this project. My special thanks go to all my colleagues from the
Photonic Technology Centre group for the invaluable help and advice. I wish to thank to
our Photonic Lab technician, who has been lending a helping hand dealing with lab
facilities.
I am deeply grateful to my parents Mohamed Nawawi Bin Senik and Jamilah
Binti Ismail, as well as to my sister and brothers for a support and care throughout my
journey of education.
Finally, I thank my dear fiancé Shahrul for his inspiration and support.
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ABSTRACT
Radio over fiber (ROF) systems is characterized by having both a fiber optic link
and free-space radio path. Such systems are important in a number of applications,
including mobile communications, wireless local area networks (LANs), and wireless
local loop, etc. However, the growing demand for higher data rates in wireless
communication systems requires new frequency bands. The millimeter-wave (mmwave) range has the highest potential here because it is currently uncluttered and can
support high data bandwidth. To ease system complexity in such systems there is
growing interest in the exploitation of photonic technologies for the distribution of the
mm-waves from a central station to a number of base stations via optical fiber links.
Several techniques have been proposed for the optical generation of mm-waves such as
direct modulation, external modulation, optical heterodyning and so on. However, in this
work we proposed and investigate an alternative to above mention methods, which is
based on Stimulated Brillouin Scattering (SBS) in an optical fiber. SBS technique was
designed and modeled by performing CW laser in a single mode optical fiber (SMF)
through optical Mach-Zehnder modulator (MZM) with two pump lasers for
amplification purposes. The analysis was done by determination of the power depletion
of generated. SBS performance with the optical fiber loop length up to 100km was
analyzed. It has been shown that SBS power is depends on the fiber loop length which is
higher and lower at certain length due to natural properties of the fiber. The design
shown the RF generation was achieved up to 60 GHz.
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ABSTRAK
Sistem radio melalui fiber (ROF) ialah sistem yang mempunyai laluan optik dan
laluan radio tanpa ruang. Sistem ini sangat penting dalam banyak aplikasi termasuk
perhubungan bergerak, perhubungan kawasan setempat tanpa wayar (LANs), lingkaran
setempat tanpa wayar dan sebagainya. Namun, permintaan yang bertambah terhadap
kadar pemprosesan data yang tinggi dalam sistem perhubungan tanpa wayar
memerlukan jalur frekuensi yang baru. Gelombang millimeter (mm-wave) sangat
berpotensi di sini kerana ia tidak berterabur dan boleh manampung lebar jalur yang
tinggi. Dalam memudahkan sistem yang komplek, minat untuk mengkaji penggunaan
teknologi fotonik dalam mengagihkan gelombang millimeter dari stesen pusat ke
beberapa stesen asas melalui rangkaian gentian optik telah bertambah. Beberapa teknik
telah dicadangkan untuk menghasilkan gelombang millimeter secara optik seperti
modulasi secara terus, modulasi dari luar, pertindihan secara optik dan sebagainya.
Namun, dalam projek ini kami telah mencadangkan dan mengkaji satu alternatif kepada
teknik-teknik di atas, di mana ia berasaskan kepada rangsangan serakan Brillouin (SBS)
di dalam fiber optik. Teknik SBS direka dan dimodel dengan memancarkan laser
gelombang terus (CW) ke dalam fiber optik satu mod (SMF) melalui modulasi MachZehnder (MZM) dengan dua laser pam untuk tujuan penguatan. Analisis telah dilakukan
dengan menentukan pengurangan kuasa pada signal yang dihasilkan. Prestasi SBS
terhadap panjang gentian optik sehingga 100km dianalisis. Ia menunjukkan, kuasa SBS
bergantung kepada panjang fiber optik dimana maximum dan minimum disebabkan oleh
sifat semulajadi fiber. Rekabentuk menunjukkan penghasilan radio frekuensi (RF) pada
60 GHz telah dicapai.
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TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xi
LIST OF FIGURES
xii
LIST OF ABBREVIATIONS
xiv
LIST OF SYMBOLS
xvi
LIST OF APPENDICES
xvii
INTRODUCTION
1
1.1
Project Background
1
1.2
Problem Statement
2
1.3
Objectives
3
1.4
Scopes of Project
3
1.5
Methodology
5
1.6
Thesis Outline
9
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2
LITERATURE REVIEW
10
2.1
Introduction
10
2.2
Radio over Fiber (ROF)
11
2.2.1 Overview
11
2.2.2 Benefits of ROF Technology
13
2.2.3 ROF System Architectures
14
Optical Transmission Link
15
2.3.1 Optical Fiber
15
2.3.2 Optical Source (Laser)
16
2.3.3 Optical Modulation
17
2.3.4 Electro-Optic Modulation System
18
2.3.5 Electro-Optic Mach Zehnder Modulator
19
2.3.6 EDFA
20
2.3.7 Optical Receiver (Photodetectors)
21
Millimeter-Waves (mm-waves) Generation
21
2.4.1 Advantages of mm-waves
22
2.4.2 Disadvantages of mm-waves
23
2.4.3 Techniques for mm-waves Generation
23
2.4.4 Techniques Based on Harmonics Generation
26
2.3
2.4
2.5
3
2.4.4.1 The FM-IM Conversion Technique
26
2.4.4.2 Modulation Sideband Techniques
29
2.4.4.2.1 The 2 f Method
30
2.4.4.2.2 The 4 f Method
32
Conclusion
33
THEORETICAL BACKGROUND
34
3.1
Introduction
34
3.2
Nonlinear Optical Effects
35
3.3
Physics of Brillouin Scattering
37
3.3.1 The Scattering of Light
37
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4
5
3.3.2 The Spontaneous Brillouin Scattering
38
3.3.3 The Stimulated Brillouin Scattering (SBS)
39
3.4
SBS in Optical Fiber
39
3.5
SBS Modeling in Optical Fiber
41
3.6
Conclusion
42
SBS SYSTEM MODEL AND SIMULATION
43
4.1
Introduction
43
4.2
SBS System Block Diagram
44
4.3
Principle of Operation
45
4.3.1 Central Station
45
4.3.2 Optical Modulator
46
4.3.3 SBS Generator
46
4.4
SBS System Model Develop with Optisystem
48
4.5
Conclusion
50
SIMULATION RESULTS AND DISCUSSION
51
5.1
Introduction
51
5.2
Using a Sine Wave Generator to Drive MZM
52
5.3
Performance Analysis
61
5.3.1 SBS Performance with the Optical Fiber Loop Length
61
5.3.2 The Effect of EDFA Length
65
5.3.3 The Effect of Varying the Wavelength of CW Laser
66
5.3.4 Comparison with Different Type of Optical Fiber Loop 67
6
CONCLUSIONS AND RECOMMENDATIONS
69
6.1
Conclusions
69
6.2
Recommendations
71
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REFERENCES
Appendice A
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xi
LIST OF TABLES
TABLE NO.
TITLE
PAGE
5.1
Parameters used for simulation
52
5.2
Parameter used for difference optical fiber loop length
61
5.3
The individual stokes power with respective to SBS loop length
64
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LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
General radio over fiber (ROF) system
2
1.2
Project flow chart
5
2.1
900 MHz fiber radio system
12
2.2
Optical transmission link
15
2.3
Mach-Zehnder device structures
20
2.4
The 2 f technique for generating millimeter-waves
31
3.1
The scattering of light
37
3.2
Spontaneous Brillouin scattering
38
4.1
Propose SBS system block diagram
44
4.2
SBS system integrated with ROF link
45
4.3
Ideal circulator subsystems
47
4.4
SBS system model develop with Optisystem
48
5.1
Electrical wave modulated by Sinusoidal Generator in
time domain
53
5.2
Modulated signals behind the MZM
54
5.3
Electrical wave modulated by NRZ Generator in time domain
55
5.4
Modulated signals behind the MZM
55
5.5
Generated electrical signals at PIN photodiode in time domain
56
5.6
Frequency spectrum of the generated electrical signal at
PIN photodiode
5.7
The signals pattern with 10 GHz modulation at 0.5 dBm light
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wave for 50 km SSMF loop length
5.8
(a) The 20 GHz electrical signal in time domain
58
(b) The 40 GHz electrical signal in time domain
58
(c) The 60 GHz electrical signal in time domain
59
Frequency spectrums of the 20 GHz, 40 GHz and 60 GHz
electrical signal
5.9
(a) A -20 dBm power of 20 GHz electrical signal
60
(b) A -41 dBm power of 40 GHz electrical signal
60
(c) A -67 dBm power of 60 GHz electrical signal
60
The intensities of the first, second and third stokes generated
signal
5.10
The intensities of the first, second, third and fourth stokes
generated signal after amplification by optical amplifier
5.11
65
The intensities of the first, second, third and fourth generated
stokes by varying the wavelength of optical source
5.13
63
The intensities of the first, second, third and fourth generated
stokes by varying the EDFA length
5.12
63
66
The intensities of the system using standard single-mode fiber
(SSMF) and multimode fiber (MMF) by varying the optical
fiber loop length
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xiv
LIST OF ABBREVIATIONS
AM
Amplitude Modulation
ASK
Amplitude Shift Keying
BER
Bit Error Rate
BS
Base Station
CS
Control Station
CW
Continuous Wave
DFB
Distributed Feedback
E/O
Electric-to-Optic
EDFA
Erbium-Doped Fiber Amplifier
ESA
Electrical Spectrum Analyzer
FM
Frequency Modulation
FP
Fabry-Perot
FSK
Frequency Shift Keying
GIPOF
Graded Index Polymer Optical Fiber
GSM
Global System for Mobile
IF
Intermediate Frequency
IM
Intensity Modulation
LAN
Local Area Network
MMF
Multimode Fiber
mm-waves
Millimeter-waves
MZM
Mach-Zehnder Modulator
NLOP
Nonlinear Optical Polymer
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O/E
Optic-to-Electric
OOK
ON-OFF Keying
PD
Photodiode
PM
Phase Modulation
PSK
Phase Shift Keying
RF
Radio Frequency
RHD
Remote Heterodyning and Detection
ROF
Radio-over-Fiber
SBS
Stimulated Brillouin Scattering
SC
Switching Centre
SMF
Single Mode Fiber
UMTS
Universal Mobile Telecommunication System
VCSEL
Vertical Cavity Surface Emitting Laser
WDM
Wavelength Division Multiplexing
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LIST OF SYMBOLS
f
-
frequency
L
-
Interaction length
d
-
Height
θ
-
Angle
β
-
Modulating index
λ
-
Wavelength
c
-
Speed of light
D
-
Fiber group dispersion
Mp
-
Modulation depth
z
-
Fiber length
Jp
-
Bessel function
E
-
Electrical field
V
-
Voltage
ε
-
Normalized bias
Ω
-
Angular frequency
Aeff
-
Effective core area
α
-
Attenuation
n
-
Number of sideband
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LIST OF APPENDICES
APPENDIX
A
TITLE
PAGE
1) N. M. Nawawi, S. M. Idrus and A. Marwanto,
“Investigation of Stimulated Brillouin Scattering for
the Generation of Millimeter Waves for Radio over
Fiber System”, NCTT-MCP2008, Johor Bharu.
77
2) N. M. Nawawi and S. M. Idrus, “Modeling of
Stimulated Brillouin Scattering for the Generation
of Millimeter Waves for Radio over Fiber System”,
RAFSS2008, Johor Bharu.
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1
CHAPTER 1
INTRODUCTION
1.1
Project Background
Over the past decade there has been substantial progress in the areas of wireless
and optical communications. The driving force behind this advancement has been the
growing demand for multimedia services, and hence broadband access. Present
consumers are no longer interested in the underlying technology; they simply need
reliable and cost effective communication systems that can support anytime, anywhere,
any media they want. As a result, broadband radio links will become more prevalent in
today’s communication systems. Furthermore, new wireless subscribers are signing up
at an increasing rate demanding more capacity while the radio spectrum is limited. To
satisfy this increasing demand, the high capacity of optical networks should be
integrated with the flexibility of radio networks. This leads us to the discussion on the
fiber-based wireless access scheme using radio-over-fiber (ROF) technology.
ROF refers to a fiber optic link where the optical signal is modulated at radio
frequencies (RF) and transmitted via the optical fiber to the receiving end. At the
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receiving end, the RF signal is demodulated and transmitted to the corresponding
wireless user as shown in Figure 1[1].
Optical Fiber
BS
Control
Station
(CS)
E/O
T/R
O/E
Base Station (BS)
E/O: Electric-to-Optic Converter
O/E: Optic-to- Electric Converter
T/R: Transmitter/ Receiver
Figure 1.1
General Radio-over-Fiber (ROF) Systems
ROF is a promising technique in providing broadband wireless access services in
the emerging optical-wireless networks. Optical millimeter (mm)-wave generation is a
key technique to realize low cost and high transmission performance in the ROF
systems [2]. Several techniques have been proposed for the optical generation of mmwaves. One of the simplest methods is the modulation of continuous-wave (CW) laser
light by an external modulator is expensive and there are several problems with the
group velocity dispersion of the optical transmission systems. Other methods rely on the
optical transport of modulated carriers at intermediate frequencies and optical
heterodyne techniques. For the first method the mm-wave signal is generated by
upconversion in the base station. This requires a high-quality local oscillator or an
optically-supported phase-locked loop in the base station. The second method suffers
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from phase differences between the two superimposed optical signals. To overcome this
phenomenon rather complicated setups have been proposed [3].
This thesis reports on an investigation an alternative to above mention methods,
which a new proposed technique and very simple that only uses standard components of
optical telecommunications. Whereby, the technique relies on the generation of
sidebands of a continuous wave (CW) laser by the nonlinear modulation of an optical
modulator, which is based on stimulated Brillouin scattering (SBS) in an optical fiber.
Two of these sidebands are to be amplified by SBS in an optical fiber whereas the rest
are to be attenuated. Then these two sidebands are superimposed in a photodiode.
Owing to the fact that both sidebands come from the same source there will be no
problem with phase noise. This thesis reports on the work involved in modeling the
proposed method using suitable commercial optical system simulator; Optisystem for
performance characterization. These efforts resulted in potential to create very stable
mm-waves with low noise.
1.2
Problem Statement
ROF system has attracted considerable attention to deliver microwave and
millimeter wave signals. It is a system that distributes the radio waveform directly from
CS to BS through optical fiber. The growing demand for higher data rates in
communication systems requires new frequency bands. The mm-waves range has the
highest potential here because it can support high data bandwidth. This project was
focused on how to generate radio signal in ROF networks using SBS technique.
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1.3
Objectives
The objectives on this project are:
1.
To investigate the characteristics and performance of stimulated Brillouin
Scattering (SBS) technique in optical fiber for the generation of millimeter
waves.
2.
To verify the design for the generation of millimeter waves employing
Stimulated Brillouin Scattering (SBS).
1.4
Scopes of Project
The scopes of this project are:
1.
Understand the basic principle of the SBS technique.
2.
Design, model and simulate the SBS for generation of mm-waves for ROF
system using Optisystem.
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1.5
Methodology
The project focuses on the designation process of the SBS system in generating
mm-wave which is very important process before entering the higher process. The
corresponding higher process includes prototype system development, measurement and
full system integration process. The overall project flow is shown in Figure 1.2.
Start
Literature review on mm-waves ROF system
Design and analysis
Modeling and simulation
Result analysis and evaluation
the performance
System
Optimization
Report Writing
Done
Figure 1.2
Project Flow Chart
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The methodology starts with review on current progress on the ROF system
especially on the generation of the mm-waves modulated RF. It was followed by
investigation SBS for the tunable generation and amplification of mm-waves. The
theoretical analysis include SBS technique, basic concepts of ROF system and some
review of harmonic generation with a Mach-Zehnder modulator (MZM) and the
advantages and limits of SBS for the amplification of the sidebands.
For the system characterization, SBS method has been designed, modeled and
simulated. The technique relies on the generation of sidebands of a continuous wave
(CW) laser. The numerical simulation will obtained using suitable commercial optical
system simulator; OptiSystem.
Optisystem is an innovative optical communication system simulation package
that designs, tests, and optimizes virtually any type of optical link in the physical layer
of a broad spectrum of optical networks, from analog video broadcasting systems to
intercontinental backbones. It is a stand-alone product that does not rely on other
simulation frameworks. Optisystem is a system level simulator based on the realistic
modeling of fiber-optic communication systems. It possesses a powerful new simulation
environment and a truly hierarchical definition of components and systems. Its
capabilities can be extended easily with the addition of user components, and can be
seamlessly interfaced to a wide range of tools.
A comprehensive Graphical User Interface (GUI) controls the optical component
layout and netlist, component models, and presentation graphics. The extensive library
of active and passive components includes realistic, wavelength-dependent parameters.
Parameter sweeps allow you to investigate the effect of particular device specifications
on system performance. Created to address the needs of research scientists, optical
telecom engineers, system integrators, students, and a wide variety of other users,
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Optisystem satisfies the demand of the booming photonics market for a powerful and
easy-to-use optical system design tool.
The most comprehensive optical communication design suite for optical system
design engineers is now even better with the release of new version, Optisystem version
6.0. The latest version of Optisystem features a number of requested enhancements to
address the design of passive optic network (PON) based FTTx, optical wireless
communication (OWC), and radio over fiber systems (ROF).
Some benefits of Optisystem software as shown below:
•
Rapid, low-cost prototyping
•
Global insight into system performance
•
Straightforward access to extensive sets of system characterization data
•
Automatic parameter scanning and optimization
•
Assessment of parameter sensitivities aiding design tolerance specifications
•
Dramatic reduction of investment risk and time-to-market
•
Visual representation of design options and scenarios to present to prospective
customers
OptiSystem allows for the design automation of virtually any type of optical link
in the physical layer, and the analysis of a broad spectrum of optical networks, from
long-haul systems to MANs and LANs.
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Optisystem’s wide range of applications includes:
•
Optical communication system design from component to system level at the
physical layer
•
CATV or TDM/WDM network design
•
Passive optical networks (PON) based FTTx
•
Free space optic (FSO) systems
•
Radio over fiber (ROF) systems
•
SONET/SDH ring design
•
Transmitter, channel, amplifier, and receiver design
•
Dispersion map design
•
Estimation of BER and system penalties with different receiver models
•
Amplified system BER and link budget calculations
Finally, compare the results of the simulation with the theoretical analysis and
previous work. Improve this method has the potential to create very stable mm-waves
with low noise.
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1.6
Thesis Outline
This thesis comprises six chapters and is organized as follows:
Chapter 1 discusses the project background, problem statement, objectives,
scope of project, followed by methodology and the thesis outline.
Chapter 2 gives an introduction of ROF system, some fundamental theories of
optical fiber transmission link and the techniques of generating mm-wave signals.
Chapter 3 deals with the theoretical background of nonlinear effects which are focused
on physics of SBS effects and the effects in optical fiber.
The SBS system model is described briefly in Chapter 4. The principle
operation of the technique and its features are reviewed. The next chapter discusses and
analyzes the results obtained from performing SBS simulations. Chapter 6 gives the
conclusions for the whole project. Besides, it also provides the suggestion for future
recommendation that can be made to make the simulation more practical and
continuously.
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CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
The chapter constituting three major parts, briefly covers the ROF system
characteristics, the basic optical fiber transmission link and some technique of
generating mm-wave signals. The first part describes ROF systems which includes the
benefits of ROF and ROF system architectures. The second part is dedicated to a
description of general optical transmission link, where digital signal transmission is
assumed as current optical networks. The third part deals with mm-waves generation
and is subdivided as follows: (1) Advantages and disadvantages of mm-wave (2) RF
signal generation and transportation techniques. In addition, a technique based on
harmonics generation is described at the end of this chapter.
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2.2
Radio over Fiber (ROF)
2.2.1 Overview
Radio-over-fiber (ROF) technology has emerged as a cost effective approach for
reducing radio system costs because it simplifies the remote antenna sites and enhances
the sharing of expensive radio equipment located at appropriately sited (e.g. centrally
located) Switching Centres (SC) or otherwise known as Central Sites/Stations (CS). On
the other hand, Graded Index Polymer Optical Fiber (GIPOF) is promising higher
capacity than copper cables, and lower installation and maintenance costs than
conventional silica fiber.
In a ROF link, laser light is modulated by a radio signal and transported over an
optical fiber medium. The laser modulation is analog since the radio-frequency carrier
signal is an analog signal. The modulation may occur at the radio signal frequency or at
some intermediate frequency if frequency conversion is utilized. The basic configuration
of an analog fiber optic link consists of a bi-directional interface containing the analog
laser transmitter and photodiode receiver located at a base station or remote antenna
unit, paired with an analog laser transmitter and photodiode receiver located at a radio
processing unit. One or more optical fibers connect the remote antenna unit to the
central processing location.
ROF systems of nowadays, are designed to perform added radio-system
functionalities besides transportation and mobility functions. These functions include
data modulation, signal processing, and frequency conversion (up and down) [4, 5]. As
show in Figure 2.1, ROF systems were primarily used to transport microwave signals,
and to achieve mobility functions in the CS.
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For a multifunctional ROF system, the required electrical signal at the input of
the ROF system depends on the ROF technology and the functionality desired. The
electrical signal may be baseband data, modulated IF, or the actual modulated RF signal
to be distributed. The electrical signal is used to modulate the optical source. The
resulting optical signal is then carried over the optical fiber link to the remote station.
Here, the data is converted back into electrical form by the photodetector. The generated
electrical signal must meet the specifications required by the wireless application be it
GSM, UMTS, wireless LAN or other.
Fiber
RF in
(Modulated)
PIN
1.3µm
PD
Circ.
Antenna
Fiber
RF out
(Modulated)
PIN
Centre Station (CS)
Figure 2.1
1.3µm
LNA
Base Station (BS)
900 MHz Fiber Radio Systems [16]
By delivering the radio signals directly, the optical fiber link avoids the necessity
to generate high frequency radio carriers at the antenna site. Since antenna sites are
usually remote from easy access, there is a lot to gain from such an arrangement.
However, the main advantage of ROF systems is the ability to concentrate most of the
expensive, high frequency equipment at a centralized location, thereby making it
possible to use simpler remote sites. Furthermore, ROF technology enables the
centralizing of mobility functions such as macro-diversity for seamless handover. The
benefits of having simple remote sites are many. They are discussed in the following
section.
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2.2.2 Benefits of ROF Technology
ROF transmission offers many advantages in wireless systems, some of which
are:
•
Huge bandwidth that enables multiplexing several radio channels; each radio
channel may belong to a different system such as wireless LAN and cellular
radio,
•
Ability to use existing dark/dim fibers to transmit the radio signal (dim fiber can
be used with WDM techniques),
•
Inherent immunity to electromagnetic interference, and
•
Allowing for transparent operation because the RF to optical modulation is
typically independent of the baseband to RF modulation.
ROF also allows for easy integration and upgrades since the electrical to optical
conversion is independent of baseband to RF modulation format. Conventional
transmission mediums such as copper coaxial may not be completely replaced by optical
fiber, but in applications where factors such as RF power loss, future system upgrades
and transparency are considered, fiber is regarded as the most practical and efficient
medium. Even though the prospects of ROF are substantial, there is still plenty of
research to be carried out in this area before widespread deployment can be considered
[6].
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2.2.3 ROF System Architectures
There are three main ROF system architectures in use in current commercial inbuilding wireless deployments. All use direct modulation of a laser diode rather than
external modulation to reduce cost and complexity. The three types of radio over fiber
are;
•
RF transmission over single mode fiber directly at the radio carrier frequency
(usually in the range 800 – 2200 MHz, depending on the radio system). This is
the simplest architecture.
•
IF transmission over multimode or single mode fiber. The RF signal from the
base station is downconverted to IF and transmitted to the remote antennas
where it is upconverted back to the original RF. This allows pre-existing
multimode fiber cables to be used, although at the expense of additional cost and
complexity.
•
Digitized IF over multimode or single mode fiber. This approach uses
downconversion to IF as in the previous type and then digitizes the signal for
transmission over optical fiber. The analogue signal is then re-constructed at IF
and converted back to RF. This has the advantages of digital transmission (no
impairments due to noise and distortion), but at the expense of even further
complexity.
The most common of these architectures is the first, RF over single mode fiber,
because it is the simplest to design and the lowest cost to implement. However, it places
the most stringent requirements on the optical components, which need to have low
noise and low distortion at high frequency [7]. The laser is usually the dominant source
of noise and distortion in a ROF link, and a significant challenge in link design is
finding the right balance between cost and performance for this component.
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2.3
Optical Transmission Link
A general optical transmission link, shown in Figure 2.2, is briefly described for
which we assume that a digital pulse signal is transmitted over optical fiber unless
otherwise specified. The optical link consists of an optical fiber, transmitter, receiver
and amplifier, each of which is dealt with in the subsequent subsections.
Optical Fiber
Receiver
Transmitter
Amplifier
Amplifier
Figure 2.2
Optical Transmission Link
2.3.1 Optical Fiber
Optical fiber is a dielectric medium for carrying information from one point to
another in the form of light. Unlike the copper form of transmission, the optical fiber is
not electrical in nature. To be more specific, fiber is essentially a thin filament of glass
that acts as a waveguide. A waveguide is a physical medium or path that allows the
propagation of electromagnetic waves, such as light. Due to the physical phenomenon of
total internal reflection, light can propagate following the length of a fiber with little
loss.
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Optical fiber has two low-attenuation regions [8]. Centered at approximately
1300 nm is a range of 200 nm in which attenuation is less than 0.5 dB/km. The total
bandwidth in this region is about 25 THz. Centered at 1550 nm is a region of similar
size with attenuation as low as 0.2 dB/km. Combined, these two regions provide a
theoretical upper bound of 50 THz of bandwidth. By using these large low-attenuation
areas for data transmission, the signal loss for a set of one or more wavelengths can be
made very small, thus reducing the number of amplifiers and repeaters actually needed.
In single channel long-distance experiments, optical signals have been sent over
hundreds of kilometers without amplification. Besides its enormous bandwidth and low
attenuation, fiber also offers low error rates. Communication systems using an optical
fiber typically operate at BER's of less than 10-11 [8]. The small size and thickness of
fiber allows more fiber to occupy the same physical space as copper, a property that is
desirable when installing local networks in buildings. Fiber is flexible, reliable in
corrosive environments, and deployable at short notice. Also, fiber transmission is
immune to electromagnetic interference and does not cause interference.
2.3.2 Optical Source (Laser)
The word “laser” is an acronym for light amplification by stimulated emission
of radiation. The key word is stimulated emission, which is what allows a laser to
produce intense high-powered beams of coherent light (light that contains one or more
distinct frequencies). There are three main types of laser that can be considered for this
type of application [7];
•
CW Laser - A laser may either be built to emit a continuous beam or a train of
short pulses. This makes fundamental differences in construction, usable laser
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media, and applications. In the continuous wave (CW) mode of operation, the
output of a laser is relatively consistent with respect to time. The population
inversion required for lasing is continually maintained by a steady pump source.
•
VCSEL (vertical cavity surface emitting Laser); these lasers operate at 850 nm
and are predominantly multi (transverse) mode. Cost is very low because they
are produced in high volume for data communications applications.
•
FP (Fabry-Perot laser); these lasers are edge emitters and predominantly operate
at longer wavelength (1310 or 1550 nm windows) with multiple longitudinal
modes. Cost is intermediate between VCSELs and DFBs.
•
DFB (distributed feedback laser); these lasers are edge-emitters and
predominantly operate at longer wavelength (1310 or 1550 nm windows) with a
single longitudinal mode. Cost is higher than for VCSEL or FP.
2.3.3 Optical Modulation
To transmit data across an optical fiber, the information must first be encoded, or
modulated, onto the laser signal. Analog techniques include amplitude modulation
(AM), frequency modulation (FM), and phase modulation (PM). Digital techniques
include amplitude shift keying (ASK), frequency shift keying (FSK), and phase shift
keying (PSK). Of all these techniques, binary ASK currently is the preferred method of
digital modulation because of its simplicity. In binary ASK, also known as on-off
keying (OOK), the signal is switched between two power levels. The lower power level
represents a 0 bit, while the higher power level represents a 1 bit.
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In systems employing OOK, modulation of the signal can be achieved by simply
turning the laser on and off (direct modulation). In general, however, this can lead to
chirp, or variations in the laser's amplitude and frequency, when the laser is turned on. A
preferred approach for high bit rates (≥10 Gb/s) is to have an external modulator that
modulates the light coming out of the laser. To this end, the Mach-Zehnder
interferometer or electro absorption modulation is widely utilized [9, 10, 11].
2.3.4 Electro-Optic Modulation System
There are two primary methods for modulating light in telecommunications
systems: direct and external modulation. Direct modulation refers to the modulation of
the source, i.e. turning a laser on and off to create pulses, while external modulation uses
a separate device to modulate the light. External modulation has become the dominant
method for high-speed long-haul telecommunications systems.
External modulators can be implemented using a variety of materials and
architectures although typically electro-optic materials are used. In electro-optic
materials the permittivity of the material is affected by the presence of electric fields.
Many electro-optic materials are also birefringent. Since the indexes of the refraction are
related to the permittivities of the materials, the phase velocities of the light inside the
materials can changed by the application of electric fields. These changes are exploited
in various ways to achieve optical modulation.
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A material used in many commercial electro-optic modulators is lithium niobate,
LiNbO3. Lithium niobate is a crystalline material that is optically transparent as well as
birefringent. Currently, most 10 GHz per channel long-haul telecommunications
systems are based on lithium niobate modulators. Several companies are now offering
40 GHz modulators in anticipation of the development of higher bandwidth systems. As
products are developed to meet future needs there is an emphasis on higher operating
speeds and greater levels of device integration. Many electro-optic materials are
currently being investigated for use in developing optoelectronic devices. Several
groups are working with nonlinear optical polymers, NLOPs, to create electro-optic
devices, such as optical modulators. NLOPs have various characteristics that may
facilitate that development of high speed, low voltage electro-optic devices [11, 12].
2.3.5 Electro-optic Mach Zehnder Modulator
The Mach Zehnder interferometer is an electro-optic device used to modulate
wave amplitude. A Mach Zehnder interferometer consists of two Y-branches placed
back to back and separated by a distance. The arm are well spaced and are controlled by
an external voltage. The first Y-branch serves to divide the incoming light wave, which
is manipulated by the spaced arms, and the output Y-branch combines the light from the
two arms.
Figure 2.3 is shown the carrier signal (light) entering the modulator is split into
two paths, one path is unchanged (unmodulated) and another one is modulated. When
the light then recombined, the two waves interfere with one another. If the two waves in
phase, the interference is constructive and the output is ON. If it is out of phase,
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interference is destructive and the wave will cancel each other, then the output is OFF.
For the light ON is represent by binary 1 and for light OFF is represent by binary 0 [13].
Figure 2.3
Mach-Zehnder device structures
2.3.6 EDFA
EDFA (erbium-doped fiber amplifier) is an optical repeater device that is used to
boost the intensity of optical signals being carried through a fiber optic communications
system. An optical fiber is doped with the rare earth element erbium so that the glass
fiber can absorb light at one frequency and emit light at another frequency. An external
semiconductor laser couples light into the fiber at infrared wavelengths of either 980 or
1480 nanometers [14]. This action excites the erbium atoms. Additional optical signals
at wavelengths between 1530 and 1620 nanometers enter the fiber and stimulate the
excited erbium atoms to emit photons at the same wavelength as the incoming signal.
This action amplifies a weak optical signal to a higher power, affecting a boost in the
signal strength.
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2.3.7 Optical Receivers (Photodetectors)
In receivers employing direct detection, a photodetector converts the incoming
photonic stream into a stream of electrons. The electron stream is then amplified and
passed through a threshold device. Whether a bit a logical zero or one is depends on
whether the stream is above or below a certain threshold for bit duration. In other words,
the decision is made based on whether or not light is present during the bit duration. The
basic detection devices for direct detection optical networks are the PN photodiode (a pn junction) and the PIN photodiode (an intrinsic material is placed between p- and ntype material). In its simplest form, the photodiode is basically a reverse-biased p-n
junction. Through the photoelectric effect, light incident on the junction will create
electron-hole pairs in both the “n” and the “p” regions of the photodiode. The electrons
released in the “p” region will cross over to the “n” region, and the holes created in the
“n” region will cross over to the “p” region, thereby resulting in a current flow [11].
2.4 Millimeter-Waves (mm-waves) Generation
Mm-wave is a common name for an electromagnetic wave of frequency between
30 GHz to 300 GHz. A system for the delivery of this high frequency microwave signal
using optical fiber between base station (BS) and end users is known as mm-waves ROF
system [15].
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Millimeter waves offer several benefits. However, mm-waves cannot be
distributed electrically due to high RF propagation losses. In addition, generating mmwave frequencies using electrical devices is challenging. These issues describe the
electronic bottleneck already discussed above. The most promising solution to the
problem is to use optical means. Low attenuation loss and large bandwidth make the
distribution of mm-waves cost effective. Furthermore, some optical based techniques
have the ability to generate unlimited frequencies. For instance, microwave frequencies
that can be generated by Remote Heterodyning and Detection (RHD) methods are
limited only by the bandwidth of photodetectors. Advantages and disadvantages of mmwaves are listed below [16].
2.4.1 Advantages of mm-waves
They provide high bandwidth due to the high frequency carriers. Secondly, due
to high RF propagation losses in free space, the propagation distances of mm-waves are
severely limited. This allows for well-defined small radio sizes (micro- and pico-cells),
where considerable frequency re-use becomes possible so that services can be delivered
simultaneously to a larger number of subscribers.
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2.4.2 Disadvantages of mm-waves
The negative side of mm-waves is the need for numerous BSs, which is a
consequence of high RF propagation losses. Unless the BSs are simple enough,
installing and maintaining the mm-wave system can be economically prohibitive owing
to the numerous required BSs.
2.4.3 Techniques for mm-waves Generation
Recently, a lot of research has been carried out to develop mm-wave generation
and transport techniques, which include the optical generation of low phase noise
wireless signals and their transport overcoming the chromatic dispersion in fiber.
Several state-of-the-art techniques that have been investigated so far are described in
this section, which are classified into the following four categories [15]:
1.
Optical heterodyning
2.
External modulation
3.
Up- and down-conversion
4.
Optical transceiver
The easiest way is the direct modulation of a laser diode. However, high
frequencies cannot be reached with this method. For a packaged 1550-nm distributed
feedback (DFB) laser, 25 GHz has been reported, whereas for unpacked 1100-nm lasers,
40 GHz has been shown but only for small signal modulation and high bias currents.
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Another problem accompanied with direct modulation is the unavoidable chirp of the
laser diode output spectrum. This chirp is suppressed if the diode is externally
modulated. External optical modulators able to modulate up to 100 GHz have been
shown [18]. On the other hand, such modulators are still not commonly available, and
they are expensive. Furthermore, the dispersion in the fiber results in a beating between
the carrier and the sidebands of the modulated signal. Hence, the received radio
frequency (RF) power shows a periodical fading along the fiber due to different phase
shifts between the lower and the upper sideband induced by the different group velocity
dispersion.
A way to overcome such dispersion problems is the mid-span-spectral-inversion,
where, in the middle of the span, the phase-conjugated signal is generated. Another
possibility is the single sideband modulation or the filtering of one of the sidebands.
Single sideband modulation with Mach–Zehnder modulators (MZMs) can be achieved
either in a suppressed carrier or in a suppressed sideband configuration. Filtering of one
sideband can be done by optical filters or by SBS [18].
A method that automatically generates single sideband signals is optical
heterodyning. Heterodyning relies on the beating of two optical carriers in a photodiode.
The frequency difference between both waves is the intended mm-wave. The efficiency
of the optical-to-millimeter-wave conversion is high, and the frequency range that can
be generated is only limited by the bandwidth of the photodetector.
If two independent lasers are used for optical heterodyning, the stochastic phase
difference between them will lead to a phase noise of the generated mm-wave signal. In
order to suppress this phase noise, many techniques have been proposed; for instance, an
optical phase-locked loop or a dual-mode DFB laser. Another possibility is optical
injection locking, where one or two slave lasers are injection locked to an optical comb
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generated by a master laser [7]. All of these methods are rather complicated. They
require specially designed equipment, and they are very sensitive to environmental
influences. For optical injection locking, a temperature shift of a fraction of a degree is
sufficient to cause the system to fall out of lock if standard DFB lasers are being used
[7].
If the two frequency components are derived from only one optical source, they
will have the same phase, and, hence, no additional equipment is needed for the control
of the phases. One possibility is the generation of higher harmonics, for instance, with
pulsed semiconductor lasers, where the microwave spectrum of the pulsed output is a
comb of frequencies with a high harmonic content. Two of these sidebands can be
selected by optical filtering-for instance, with a Fabry–Perot filter to beat together in a
high-speed photodiode. The advantage of these techniques is that they can generate mmwave signals with 100% modulation depth [17, 18]. Only one optical source is used and
so the phase noise of the laser modes is correlated, which results in very low phase noise
electrical signals. In [19], four-wave mixing in a dispersion-shifted fiber was used for
the frequency comb generation, and arrayed waveguide gratings filtered the required
sidebands. With this technique, a 60-GHz optical fiber link over a distance of 108 km
was shown. With an amplified fiber loop optical frequency comb generator, more than
100 lines over a 1.8-THz bandwidth in the 1.55-μm band are possible [20]. However, the
optical power of the sidebands is rather low and will be further reduced by optical
filtering, so additional optical amplifiers are required for this method, which introduce
noise to the system and make it more complex and less reliable.
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2.4.4 Techniques Based on Harmonics Generation
2.4.4.1 The FM–IM Conversion Technique
The FM-IM conversion technique is interesting in that it thrives on the otherwise
undesired fiber chromatic dispersion to work. The conversion from an FM modulated
signal to an Intensity Modulated one is performed by the fiber’s chromatic dispersion
itself. An FM laser is FM modulated by applying a drive signal to one of its terminals.
This produces an optical spectrum that consists of spectral lines spaced by the drive
frequency. The FM optical signal is then propagated over dispersive fiber. Due to
chromatic dispersion effects, the relative phasing of the optical sidebands is altered
leading to intensity fluctuations of light at harmonics of the drive frequency. For the
case of an FM modulated optical signal and standard SMF with chromatic dispersion,
the instantaneous optical intensity received after propagating through the fiber is given
by
( )=
+∑
2
cos(
)
(2-1)
where Ip is the p th harmonic component of intensity variation given by equation. (2-2),
with Io being the dc photocurrent. The parameter ω is the modulating angular frequency,
and ξp is the phase of the p th harmonic. The p th harmonic component Ip is given by
=
(2
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(2-2)
27
where Jp (x) is the Bessel function of the first kind, β is the FM modulating index (or
phase modulation index) and φ is an angle characterizing the fiber dispersion given by
)
4
(2-3)
where λ is the free space wavelength of the laser, c is the speed of light, z is the fiber
length, and D is the fiber group dispersion parameter.
If the modulation depth Mp of the p th harmonic is defined as the ratio of the
amplitude of the alternating photocurrent at the p th harmonic to the dc photocurrent,
then Mp will be given by
=
(2
(
))
(2-4)
The FM-IM technique was used to generate mm-waves up to 60 GHz (15th
harmonic of 4 GHz drive signal). In theory the maximum achievable modulation depth
is 60% for the 10th harmonic. However, only 13% modulation depth was achieved in
practice. This was attributed to inherent intensity modulation present in the laser output.
The FM-IM modulation technique has also been used to overcome the chromatic
dispersion limit of SMF in digital transmission systems where it is referred to as
Dispersion Supported Transmission (DST) [20].
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Advantages
FM-IM conversion technique can be used to generate mm-waves at very high
frequencies efficiently. It is a simple technique to implement, which exploits the
undesirable fiber chromatic dispersion to operate.
Disadvantages
The obvious drawback of this technique is that the modulation depth varies with
the fiber length. However, it can be argued that varying the FM index can compensate
for the effect of length dependency of the modulation depth. Unfortunately, lasers with
good broadband FM response are not readily available. The FM laser must be capable of
wide optical frequency deviation at microwave rates. In general the peak-to-peak
frequency deviation must at least be equal to the millimeter-wave frequency desired. To
solve the problem of intensity modulation inherent in the directly modulated FM laser,
an external phase modulator in combination with a CW laser could be used. Using this
approach, theoretical modulation depths are realizable in practice.
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2.4.4.2 Modulation Sideband Techniques
There are two modulation side band techniques dubbed 2f and 4f methods.
Unlike the FM-IM technique, these techniques generate high order harmonics without
recourse to dispersive fiber by relying on the non-linear transfer characteristic of the
Mach Zehnder amplitude modulator (MZM). The output of the MZM in terms of the Efield can be described by:
( )=
(
(
(2-5)
where Ein(t) is the optical field applied to the input of the modulator, Vmod(t) is the
modulating voltage applied to the modulator, and Vπ is the modulating voltage required
to totally suppress the output. If the modulating voltage Vmod(t) is sinusoidal, it can be
written in the form
( )=
(1 + ) +
cos (
(2-6)
where ε and α are the normalized bias and drive levels respectively. Equation (2-5) then
becomes
( )=
[(1 + ) +
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]
(2-7)
30
where Ein(t) =cos(Ωt) , and Ω is the angular frequency of the applied optical field.
Expanding equation (2-7) into a series of Bessel functions, leads to
( )=
−
+
−
1
2
2
cos
cos
cos
cos
2
(1 + )
(Ω )
(1 + )
(Ω
(1 + )
(Ω
(1 + )
(Ω
)
)
) + ⋯ (2-8)
where Ji is the i th Bessel function of the first kind. Equation (2-8) shows the amplitudes
of the different optical harmonic components in the output signal of the modulated
MZM. The harmonics are separated by the modulating angular frequency ω and are
centered on the optical angular frequency, Ω. By adjusting the bias to appropriate levels
ε = 0 or ε =1, we obtain either the 2 f or the 4 f methods respectively [18, 20].
2.4.4.2.1 The 2f Method
To realize this method, the MZM is biased at Vπ, which means that ε = 0. This
will suppress the component at the optical central frequency, Ω as well as all other even
components at Ω+/-2ω , Ω+/-4ω etc. What remains are two strong components separated
by 2ω and centered on Ω, and higher order odd terms. The higher order terms have
lower amplitudes and can be reduced to 15dB below the two major components by
careful control of the bias point. The modulated optical signal is transported across the
fiber length up to the remote station. When the two strong components separated by 2ω
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impinge on the photodiode, they are heterodyned to generate a microwave signal with
angular frequency equal to 2ω. In other words, the generated microwave signal has a
frequency that is double the frequency of the modulating signal f
mm
= 2 fmod. This
doubling in frequency is what leads to the name 2 f method [16]. Adding data
modulation is achieved by filtering one of the optical sideband components and then
modulating it with the data before combining and transmitting both components, as
shown in Figure 2.4.
Figure 2.4
The 2 f Technique for Generating Millimeter-Waves [16]
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2.4.4.2.2 4f Method
The 4 f method is an extension to the frequency doubling 2 f method discussed
above. In this case the bias level is chosen such that ε =1. This leads to the suppression
of all odd harmonics. The optical spectrum then consists of spectral lines located at the
central optical angular frequency, Ω and on each side of the central frequency separated
by 2ω. By carefully choosing the drive voltage α such that Jo(απ/2) = 0 the central
component at Ω can be suppressed. This happens when απ/2 ≈ 2.4 or α ≈1.53. The
resulting optical spectrum now consists of two main components separated by four times
the drive frequency of the modulator. Heterodyning at the photodiode produces a high
frequency electrical signal mod f mm = 4 fmod at four times the drive frequency, hence the
term 4 f method. Data modulation is added in a similar fashion to the 2 f method [16,
20].
Advantages of the 2 f and 4 f methods
Both the 2 f and 4 f methods rely on optical heterodyning. Therefore, they are
capable of generating high frequency mm-waves. Since the same laser generates both
optical fields, the phase noise is highly correlated resulting in very narrow linewidth
mm-waves. In fact, the performance of these methods in terms of phase noise is
comparable to the OPLL system. The modulation depths achievable with these
techniques in practice are larger than in FM-IM techniques.
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Disadvantage of the 2 f and 4 f methods
The main disadvantage of these techniques is the need for filtering one of the
sidebands for data modulation. Temperature control is very important in order to keep
the filter aligned with the optical side band to be filtered.
2.5
Conclusion
In this chapter a brief description of conventional optical transmission link and
basic optical components have been given, and ROF system architectures have also been
described. The state-of-the-art techniques for distributing RF signals over fiber optic
link were reviewed. The different ROF techniques for generation of mm-waves may be
classified in terms of the frequency at which the signals are transported and the optical
modulation and detection principles involved.
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CHAPTER 3
THEORETICAL BACKGROUND
3.1
Introduction
This chapter deals with the theoretical background of nonlinear effects which is
focused on physics of SBS effects and its effects in optical fiber. These two topics are
essential to understand the contents of the dissertation.
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3.2
Nonlinear Optical Effects
Nonlinearities refer to optical phenomena involving a nonlinear response to a
driving light field. Lasers allow generating light with very high intensities. These can
give rise to a number of nonlinear effects, the most important of which are:
Parametric nonlinearities occur in certain crystal materials with χ(2) nonlinearity,
•
giving rise to effects like frequency doubling, sum and difference frequency
generation, and parametric amplification (nonlinear frequency conversion).
•
The Kerr effect raises the refractive index by an amount which is proportional to
the intensity, leading to effects like self-focusing, self-phase modulation, and
four-wave mixing.
•
Spontaneous and stimulated Raman scattering is the interaction of light with
"optical phonons".
•
Spontaneous and stimulated Brillouin scattering is the interaction of light with
"acoustical phonons" and typically involves counterpropagating waves.
•
Two-photon absorption is a process where two photons are simultaneously
absorbed, leading to an excitation for which a single photon energy would not be
sufficient.
There are also a number of other effects which are not directly based on optical
nonlinearities, but are nevertheless affecting optical phenomena:
•
Saturation of gain occurs particularly in lasers and amplifiers. Similarly, there
are nonlinear losses in saturable absorbers, e.g. in SESAMs used for passive
mode locking or Q switching.
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•
Photorefractive effects are observed in certain ferroelectric crystals such as e.g.
LiNbO3. They are used e.g. for holographic data storage, and can be detrimental
in nonlinear frequency conversion.
•
There are various kinds of effects involving heating, e.g. thermal lensing in laser
gain media or thermal detuning of optical resonators (e.g. enhancement cavities).
In optical fibers, there is a particularly long interaction length combined with the
high intensity resulting from a small mode area. Therefore, nonlinearities can have
strong effects in fibers. Particularly the effects related to the χ(3) nonlinearity; Kerr
effect, Raman scattering, Brillouin scattering, are often important, despite of the
relatively weak intrinsic nonlinear coefficient of silica: either they act as essential
nonlinearities for achieving certain functions (e.g. pulse compression), or they constitute
limiting effects in high power fiber lasers and amplifiers.
Strong nonlinearities also occur at intensities which are high enough to cause
ionization in the medium. This can lead to optical breakdown, possibly even associated
with damage of the material. In gases, extremely high optical intensities can be applied,
which can lead e.g. to high harmonic generation [21].
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3.3
Physics of Brillouin scattering
3.3.1 The scattering of light
When light travels through a transparent media, the most part of it travels
straight forward, but a small fraction of the light is scattered. The inhomogeneities of the
refractive index of the media are responsible for this phenomenon. Rayleigh scattering is
related to the inhomogeneities due to the material structure. The air, the glass are well
known examples where the small refractive index fluctuations induced by their
amorphous nature scatter light in all directions without changing the frequency of the
scattered light, because the inhomogeneities are frozen in the material structure.
Figure 3.1
The Scattering of Light
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3.3.2 The spontaneous Brillouin scattering
Index variations induced by the pressure differences of an acoustic wave
travelling through a transparent material can also scatter light. As described on the
Figure 3.2 below, this scattering occurs for a given direction, as in the case of a Bragg
grating, and induces a Doppler frequency shift of the scattered light, because the
pressure variations of an acoustic wave are periodic and travelling in the material. This
scattering, called spontaneous Brillouin scattering, can also be described using the
quantum physics: a photon from a pump lightwave is transformed in a new Stokes
photon of lower frequency and a new phonon adding to the acoustic wave.
Pump wave
Acoustic
wave
Stokes
lightwave
Figure 3.2
Spontaneous Brillouin Scattering
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3.3.3 The simulated Brillouin scattering
Consider an electrostrictive material where acoustic noise is due to the Bownian
motion of its molecules (thermal noise). Part of the light traveling through this media,
called here pump light, is backscattered by this acoustic noise: it is the spontaneous
Brillouin scattering. This backscattered light, called Stokes light, propagates in the
opposite direction and interferes with the pump light. Thus, due to the electrostriction,
an acoustic wave is generated and stimulates the Brillouin scattering even more, which
reinforces the acoustic wave, and so on. This loop process described here after is called
stimulated Brillouin scattering (SBS) and is comparable to the Larsen effect well known
by the singers.
Not considering the acousitc wave, whose energy is neglectible regarding to the
optical waves, this SBS process can be resumed as a energy transfer from the pump
wave to the Stokes wave. Stimulated Brillouin scattering is thus noting else than an
optical gain experienced by the stokes wave traveling through the electrostrictive
material in presence of the pump wave. The stimulated Brillouin scattering can be used
for building fiber optical amplifiers and narrow linewidth fiber lasers.
3.4
SBS in Optical Fiber
SBS is a problem for high laser power in long fibers. If there is high laser power
with a narrow linewidth along the fiber, the SBS effect causes much light to be
reflected. This limits the power that can be transmitted and makes the signal noisy.
Therefore SBS is an issue for optical transmitters in optical networks and for
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instruments that test components or systems with long fibers. Such tests can include
measuring the power budget of an amplified or unamplified transmission span, or testing
Raman amplifier configurations. Fibers exhibiting SBS at power levels of interest to
telecommunications are usually at least several kilometers in length, but this depends on
the type of fiber.
The origin of SBS lies in the backscattering of signal light by acoustic waves in
the optical material, which is weak in short fibers. The backscattered light is shifted to
lower optical frequency (higher wavelength) by the Brillouin-shift frequency, which
depends on the fiber material. For common single-mode silica fiber, the shift is about 11
GHz (0.09 nm at 1550 nm). The backscattered light in a fiber can then stimulate more of
the forward traveling light to be backscattered. When there is enough signal power, the
backscattered light can gain more power by this stimulated backscattering than it loses
due to fiber attenuation. When the fiber is long enough, the backscattered power keeps
increasing along the fiber in an avalanche like process and can take most of the input
optical power [23].
SBS is a nonlinear effect, because the amount of light backscattered, and the
amount of light transmitted by the fiber, does not depend linearly on the power input to
the fiber. At low input powers the backscattering is dominated by simple Brillouin and
Rayleigh scattering which are linear and differ from each other by the Brillouin shift.
But as the power is increased, the Brillouin scattered light is increasingly amplified by
the stimulation process. At a power level called the SBS threshold, the amount of
backscattered light increases very rapidly with increasing input power until it constitutes
most of the input light. The transmitted power at the fiber output saturates at a level that
barely increases with increased input power. For single-mode fiber, SMF, of lengths
above 10 km, the SBS threshold can lie in the range of 6 - 10 dBm. Above this
threshold, the insertion loss of the fiber is not independent of input power [23].
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In addition to the power loss problem associated with SBS, there is also an
increase in Relative Intensity Noise, RIN, on the transmitted signal. Rapid fluctuation in
power is caused by the variability of the backscattered power due to the sensitivity of
this nonlinear feedback-coupled effect on polarization and environmental influence, and
on the beat noise resulting from all the spontaneously generated scattering along the
fiber.
3.5
SBS Modeling in Optical Fiber
SBS in optical fiber only occurs in backward direction, that is, the generation of
Stokes wave only. The SBS dynamics can be described by the coupled differential
equation system given as
=−
[∆
+
]
−
(2-9)
=−
[∆
−
]
+
(2-10)
with PS and Pp as the powers of the signal wave and the pump wave, α as the attenuation
in the fiber, Aeff as the effective core area, and gB as the Brillouin gain. The variables Δk1
and Δk2 are phase mismatch terms that can be described by
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∆
=
(∆ )
(2-11)
and
∆
=
∆
(∆ )
(2-12)
whereas Δk = 1/va(wS-wSMAX). In these equations, αa is the attenuation, va is the velocity
of the acoustic wave, and wS-wSMAX is the detuning of the signal frequency from the
maximum of Brillouin gain. The phase of the amplified Stokes wave is determined by
the term associated with the complex number j in (2-10). Therefore, if Δk2 = 0, then the
phase of the amplified sideband remains the same during the amplification process.
According to (2-12), this is the case if the frequency detuning is zero. Hence, one can
assume that the effect of the phase noise due to SBS to the system is negligible small
[17, 18].
3.6
Conclusion
Chapter 3 gives a description of the nonlinear optical effects. Nonlinearities can
have strong effects in optical fibers. The last important of corresponding effect that
affects the transmission is the stimulated Brillouin scattering (SBS). The origin of SBS
lies in the backscattering of signal light by acoustic waves in the optical material, which
is reacted due to the fiber’s length.
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CHAPTER 4
SBS SYSTEM MODEL AND SIMULATION
4.1
Introduction
This chapter describes and analyses the principle of SBS for generating of RF
signals. A theoretical model of an SBS system, without any fiber link is developed. First
part represents the system block diagram of SBS technique consists of optical modulator
and SBS generator, and the basic optical communication components that has been used.
The principle operation of the technique and its features were revealed in this subchapter. SBS simulation model using Optisystem can be found in the last part of the
chapter. The parameters that have been used in this project were clearly stated.
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4.2
SBS System Block Diagram
Figure 4.1 show the system block diagram of SBS technique that has been used
in this project. This technique was designed and modeled by performing CW laser in a
single mode optical fiber (SMF) through optical Mach-Zehnder modulator (MZM) with
two pump lasers for amplification purposes. MZM is nonlinear modulator that capable
for generation of sidebands. These sidebands will be amplified by SBS in a fiber loop,
whereas the rest will be attenuated due to natural attenuation in the fiber. Electrical
generator was used to drive the MZM at certain frequency carrier. Circulator has been
selected to circulate the signal from coupler and the output signal of SBS fiber loop. The
amplified sidebands are then superimposed in PIN-photodiode which is the easiest way
to generate mm-wave.
Figure 4.1
Propose SBS System Block Diagram
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SBS
Generator
Optical
Modulator
Central Station (CS)
Figure 4.2
4.3
SBS System Integrated With ROF Link.
Principle of Operation
4.3.1 Central Station
The CS consists of optical modulator and SBS generator. Optical modulator can
be any type of modulator as long as it can generate the harmonics that separated by
frequency carrier. It means that we can use an arbitrary of laser and electrical generator.
However, in this particular project, we stated to investigate the design using the CW
laser and an intensity modulator (IM).
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4.3.2 Optical Modulator
The optical modulator consists of a CW laser, an intensity modulator (IM), an
electrical drive signal operating at a frequency, fsw , and the data to be transported. The
drive signal is used to sweep the optical frequency of the CW laser resulting in a peakto-peak optical frequency deviation. To generate an un-modulated microwave or
millimeter-wave carrier at the BS, this swept optical signal is fed directly into the SBS
fiber loop. Otherwise, the swept optical signal is fed into an IM such as the Mach
Zehnder Modulator (MZM), where it is intensity modulated before being distributed by
the fiber network. In this case, the signal laser directly generates sidebands of the
modulation signal due to its nonlinear characteristic line. These sidebands can be
amplified by the SBS in optical fiber.
4.3.3 SBS Generator
The output of optical modulator is fed into the SBS generator where the SBS
amplifications and up-conversions were occurred. Pump lasers were used to amplify the
selected sidebands produced by MZM by control the frequencies of these pump lasers.
The three ports circulator will circulate the signal from port 1 (output from the coupler)
into the port 2, and the signal from port 2 into port 3 as shown in Figure 4.3. Using ideal
circulator, we can control the insertion loss to be zero and there is no return loss or ideal
isolation. The two frequency components from the output of circulator are then be
superimposed in photodiode which is one of the easiest way for generating mm-waves.
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Port 2
Port 3
Port 1
Figure 4.3
Ideal Circulator Subsystems
SBS is a nonlinear effect due to the amount of light backscattered and the
amount of light transmitted by the fiber does not depend linearly on the power input to
the fiber. At low input powers the backscattering is dominated by simple Brillouin and
Rayleigh scattering which are linear and differ from each other by the Brillouin shift.
But as the power is increased, the Brillouin scattered light is increasingly amplified by
the stimulation process. At a power level called the SBS threshold, the amount of
backscattered light increases very rapidly with increasing input power until it constitutes
most of the input light. The transmitted power at the fiber output saturates at a level that
barely increases with increased input power. For single-mode fiber, SMF, of lengths
above 10 km, the SBS threshold can lie in the range of 6 - 10 dBm. Above this
threshold, the insertion loss of the fiber is not independent of input power.
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4.4
SBS System Model Develop with Optisystem
The generation of millimeter-waves for RoF system using SBS technique using
Optisystem software is given in the following Figure 4.4.
Figure 4.4
SBS System Model Develop with Optisystem
The Mach-Zehnder Modulator (MZM) is driven by the electrical sine generator
in analog domain working with a fixed frequency; in this design, fRF = 10 GHz. A 0.5
dBm light wave emitted from continuous wave (CW) laser at 1550 nm from a
narrowband linewidth of 1 MHz is modulated by MZM. The voltage that is applied on
the MZM is high enough so that the laser wave is modulated nonlinearly with the
frequency of the electrical generator. Several optical sidebands separated by fRF from the
optical carrier are generated by MZM nonlinearity. These signals are injected into 50km
long of standard single mode optical fiber (SSMF). The pump source generates a
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combined output signal of two pump lasers. This pump source is injected into SSMF via
an optical circulator and propagates at the opposite direction of the modulated signals.
The wavelength of each pump laser is adjusted in the manner of 11GHz higher than one
of the frequencies in the modulated signal. The power of signal wave is controlled by an
Er-doped fiber amplifier (EDFA). SBS relies on the generation of sidebands of CW laser
by nonlinear modulation. These two sidebands will be amplified by SBS in an optical
fiber, whereas the rest will be attenuated due to natural attenuation in the fiber [3][13].
The millimeter-wave band output signal is detected by a photodiode (PD).
The frequency of the mm-wave depends on the RF of the electrical generator and
on the sidebands that were chosen for amplification. The generated mm-wave has the
frequency
fmm=2nf
[13]
with n as the number of the sideband used and f as the RF of the electrical generator.
With f = 10 GHz, millimeter-waves with frequencies of 20, 40, 60, . . . GHz are
possible. If the frequency of the generator is f = 5 GHz, output frequencies of 10, 20, 30,
. . . GHz can be produced, and so on.
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4.5
Conclusion
The SBS system has been modeled and its principle of operations were analysed
theoretically. SBS system was divided into two main parts, which are optical modulator
and SBS generator. Optical modulator generates several frequency components, which
are harmonics of the electrical signal, fRF. It can be any type of modulator as long as it
can generate the harmonics that separated by frequency carrier. The amplifications and
up-conversions of the sidebands were occurred in SBS generator part.
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CHAPTER 5
SIMULATION RESULTS
AND DISCUSSION
5.1
Introduction
The SBS technique for generation mm-waves for ROF system designed in
Chapter 4 was simulated in Optisystem software. This chapter presents the simulation
results and the analysis of the results. It has to be mentioned that there are many factors
that are not included or considered in the simulation while they exist in reality, such as
pump lasers linewidths and etc. At this moment, the simulation will only consider some
important combinations of parameters that dominant in optical data transmission for
project simulation purpose. Therefore, the results for this project were carried out based
on this assumption.
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5.2
Using a Sine Wave Generator to Drive the MZ Modulator
In this project, the simulation is done based on the basic simulation setup
parameters and available commercial values. The following table shows the value of
these parameters.
Table 5.1 : Parameters used for simulation
Parameter
Value
Bit Rate
10 Gbps
Time Window
1.28e-0.08 s
Sample Rate
640 GHz
Sequence Length
128 Bits
Sample per Bit
64
Number of Samples
8192
Sensitivity
-100 dBm
Resolution
0.1 nm
Fiber Loop Length
50 km
Optical Power of CW laser
0.5 dBm
Linewidth of CW laser
1 MHz
Wavelength of CW laser
1550 nm
Frequency of Electrical Generator, fRF
10 GHz
Dispersion of Optical Fiber
16.75 ps/nm/km
Attenuation of Optical Fiber
0.2 dB/km
Effective Area of Optical Fiber, Aeff
80 µm2
Brillouin Gain, gB
4.6e-11 m/W
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The shape of the drive signal, fRF has an effect on the generated millimeter-wave
signal. There are lots of electrical generators that available in Optisystem such as
sinusoidal, triangular, sawtooth wave generator and etc.. However, in this work we only
consider the sinusoidal electrical wave generator to drive the MZM.
The following Figure 5.1 shows the electrical signal that generated by Sinusoidal
Wave at RF frequency of fRF = 10 GHz. This signal will be modulated nonlinearly by the
external modulator, MZM and used CW laser at 0.5 dBm as a carrier. Figure 5.2
confirms that the optical spectrum consists of spectral lines spaced by the drive
frequency, fRF = 10 GHz. As can be seen, the MZM generates the harmonics of the
signal up to four sidebands at 1550 nm wavelength of laser.
Figure 5.1
Electrical wave modulated by Sinusoidal Generator in time domain
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10 GHz
Figure 5.2
Modulated signals behind the MZM
Figure 5.3 shows the generated electrical signal in digital domain. It was done by
replaced the sinusoidal electrical wave generator by non-return to zero (NRZ) pulse
generator and pseudo-random bit sequence) generator. The data bits are generated by a
random number generator; it generates a bit sequence of 0 and 1 with equal probability.
The output behind the MZM can be found in Figure 5.4.
The digital electrical generator for SBS technique leads to difficulty to
distinguish the order of sidebands generated by MZM as shown in Figure 5.4.
Furthermore, there is no option to state the RF frequency carrier in Optisystem software
for this type of electrical generator. Therefore, the analog with sinusoidal electrical wave
generator has been used in this project.
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Figure 5.3
Electrical wave modulated by NRZ Generator in time domain
Figure 5.4
Modulated signals behind the MZM
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Figure 5.5 and 5.6 show the output of the PIN photodiode in time and frequency
spectrum respectively. Oscilloscope Visualizer was used to display the time plot of the
generated electrical signal.
Meanwhile, ESA (RF spectrum analyzer) was used to detect the PD output in
frequency domain. The detected frequency spectrum can be found in Figure 5.6. The
figure shows the existence of amplified component at 20 GHz, 40 GHz and 60 GHz.
Harmonics components have decreased the power intensity as expected, which the
power of each harmonic decreased according to the order of harmonics [13]. It shows
that the noise floor between 20 GHz and 40 GHz stokes and between 40 GHz and 60
GHz stokes both are 12 dB. In this experiment, RF 20 GHz is referred to the first stoke,
RF 40 GHz is referred to second stoke, third stoke for RF 60 GHz and so on.
Figure 5.5
Generated electrical signals at PIN photodiode in time domain
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20 GHz, -20 dBm
40 GHz, -41 dBm
60 GHz, -67 dBm
Figure 5.6
Frequency spectrum of the generated electrical signal at PIN photodiode
Figure 5.7 shows the signal pattern of the first, second and third stokes with 10
GHz modulation at 0.5 dBm light wave for 50 km SSMF loop length, measured after PD
in time domain. Oscilloscope visualizer was used to display the time plot of the
generated electrical signal. Bandpass rectangular filter (BPF) is used to centre of the
desired stoke components results in electrical signals of regular intensity patterns.
It is clear that the only difference between signal patterns at 20 GHz and 40 GHz
(apart from frequency) is the amplitude (a.u). The amplitude of higher stokes was
decreased from 4 mV to about 350µm. As can be seen in Figure 5.7 (c), the amplitude is
fluctuated and very small compared to figure (a) and (b). This confirms that apart from
the fundamental frequency, the higher order stokes may also be used to transmit data.
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(a)
(b)
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(c)
Figure 5.7
The signals pattern with 10 GHz modulation at 0.5 dBm light wave for
50 km SSMF loop length (a) The 20 GHz electrical signal in time domain; (b) The 40
GHz electrical signal in time domain; (c) The 60 GHz electrical signal in time domain
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The following figures show the frequency spectrum of electrical signal after
filtered by Rectangular Bandpass Filter at 15 GHz. Each signal is carried by their own
frequency at 20 GHz, 40 GHz and 60 GHz respectively.
(a)
(b)
(c)
Figure 5.8
Frequency spectrums of the 20 GHz, 40 GHz and 60 GHz electrical
signal. (a) A -20 dBm power of 20 GHz electrical signal. (b) A -41 dBm power of 40
GHz electrical signal. (c) A -67 dBm power of 60 GHz electrical signal
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5.3
Performance Analysis
5.3.1 SBS Performance with the Optical Fiber Loop Length
The simulation has been done for difference optical fiber loop length where the
range of lengths is from 1km to 100km. The results given below were obtained based on
the fixed parameters show in Table 5.2.
Table 5.2 : Parameter used for difference optical fiber loop length
Parameter
Value
Fiber Loop Length
0 km to 100 km
Optical Power of CW laser
0.5 dBm
Wavelength of CW laser
1552.52 nm
Frequency of Electrical Generator, fRF
10 GHz
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The results from this part of analysis show that the intensity of relative harmonic
power was degraded depending on the optical fiber loop length. Figure 5.9 shows the
comparison in terms of the intensities of the First, Second and Third Stokes Generated
by the Sine-wave Generator; 20 GHz, 40 GHz and 60 GHz respectively.
As can be seen, for the first stoke (black line) the graph was dropped steadily
from 20 km until around 38 km and the relative power was about -90 dBm. However,
the graph rose back to -67 dBm at 52 km and was fallen down again at 74 km. For the
second stoke (red line), it can be seen that was a wild fluctuations from 10 km until 70
km. Without optical amplifier, the third (blue line) was only observed at 10 km optical
fiber loop length.
Figure 5.10 show the SBS performance with EDFA. In term of power intensities,
the amplifier was boosted up the power up to 0dBm at 20km for the first stoke. As can
be seen, the first stokes has higher intensity compared to second, third and fourth stokes.
It also shows that the SBS effect was started occur at 10 km and then will degraded the
power intensities in longer fiber. We were managed to get the fourth stoke at 80 GHz in
this designed, however the power intensity is quite low.
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#1st Stoke
#2nd Stoke
#3rd Stoke
Figure 5.9
The intensities of the first, second and third stokes generated signal
#1st Stoke
#2nd Stoke
#3rd Stoke
#4th Stoke
Figure 5.10
The intensities of the first, second, third and fourth stokes generated
signal after amplification by optical amplifier
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Table 5.3 shows the analysis of stokes power at difference length with and
without optical amplifier.
Table 5.3 : The individual stokes power with respective to SBS loop length
Fiber Loop
Length
20 km
50 km
100 km
Δ
Nth
sidebands
1
Without
amplifier
-54 dBm
With
amplifier
-4 dBm
50 dB
2
-94 dBm
-16 dBm
78 dB
3
-
-32 dBm
68 dB
1
-67 dBm
-20 dBm
47 dB
2
-
-38 dBm
62 dB
3
-
-68 dBm
32 dB
1
-90 dBm
-42 dBm
48 dB
2
-
-64 dBm
36 dB
3
-
-88 dBm
12 dB
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5.3.2 The Effect of EDFA Length
The second part of analysis discusses the effect of EDFA length. The simulation
was done by varying the optical amplifier (EDFA) length within range 1m until 5m. The
result given below was obtained based on the fixed parameters show in Table 5.2. For
the simulation, the optical fiber loop length was fixed to 50 km.
#1st Stoke
#2nd Stoke
#3rd Stoke
#4th Stoke
Figure 5.11
The intensities of the first, second, third and fourth generated stokes by
varying the EDFA length
Figure 5.11 shows the comparison intensities of the first, second, third and fourth
generated harmonics; 20 GHz, 40 GHz, 60 GHz and 80 GHz respectively. The
magnitude of all stokes linearly increased with EDFA length up to 4m. The
amplification stabilized with EDFA length more than 5m onward. The first stoke (brown
line) achieved steady state at -4 dBm, and -16 dBm for second harmonic (red line). The
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relative stokes power can be achieved near -30 dBm and -46 dBm for third (green line)
and fourth harmonics (blue line) respectively.
5.3.3 The Effect of Varying the Wavelength of the CW Laser
The following result has been achieved by varying the wavelength of the CW
laser within range 1200 nm until 1600 nm. Table 5.2 on page 65 shows the simulation
parameter. For this result, the optical fiber loop length was fixed to 50 km.
#1st
#2nd
#3rd
#4st
Figure 5.12
The intensities of the first, second, third and fourth generated stokes by
varying the wavelength of optical source
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Figure 5.12 shows the difference performance of four generated harmonics when
varies the wavelength. Within 1250 nm to 1340 nm, the performances for all stokes
were higher. It may because of the low attenuation loss at 1300 nm window. At 1540
nm to 1680 nm windows, the graphs were increased dramatically for all generated
stokes. It is shown that the SBS much more dominant at C-Band which the wavelength
range between 1530 nm and 1562 nm.
5.3.4 Comparison with Different Type of Optical Fiber Loop
The performance of the optical fiber link depends on the optical fiber that be
used. Single-mode optical fiber (SMF) is basically used for long haul transmission link
and high bit rate system. It was capable with laser as an optical source and PIN or APD
at the receiver part. Meanwhile, multimode fiber (MMF) is normally used for short
distance and low bit rate system. This optical fiber was capable working with LED as a
light source and PN at the receiver part.
All the analysis before have been done using standard single mode fiber (SSMF).
In this part of analysis, the performance of SBS technique has been carried out using
another type of fiber which is MMF. The graph for both performances was shown in
figure below.
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SSMF
MMF
Figure 5.13
The intensities of the system using standard single-mode fiber (SSMF)
and multimode fiber (MMF) by varying the optical fiber loop length
Figure 5.13 clearly shows that the design of SBS model in this project is not suit
for MMF as optical fiber loop. As can be seen, there was no signal at all after 8 km of
optical fiber loop length (Sensitivity of the PIN photodiode is -100 dBm).
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CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusions
The study of nonlinear effect is essential in future implementation of optical
communication. Stimulated Brillouin Scattering (SBS) is a nonlinear effect in an optical
fiber due to the amount of light backscattered, and the amount of light transmitted by the
fiber, does not depend linearly on the power input to the fiber.
In this project, SBS is used as a method for the tunable generation of mm-waves
for ROF. After all, the theory and concept of the SBS frequency conversion technique
for generation mm-waves for ROF have been studied. ROF system using SBS technique
for generation of modulated RF signal at mm-waves frequency was completely designed
and modeled using Optisystem software. The frequency of the generated wave depends
on the frequency of the electrical generator and the wavelength of the pump waves, so
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with a common control of these values it is possible to easily tune the output frequency
of the device.
The generation of mm-waves for RoF system using SBS in SSMF has been
demonstrated. The proposed technique is necessary for any electrical generator
frequency other than 10 GHz. Simulation results have demonstrated that the designed
SBS technique for ROF system has a potential to generate high mm-waves. A 0.5 dBm
of light wave is carried by 10 GHz RF signal were successfully generated up to 60 GHz
millimeter-wave band corresponding to the 3rd stokes. Test the design using an arbitrary
wave generator for optimum power performance may be a future work for this paper.
The results in this work are significant for publication of papers that can be
found in Appendix A.
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6.2
Recommendations
Additional work is planned to further validate the performance of SBS design
using an arbitrary wave generator such as triangular wave, sawtooth wave or other type
of electrical generator. The shape and principle operation of this generator will be
studies and its relation with sinusoidal electrical wave operation will be investigated.
For this project, only one carrier is used for simulation purpose which is RF
frequency of 10 GHz. However, for the future work, I would recommend to extend the
designed system to carry multicarrier multiplexed system such as OFDM systems,
which play an important role in communication system.
The investigation of SBS technique can also be done in other software such as
MATLAB using mathematical simulation. This provides an alternative way to
investigate the performance and characteristic of the SBS technique for generation of
mm-waves for ROF system.
Last but not least, I would recommend the SBS generator system to be setup for
practical measurement.
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M. Arsat, “The Subcarrier Multiplexing for Radio over Fiber”, M. Eng. Thesis,
Universiti Teknologi Malaysia, 2007.
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[15]
K. Kitayama, “Architectural considerations of radio-on-fiber millimeter-wave
wireless access systems”, Signals, Systems, and Electron., 1998 URSI
International Symposium, pp. 378.383, 1998.
[16]
A. Ng’oma, “Design of a Radio-over-Fibre System for Wireless LANs”, Thesis.
TUE. WP6, Pub. 2002, v01
[17]
Markus
Junker, Thomas Schneider, Max
J. Ammanno, Andreas T.
Schwarzbacher, and Kai-Uwe Lauterbach, “Carrier Generation in the Millimetre
Wave Range based on Stimulated Brillouin Scattering for Radio over Fibre
Downlink Systems” Dublin Institute of Technology, pp. 191-195,June 28-30
2006.
[18]
T. Schneider, D. Hannover, and M. Junker,”Investigation of Brillouin Scattering
in Optical for the Generation of Millimeter Waves”, J. Lightw. Technol., vol. 24,
pp. 295-304, Jan 2006.
[19]
K. I. Kitayama, “Highly stabilized millimeter wave generation by using fiberoptic frequency-tunable comb generator,” J. Lightw. Technol., vol. 15, no. 5, pp.
883–893, May 1997.
[20]
A.
Ng’oma,
“Radio-over-fibre
technology
for
broadband
wireless
communication systems” Technische Universiteit Eindhoven, 2005.
[21]
A. Djupsjobacka, G. Jacobsen, and B. Tromborg, “Dynamic Stimulated Brillouin
Scattering Analysis”, J. Lightw. Technol., vol. 18, no. 3, pp. 416–424, March
2000.
[22]
A. C. Wong, “Experimental Study of Stimulated Brillouin Scattering in Open
Cells and Multimode Optical Fibers”, M. Sc. Thesis, University of Adelaide,
June 2005.
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[23]
M. Kelly, “Controlling SBS in Measurements of Long Optical Fiber Paths”,
Apllication Note, Agilent Technology, May 06, 2003.
[24]
S.M. Idrus, and R.J. Green, “Photoparametric Up-Converter For MillimeterWave Fiber-Radio System” International IrDA/IEE/IEEE Seminar, Warwick,
Sept. 2003.
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APPENDIX A
1) N. M. Nawawi, S. M. Idrus and A. Marwanto, “Investigation of Stimulated
Brillouin Scattering for the Generation of Millimeter Waves for Radio over
Fiber System”, NCTT-MCP2008, Johor Bharu.
2) N. M. Nawawi and S. M. Idrus, “Modeling of Stimulated Brillouin
Scattering for the Generation of Millimeter Waves for Radio over Fiber
System”, RAFSS2008, Johor Bharu.
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Investigation of Stimulated Brillouin Scattering for
the Generation of Millimeter Waves for Radio over
Fiber System
N. M. Nawawi
S. M. Idrus
School of Computer and Communication
Universiti Malaysia Perlis
02600 Arau, Perlis, Malaysia
E-mail: [email protected]
Photonic Technology Centre
Faculty of Electrical Eng., Universiti Teknologi Malaysia
81310 Skudai, Johor Darul Takzim, Malaysia
E-mail: [email protected]
Abstract— Radio over fiber (RoF) is a promising technique in
providing broadband wireless access services in the emerging
optical-wireless networks. Optical millimeter-wave (mm-wave)
generation is a key technique to realize low cost and high
transmission performance in the RoF systems. Several
techniques have been proposed for the optical generation of
mm-waves such as direct modulation, external modulation,
optical heterodyning and so on. However, in this work we
proposed and investigate an alternative to above mention
methods, which is based on Stimulated Brillouin Scattering
(SBS) in an optical fiber. SBS technique was designed and
modeled by performing CW laser in a single mode optical fiber
(SMF) through optical Mach-Zehnder modulator (MZM) with
two pump lasers for amplification purposes. The analysis was
done by determination of the power depletion of generated
stokes caused by the combined effect of dispersion, fiber
attenuation and nonlinear fiber effects; i.e. self-phase
modulation (SPM) and SBS. SBS performance with the optical
fiber loop length up to 100km was analyzed. It has been shown
that SBS power is depends on the fiber loop length which is
higher and lower at certain length due to natural properties of
the fiber. The design shown the RF generation was achieved at
40 GHz.
networks. This leads us to the discussion on the fiber-based
wireless access scheme using radio-over-fiber (RoF)
technology.
RoF system refers to the system that distributes the radio
waveform directly from control station (CS) to base station
(BS) through optical fiber [1]. Several techniques have been
proposed for the optical generation of mm-waves [2]. One
of the simplest methods is the modulation of continuouswave (CW) laser light by an external modulator is expensive
and there are several problems with the group velocity
dispersion of the optical transmission systems. Other
methods rely on the optical transport of modulated carriers
at intermediate frequencies and optical heterodyne
techniques. For the first method the mm-wave signal is
generated by upconversion in the base station. This requires
a high-quality local oscillator or an optically-supported
phase-locked loop in the base station. The second method
suffers from phase differences between the two
superimposed optical signals. To overcome this
phenomenon rather complicated setups have been proposed
[3].
Stimulated Brillouin Scattering (SBS) has mostly been
recognized as one of the causes degrading system
performance in fiber-optic networks due to the effect that
the signal energy is transferred to the backscattering signal
and SBS has low threshold. However, SBS has beneficial
characteristics such as frequency selective amplification that
can be amplified to microwave and mm-wave photonics
applications [4].
Keywords- Radio over Fiber (RoF) system, stimulated
Brillouin scattering (SBS), millimeter-waves generation, MachZehnder, nonlinear optics.
I.
INTRODUCTION
Over the past decade there has been substantial progress
in the areas of wireless and optical communications. The
driving force behind this advancement has been the growing
demand for multimedia services, and hence broadband
access. Present consumers are no longer interested in the
underlying technology; they simply need reliable and cost
effective communication systems that can support anytime,
anywhere, any media they want. As a result, broadband
radio links will become more prevalent in today’s
communication systems. Furthermore, new wireless
subscribers are signing up at an increasing rate demanding
more capacity while the radio spectrum is limited. To satisfy
this increasing demand, the high capacity of optical
networks should be integrated with the flexibility of radio
II.
PRINCIPLE OF SBS OPERATION
SBS is a nonlinear effect due to the amount of light
backscattered and the amount of light transmitted by the
fiber does not depend linearly on the power input to the
fiber. At low input powers the backscattering is dominated
by simple Brillouin and Rayleigh scattering which are linear
and differ from each other by the Brillouin shift. But as the
power is increased, the Brillouin scattered light is
increasingly amplified by the stimulation process. At a
power level called the SBS threshold, the amount of
Sponsored by the Ministry of Science, Technology and Innovation
Malaysia (EScience funding 79026) and Universiti Malaysia Perlis
(UNIMAP)
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78
backscattered light increases very rapidly with increasing
input power until it constitutes most of the input light. The
transmitted power at the fiber output saturates at a level that
barely increases with increased input power. For singlemode fiber, SMF, of lengths above 10 km, the SBS
threshold can lie in the range of 6 - 10 dBm. Above this
threshold, the insertion loss of the fiber is not independent
of input power.
The generation of millimeter-waves for RoF system
using SBS technique is shown in Fig. 1. The MZM is driven
by the electrical sine generator in analog domain working
with a fixed frequency; fRF = 10 GHz. A 0.5 dBm light wave
emitted from continuous wave (CW) laser at 1550 nm from
a narrowband linewidth of 1 MHz is modulated by MZM.
The voltage that is applied on the MZM is high enough so
that the laser wave is modulated nonlinearly with the
frequency of the electrical generator. Several optical
sidebands separated by fRF from the optical carrier are
generated by MZM nonlinearity. These signals are injected
into up to 100 km long of standard single mode optical fiber
(SSMF) loop. The pump source generates a combined
output signal of two pump lasers. This pump source is
injected into SSMF via an optical circulator and propagates
at the opposite direction of the modulated signals. The
wavelength of each pump laser is adjusted in the manner of
11GHz higher than one of the frequencies in the modulated
signal.
fmm=2nf
[5]
with n as the number of the sideband used and f as the RF of
the electrical generator. With f = 10 GHz, millimeter-waves
with frequencies of 20, 40, 60, . . . GHz are possible. If the
frequency of the generator is f = 5 GHz, output frequencies
of 10, 20, 30, . . . GHz can be produced, and so on.
I.
RESULTS AND DISCUSSION
In this work, the simulation is done based on the basic
simulation setup parameters and available commercial
values. The following table shows the value of these
parameters.
TABLE 1
FIXED PARAMETER FOR SIMULATION SETUP
Parameter
Value
10 GHz
Sinusoidal Wave
CW
Laser
The power of signal wave is controlled by an Er-doped fiber
amplifier (EDFA). SBS relies on the generation of
sidebands of CW laser by nonlinear modulation. These two
sidebands will be amplified by SBS in an optical fiber,
whereas the rest will be attenuated due to natural attenuation
in the fiber [3][5]. The millimeter-wave band output signal
is detected by a photodiode (PD).
The frequency of the mm-wave depends on the RF of
the electrical generator and on the sidebands that were
chosen for amplification. The generated mm-wave has the
frequency
EDFA
SSMF Loop
MZM
Pump
Laser 1
Circulator
Pump
Laser 2
PD
ESA
A
Fig. 1. Experimental setup for the generation of millimeter-waves.
(CW: continuous wave, MZM: Mach-Zehnder modulator, EDFA: Er.
doped fiber amplifier, SSMF: standard single mode fiber, PD:
photodiode, ESA: electrical spectrum analyzer)
Bit Rate
10 Gbps
Time Window
1.28e-0.08 s
Sample Rate
640 GHz
Sequence Length
128 Bits
Sample per Bit
64
Number of Samples
8192
Sensitivity
-100 dBm
Resolution
0.1 nm
Fiber Loop Length
50 km
Optical Power of CW laser
0.5 dBm
Linewidth of CW laser
1 MHz
Wavelength of CW laser
1550 nm
Frequency of Electrical Generator, fRF
10 GHz
Dispersion of Optical Fiber
16.75ps/nm/km
Attenuation of Optical Fiber
0.2 dB/km
Effective Area of Optical Fiber, Aeff
80 µm2
Brillouin Gain, gB
4.6e-11 m/W
Fig. 2 shows the signals pattern of the first and second
stokes with 10 GHz modulation at 0.5 dBm light wave for
50 km SSMF loop length, measured after PD in time
domain. Oscilloscope visualizer was used to display the
time plot of the generated electrical signal. Bandpass
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79
rectangular filter (BPF) is used to centre of the desired stoke
components results in electrical signals of regular intensity
patterns. It is clear that the only difference between signal
patterns at 20 GHz and 40 GHz (apart from frequency) is
the amplitude (a.u). The amplitude of higher stokes was
decreased from 4 mV to about 350µm. This confirms that
apart from the fundamental frequency, the higher order
stokes may also be used to transmit data.
RF 20 GHz (Rectangular BPF 1.5*Bit Bate Hz)
Fig. 3. Comparing intensities of first and second stokes generated by
sine generator with amplifier.
TABLE 2
ANALYSIS OF STOKES POWER AT D IFFERENCE SSMF LOOP LENGTH
Fiber Loop
Length
20 km
50 km
100 km
(a)
Nth
sidebands
1
2
1
2
1
2
Without
amplifier
-54 dBm
-94 dBm
-67 dBm
-90 dBm
-
With
amplifier
-4 dBm
-16 dBm
-20 dBm
-38 dBm
-42 dBm
-64 dBm
RF 40 GHz (Rectangular BPF 1.5*Bit Bate Hz)
II. CONCLUSION
We have demonstrated the generation of millimeterwaves for RoF system using SBS in SSMF. The proposed
technique is necessary for any electrical generator frequency
other than 10 GHz. A 0.5 dBm of light wave is carried by
10 GHz RF signal were successfully generated up to 40
GHz millimeter-wave band corresponding to the 2nd stokes.
Test the design using an arbitrary wave generator for
optimum power performance may be a future work for this
paper.
(b)
Fig. 2. The signals pattern with 10 GHz modulation at 0.5 dBm light
wave for 50 km SSMF loop length. (a) The 20 GHz bandpass filtered
electrical signal in time domain; (b) The 40 GHz bandpass filtered
electrical signal in time domain.
Fig. 4 represents the performance analysis when varies
the SSMF loop length within range 1 km until 100km with
optical amplifier. In term of power intensities, the amplifier
was boosted up the power up to 0dBm at 20km for the first
stoke. As can be seen, the first stokes has higher intensity
compared to second stoke. It also shows that the SBS effect
was started occur at 10 km and then will degraded the power
intensities in longer fiber. Table 2 shows the analysis of
stokes power at difference length with and without optical
amplifier.
ACKNOWLEDGMENT
The authors gratefully acknowledge the Ministry of Science,
Technology and Innovation Malaysia for the financial
support through EScience funding 79026. Our gratitude also
goes to the administration of the Universiti Malaysia Perlis
(UNIMAP) for the financial support.
REFERENCES
[1] X. N. Fernando and S. Z. Pinter, “Radio over Fiber for Broadband
Wireless Access”, Department of Electrical and Computer
Engineering, Ryerson University, Toronto, Canada, 2005.
[2] Lin Chen, Hong Wen, and Shuangchun Wen, “A Radio-Over-Fiber
System with a Novel Scheme for Millimeter-Wave Generation and
Wavelength Reuse for Up-Link Connection” IEEE Photonics
Technology Letters, Vol. 18, No. 19, October 1, 2006.
[3] T. Schneider, M. Junker and D. Hannover, “Generation of millimetrewave signals by stimulated Brillouin scattering for radio over fibre
systems”, Vol. 40, Nov. 2004.
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80
[4] Chul Soo Park, Chung GhuiLee and Chang-Soo Park, “Photonic
Frequency Upconversion Based on Stimulated Brillouin Scattering”,
IEEE Photonics Technology Letters, Vol. 19, No. 10, May. 15, 2007.
[5] T. Schneider, D. Hannover, and M. Junker,”Investigation of Brillouin
Scattering in Optical for the Generation of Millimeter Waves”, J.
Lightw. Technol., vol. 24,pp. 295-304, Jan 2006.
[6] S.M. Idrus, and R.J. Green, “Photoparametric Up-Converter For
Millimeter-Wave Fiber-Radio System” International IrDA/IEE/IEEE
Seminar, Warwick, Sept. 2003.
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81
Modeling of Stimulated Brillouin Scattering for the Generation of Millimeter
Waves for Radio over Fiber System
N. M. Nawawi1, S.M.Idrus2 and A. Marwanto3
Photonic Technology Centre,
Faculty of Electrical Engineering,
University Technology of Malaysia,
81310, Skudai, Johor Darul Takzim.
Tel :+607-5535302
2
3
Email: [email protected], [email protected], [email protected]
Abstract
Radio over fiber (RoF) is a promising technique in providing broadband wireless access services in the emerging
optical-wireless networks. Optical millimeter-wave (mm-wave) generation is a key technique to realize low cost
and high transmission performance in the RoF systems. Several techniques have been proposed for the optical
generation of mm-waves such as direct modulation, external modulation, optical heterodyning and so on.
However, in this work we propose and investigate an alternative to above mention methods, which is based on
Stimulated Brillouin Scattering (SBS) in an optical fiber. SBS technique was designed and modeled by performing
CW laser in a single mode optical fiber (SMF) through optical Mach-Zehnder modulator (MZM) with two pump
lasers for amplification purposes. The analysis was done by determination of the power depletion of generated
stokes caused by the combined effect of dispersion, fiber attenuation and nonlinear fiber effects; i.e. self-phase
modulation (SPM) and SBS. The design shown the RF generation at 20 GHz was achieved. SBS performance
with the EDFA length up to 8m was analyzed. It has been shown that SBS amplification stabilized at EDFA more
than 5m onward. This paper will present the proposed SBS technique, system model and simulation result.
Keywords: Radio over Fiber (ROF) system, stimulated Brillouin scattering (SBS), millimeter-waves generation,
Mach-Zehnder, nonlinear optics.
Introduction
ROF system has attracted considerable attention to deliver microwave and millimeter wave signals. It
is a system that distributes the radio waveform directly from CS to BS through optical fiber[1]. There
are some techniques have been proposed for the optical generation of mm-waves [2]. One of the
simplest methods is the modulation of continuous-wave (CW) laser light by an external modulator is
expensive and there are several problems with the group velocity dispersion of the optical
transmission systems. Other methods rely on the optical transport of modulated carriers at
intermediate frequencies and optical heterodyne techniques. For the first method the mm-wave signal
is generated by upconversion in the base station. This requires a high-quality local oscillator or an
optically-supported phase-locked loop in the base station. The second method suffers from phase
differences between the two superimposed optical signals. To overcome this phenomenon rather
complicated setups have been proposed [3].
The SBS – ROF System Model
Stimulated Brillouin Scattering (SBS) has mostly been recognized as one of the causes degrading
system performance in fiber-optic networks due to the effect that the signal energy is transferred to the
backscattering signal and SBS has low threshold. However, SBS has beneficial characteristics such
as frequency selective amplification that can be amplified to microwave and mm-wave photonics
applications [4].
This chapter describes and analyses the principle of SBS for generating of RF signals. A theoretical
model of an SBS system, without any fiber link is developed. First part represents the system block
diagram of SBS technique consists of optical modulator and SBS generator, and the basic optical
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82
communication components that has been used. The principle of operation of the technique and its
features were revealed. The parameters that have been used in this project were clearly stated.
SBS System Block Diagram
Figure 1 show the system block diagram of SBS technique that has been used in this project. The
technique was designed and modeled by performing CW laser in a single mode optical fiber (SMF)
through optical Mach-Zehnder modulator (MZM) with two pump lasers for amplification purposes.
MZM is nonlinear modulator that capable for generation of sidebands. These sidebands will be
amplified by SBS in a fiber loop, whereas the rest will be attenuated due to natural attenuation in the
fiber. Electrical generator was used to drive the MZM at certain frequency carrier. Circulator has been
selected to circulate the signal from coupler and the output signal of SBS fiber loop. The amplified
sidebands are then superimposed in PIN-photodiode which is the easiest way to generate mm-wave.
Figure 1:
Propose SBS System Block Diagram
Principle of Operation
Central Station
The CS consists of optical modulator and SBS generator. Optical modulator can be any type of
modulator as long as it can generate the harmonics that separated by frequency carrier. It means that
we can use an arbitrary of laser and electrical generator. However, in this particular project, we stated
to investigate the design using the CW laser and an intensity modulator (IM).
Optical Modulator
The optical modulator consists of a CW laser, an intensity modulator (IM), an electrical drive signal
operating at a frequency, fsw, and the data to be transported. The drive signal is used to sweep the
optical frequency of the CW laser resulting in a peak-to-peak optical frequency deviation. To generate
an un-modulated microwave or millimeter-wave carrier at the BS, this swept optical signal is fed
directly into the SBS fiber loop. Otherwise, the swept optical signal is fed into an IM such as the Mach
Zehnder Modulator (MZM), where it is intensity modulated before being distributed by the fiber
network. In this case, the signal laser directly generates sidebands of the modulation signal due to its
nonlinear characteristic line. These sidebands can be amplified by the SBS in optical fiber.
SBS Generator
The output of optical modulator is fed into the SBS generator where the SBS amplifications and upconversions were occurred. Pump lasers were used to amplify the selected sidebands produced by
MZM by control the frequencies of these pump lasers. The three ports circulator will circulate the
signal from port 1 (output from the coupler) into the port 2, and the signal from port 2 into port 3. Using
ideal circulator, we can control the insertion loss to be zero and there is no return loss or ideal
isolation. The two frequency components from the output of circulator are then be superimposed in
photodiode which is one of the easiest way for generating mm-waves.
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83
SBS
Optical Modulator
Central Station (CS)
Figure 2:
SBS System Integrated With ROF Link.
SBS System Model Develop with Optisystem
The generation of millimeter-waves for RoF system using SBS technique using Optisystem software is
given in the following Figure 3.
Figure 3:
SBS System Model Develop with Optisystem
The Mach-Zehnder Modulator (MZM) is driven by the electrical sine generator in analog domain
working with a fixed frequency; in this design, fRF = 10 GHz. A 0.5 dBm light wave emitted from
continuous wave (CW) laser at 1550 nm from a narrowband linewidth of 1 MHz is modulated by MZM.
The voltage that is applied on the MZM is high enough so that the laser wave is modulated nonlinearly
with the frequency of the electrical generator. Several optical sidebands separated by fRF from the
optical carrier are generated by MZM nonlinearity. These signals are injected into 50km long of
standard single mode optical fiber (SSMF). The pump source generates a combined output signal of
two pump lasers. This pump source is injected into SSMF via an optical circulator and propagates at
the opposite direction of the modulated signals. The wavelength of each pump laser is adjusted in the
manner of 11GHz higher than one of the frequencies in the modulated signal. The power of signal
wave is controlled by an Er-doped fiber amplifier (EDFA). SBS relies on the generation of sidebands of
CW laser by nonlinear modulation. These two sidebands will be amplified by SBS in an optical fiber,
whereas the rest will be attenuated due to natural attenuation in the fiber [3][13]. The millimeter-wave
band output signal is detected by a photodiode (PD).
The frequency of the mm-wave depends on the RF of the electrical generator and on the sidebands
that were chosen for amplification. The generated mm-wave has the frequency
fmm = 2nf
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[13]
84
with n as the number of the sideband used and f as the RF of the electrical generator. With f = 10
GHz, millimeter-waves with frequencies of 20, 40, 60, . . . GHz are possible. If the frequency of the
generator is f = 5 GHz, output frequencies of 10, 20, 30, . . . GHz can be produced, and so on.
Results and Discussion
In this work, the simulation is done based on the basic simulation setup parameters and available
commercial values. The following table shows the value of these parameters.
Table 1:
Parameter for Simulation Setup
Parameter
Value
Bit Rate
10 Gbps
Time Window
1.28e-0.08 s
Sample Rate
640 GHz
Sequence Length
128 Bits
Sample per Bit
64
Number of Samples
8192
Sensitivity
-100 dBm
Resolution
0.1 nm
Fiber Loop Length
50 km
Optical Power of CW laser
0.5 dBm
Linewidth of CW laser
1 MHz
Wavelength of CW laser
1550 nm
Frequency of Electrical Generator, fRF
10 GHz
Dispersion of Optical Fiber
16.75ps/nm/km
Attenuation of Optical Fiber
0.2 dB/km
Effective Area of Optical Fiber, Aeff
80 µm
Brillouin Gain, gB
4.6e-11 m/W
2
The simulation was done by varying the optical amplifier (EDFA) length within range 1m until 5m. The
result given below was obtained based on the fixed parameters show in Table 1. For the simulation,
the optical fiber loop length was fixed to 50 km.
Figure 4
The intensities of the first generated stokes by varying the EDFA length
Figure 4 shows the intensities of the first generated harmonics at 20 GHz. The magnitude is linearly
increased with EDFA length up to 4m. The amplification stabilized with EDFA length more than 5m
onward. The steady state was achieved at about -18 dBm.
Figure 5 represents the performance analysis when varies the SSMF loop length within range 1 km
until 100km with optical amplifier. In term of power intensities, the amplifier was boosted up the power
up to -4dBm at 20km. As can be seen, the SBS effect was started occur at 10 km and then will
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85
degraded the power intensities in longer fiber. Table 2 shows the analysis of stokes power at
difference length with and without optical amplifier.
Figure 5:
The intensities of 20GHz stoke generated by sine generator with amplifier.
Table 2:
Analysis of Stokes Power at Difference SSMF Loop Length
Fiber Loop
Length
Nth
sidebands
Without
amplifier
With
amplifier
20 km
1
-54 dBm
-4 dBm
50 km
1
-67 dBm
-20 dBm
100 km
1
-90 dBm
-42 dBm
Conclusion
The SBS system was divided into two main parts, which are optical modulator and SBS generator.
Optical modulator generates several frequency components, which are harmonics of the electrical
signal, fRF. It can be any type of modulator as long as it can generate the harmonics that separated by
frequency carrier. The amplifications and up-conversions of the sidebands were occurred in SBS
generator part. The generation of mm-waves for RoF system using SBS in SSMF has been
demonstrated using SBS in SSMF. The proposed technique is necessary for any electrical generator
frequency other than 10 GHz. A 0.5 dBm of light wave is carried by 10 GHz RF signal were
successfully generated up to 20 GHz millimeter-wave band corresponding to the 1st stokes. Finally, for
future work the system design should be tested using an arbitrary wave generator for optimum power
performance.
Acknowledgements
The authors gratefully acknowledge the Ministry of Science, Technology and Innovation Malaysia for
the financial support through EScience funding 79236.
References
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2.
3.
4.
5.
6.
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Lin Chen, Hong Wen, and Shuangchun Wen, “A Radio-Over-Fiber System with a Novel
Scheme for Millimeter-Wave Generation and Wavelength Reuse for Up-Link Connection” IEEE
Photonics Technology Letters, Vol. 18, No. 19, October 1, 2006.
T. Schneider, M. Junker and D. Hannover, “Generation of millimetre-wave signals by stimulated
Brillouin scattering for radio over fibre systems”, Vol. 40, Nov. 2004.
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for WDM Lightwave Networks”, Proc. IEEE, vol. 85, no. 8, pp. 1274.1307, Aug. 1997.
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H. Al-Raweshidy and S. Komaki, editors, Radio over Fiber Technologies for Mobile
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G. P. Agrawal, “Fiber-Optic Communication Systems”, John Wiley & Sons, Inc., 2002.
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