MACH-ZEHNDER INTERFEROMETER
ESMAEL .H .M YAHYA
Universiti Teknologi Malaysia
iii
To
My Beloved Mother, Father, Brothers and sisters.
iv
ACKNOWLEDGMENT
In the name of Allah, Most Gracious, and Most Merciful
Praise be to Almighty Allah (Subhanahu Wa Ta’ala) who gave me the
courage and patience to carry out this work. Pease and blessing of Allah be upon his
last prophet Mohammed (Sallulaho-Alaihe Wassalam) and all his companions
(Sahaba), (Razi-Allaho-Anhum) who devoted their lives towards the prosperity and
spread of Islam.
My deep appreciation and heartfelt gratitude goes to my supervisor,
Assoc.prof.Dr. Abu Sahmah Mohd Supa´at for his kindness, constant endeavor, and
guidance and the numerous moments of attention he devoted through out this work.
Family support plays a vital role in the success of any individual. I would like
to convey a heartfelt thanks to my parents, my brother Essam, all my brothers, and
other family members including all my uncles, ants and their families; their prayers
and encouragement always helped me take the right step in life.
A heartfelt gratitude and acknowledgement are due to the Libyan community
in UTM, Skudai for their kindness, care, valuable advices and cooperation, which
generates a similar environment as what I left.
v
ABSTRACT
Beam propagation method (BPM) was used to study 2x2 MachZehnder interferometer switch with electro-optical effects in titanium diffused
lithium niobate (Ti − LiNbO3 ) based directional coupler was used to develop the
design. This design is capable of de-multiplexing the wavelength1300nm. This
project intends to design high performance NxN electro-optic switch. This optical
device is widely used in optical network, especially in the optical link of fiber-to-thehome (FTTH). The design is carried out using BPM_CAD, which is a very powerful
and user-friendly optics waveguides modeling method as it core element. Research
on optical waveguide switching using directional coupler (DC) and Mach-Zehnder
interferometer (MZI) has been going on and already created great interest among the
researchers. There are different types of material being used in much different way
apart from the most common electro-optic materials such as lithium niobate LiNbO3 .
Recently, the study was also confined to the use of silica on silicon technology
considering that the cost of the technology. Other non-linear-optic materials such as
polymers have been embedded into part of the silica waveguide.
vi
ABSTRAK
Beam propagation method (BPM) digunakan untuk mengkaji 2x2 MachZehnder interferometer suis dengan efek-efek (Ti − LiNbO3 ) based directional
coupler dalam membangunlcan relcaan. Relcaan ini mampu dalam de-multiplexing
pauy gelombang 1300nm. Projek ini ingin merelca NxN elektro-optik suis yang
member fungsi yang tinggi. Alat optical ini digmalcan secasa berleluasa dalam
rangkaian optikal terutamanya dalam link optikal bagi fiber-to-the-home (FTTH).
Rekaan dilaksanakan dengan menggunakan BPM_CAD yang merupakan satu cara
pemodelan paduan gelombang optic sebagai elemen utama yang sangat berkuasa dan
sesuai untuk pengguna. Penyelidikan dalam pensuisan panduan gelombang optik
menggunatan directional coupler (DC) and Mach-Zehnder interferometer (MZI)
telah pun berjalan dan telah mencetuskan benyak minat dalam para penyelidik.
Selain dari pada elektro-optik material biasa sperti lithium niobate ( LiNbO3 ) ,
pelbagai jenis material yang berbeza yang digunakan dalam cara yang berlaina. Sejak
kebelakangan ini, kajian dihakan kepada penggunaan silika dalam teknologi silika
dengan mengambil kira kos teknolog. Optik material bukan linear yang lain seperti
polimer telah digunakan sebagai salah satu behagian dalam pandnan gelombang
silica.
vii
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
DECLARATION
DEDICATION
ACKNOWLEDGEMNET
ABSTRACT
ABSTRAK
TABLES OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF ABREVIATIONS
LIST OF APPENDICES
1
PROJECT OVERVIEW
1
1.1
Introduction
1
1.2
Objective
2
1.3
Scope of Project
2
1.4
Problem Statement
3
1.5
Methodology
3
1.5.1
Case Study
3
1.5.2
Literature Review
3
1.5.3
Optical Switch Design
3
viii
2
OPTICAL WAVEGUIDE ANALYSIS
6
2.1
Waveguide
6
2.2
Optical link of fiber-to-the-home (FTTH)
7
2.3
Optical Fiber Communication System
9
2.3.1
Multiplexing Methods in Optical
Networks
2.4
3
WDM System Performance
9
13
OPTICAL SWITCHING CONCEPTS AND
DEVICES
3.1
PIC Space Switches
16
3.1.1
16
Mechanical witches
3.2
LiNbO3 Directional Coupler
20
3.3
Coupling Efficiency
21
3.4
Types of Optical Switching
22
3.5
Passive Optical Sitching Device and
Operational Principles
3.6
Fiber Coupler
24
3.7
Waveguide Coupler
30
3.8
Mach-Zehnder Interferometer
34
3.9
Application of Integrated Optics in The
Evolution of Optical Switching Technology
3.10
Planar waveguide Integrated optical in
optical switching
3.11
Active optical switching devices and
operational principles
3.12
4
24
Electro-optic Mach Zehnder Interferometer
39
41
46
47
DESIGNING OPTICAL SWITCH
4.1
Titanium Diffusion in Lithium Niobate
Process
52
4.2
Electro-Optic Effect
55
4.3
Optical Switching Using Electro-Optic
58
ix
Effect
4.4
Phase Mismatch
60
4.5
Switching Voltage
61
4.6
Coupling Efficiency Control of 2x2 Optical
Switch
4.7
Analysis on Effect of Changing Separation
Distance between Waveguides (d)
4.8
Design 2x2 Optical Switch using Mach-
Zehnder Interferometer
4.9.1
First Design of Mach-Zehnder 2x2
optical switch
4.9.2
Second Design of Mach-Zehnder
2x2 Optical Switch
4.10
Configuration of BPM_CAD for Diffused
Waveguide in BPM_CAD
4.11
65
Analysis on Effect of Changing
Wavelength (λ0 )
4.9
64
Simulation Results of First Design of
Mach-Zehnder 2x2 Optical Switch Zero Voltage
67
69
71
72
73
74
4.11.1 Simulation Results of First Design
of Mach-Zehnder 2x2 Optical Switch with
75
Switching Voltage
4.12
Simulation Results of 2x2 Optical Switch
with Zero Voltage
4.12.1 Simulation results of 2x2 Optical
Switch with Switching Voltage
5
76
78
CONCLUSIONS AND RECOMMENDATION
5.1
REFERENCES
APPENDICES A
Conclusions
81
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
4.2
Electro-Optic Effect
55
4.7
Analysis on Effect of Changing Separation Distance
65
between Waveguides (d)
4.8
λ
Analysis on Effect of Changing Wavelength ( 0 )
67
4.9
Design 2x2 Optical Switch using Mach-Zehnder
69
Interferometer
4.10
Configuration of BPM_CAD for Diffused Waveguide in
BPM_CAD
69
xi
LIST OF FIGURES
FIGURE NO.
2.1
TITLE
Rays
propagating
waveguide,
by
total
PAGE
reflection
in
a
slab
5
H x Component of the Magnetical Field, H z
Component of the Magnetical Field,
Ey
Component of the
Electrical Field
2.2
Fiber to the home
8
2.3
Attenuation spectrums for an ultra-low-loss single mode
9
fiber
2.4
Two
multiplexing
techniques
for
increasing
the
10
transmission capacity of optical networks. (a) Time
division multiplexing and (b) wavelength division
multiplexing. The modulated signal provides the time
frames available for each logical state (0 or 1)
2.5
Three network topologies. (a) Star (broadcast and select
11
network) (b) Ring and (c) bus
2.6
Typical structures of a (optical) cross connect which is
13
used for interchanging the three wavelength channels in
the three inputs of the OXC
2.7
The intra channel crosstalk penalties for 1, 10 and 100
crosstalk introducing elements, as functions of the
crosstalk level of each element in the network for a BER
of 10-9. All elements are assumed to produce crosstalk at
equal powers
14
xii
3.1
The wave guiding structures of the most commonly used
17
switch architectures. In (a), (b), (c) and (d) switches are
depicted which employ a refractive index change for the
switching property, the switch in (e) is based on the
functionality of a semiconductor optical amplifier (SOA).
The grey areas represent the parts with adjustable
effective refractive indices
3.2
A Directional coupler designed by BPM-CAD for 2x2 DC
19
switch
3.3
Relationship between coupling ratio and phase-mismatch
21
parameter
3.4
Relationship between coupling Efficiency and applied
22
voltage
3.5
4x4 Active optical switches
23
3.6
4x4 Active optical switch
23
3.7
Fiber coupler
24
3.8
Normalized coupled powers
P2 / P1
and P1 / P0 as a
26
function of the coupler draw length for a 1300nm power
level P0 launched into fiber 1
3.9
Dependence on wavelength of the coupled powers in
26
completed 15mm long coupler
3.10
Generic 2x2 guided- wave coupler
28
3.11
An uniformly asymmetric directional waveguide coupler
30
in which one guide has a narrower width in coupling
region.
3.12
Theoretical through-path and coupled power distribution
32
as a function of the guide length in a symmetric 2x2
guided-wave coupler with k = 0.6mm −1 and α = 0.02 mm −1
3.13
wavelength response of the coupled power P2 / P0
33
3.14
2x2 Mach-Zehnder interferometer
35
3.15
Four channel wavelength multiplexer there 2x2 MZI
37
3.16
A planar slab waveguide. The film with h refractive index
41
xiii
n1 acts as the guiding layer and the cover layer is usually
air where n3 = n0 = 1
3.17
A planar slab waveguide. The film with h refractive index
43
n1 acts as the guiding layer and the cover layer is usually
air where n3 = n0 = 1
3.18
cross section of some strip waveguide structures structure
(a) Ridge guide (b) diffused channel
44
(c) rib guide
3.19
A simple strip waveguide phase modulator
48
3.20
A Y-junction interferometric modulator based on the
49
Mach Zehnder interferometer
4.1
Flow chat of optical switch design
51
4.2
dependency of optical power transfer ratio, ℑ , on phase
60
mismatch ∆βLo
4.3
A design of 2x2 electro-optic switch based Mach-Zehnder
62
interferometer
4.4
4.5
4.6
Effect of changing separation distance, d, at V=12
67
λ 0 at V=12
69
Effect of changing separation distance,
First Design a 2x2 optical switch of Mach-Zehnder
71
interferometer without electrode region
4.7
First Design a 2x2 optical switch of Mach-Zehnder
71
interferometer
4.8
Design a 2x2 optical switch based on Mach-Zehnder
72
interferometer without electrode region
4.9
Design a 2x2 optical switch based on Mach-Zehnder
72
interferometer with electrode region
4.10
Simulation results of a 2x2 optical switch when
74
V2 = 0 volt Optical signal is fully coupled from Pin1
to Pout 2
4.11
Simulation results of a 2x2 optical switch when
V2 = 0 volt
Optical field and effective refractive index at the output
75
xiv
4.12
simulation results of a 2x2 optical switch when
76
V2 = 12 volt Optical signal is fully coupled from Pin 1
to Pout1
4.13
Simulation results of a 2x2 optical switch when
77
V2 = 0 volt Optical signal is fully coupled from Pin 2
to Pout1 .
4.14
Simulation results of a 2x2 optical switch when
78
V2 = 0 volt Optical field and effective refractive index at
the output
4.15
Simulation results of a 2x2 optical switch when
79
V2 = 12 Volt Optical signal is switched from Pin 2 to Pout 2
4.16
Simulation results of a 2x2 optical switch when
80
V2 = 12 Volt Optical filed and effective refractive index at
the output
5.1
Fiber-To-The-Home system architecture
82
xv
LIST OF SYMBOLS
av
-
di
-
Modal Field Amplitude
Thickness of Layer i
D
r
E
-
Depth of a Switching Matrix
-
Vectorial Electrical Field
Ex
-
Ey
-
Ez
-
fm
-
r
H
-
Hx
-
Hy
-
Hz
-
h
-
Slab Height
H
-
Rib Height Including Slab
heff
-
H eff
-
j
-
k0
-
ky
-
kz
-
x Component of the Electrical Field
y Component of the Electrical Field
z Component of the Electrical Field
Modulation Frequency
Vectorial Magnetical Field
x Component of the Magnetical Field
y Component of the Magnetical Field
z Component of the Magnetical Field
Effective Slab Height
Effective Rib Height
−1
Wave number of Free Space
Wave number in y -Direction
Wave number in z -Direction
xvi
k
-
L
-
Lc
-
l
-
Lb
-
lb
-
M
-
M iTM
-
n
-
n
-
N
-
ni
-
neff
-
Mean Wave number
Device Length
Transfer of Coupling Length
Mode Order
Length Spanned by a s-Bend
Path Length of a s-Bend
Density of Light Scatterers
Transfer matrix of Layer i for TM wave
Refractive Index
Complex Refractive Index
Number of Layers
Refractive Index of Layer i
Effective Refractive Index
n sub -
Refractive Index of the Substrate
Pin
-
Power at the Input Port
Pout
-
P
-
Number of Single Switching Elements Switching Matrix
q
-
Fit Parameter
R
-
Phase Bend Radius
Rx
-
Phase Bend Radius x -Direction
Ry
-
Phase Bend Radius in y -Direction
T
-
Temperature
v
-
Imaginary Complex Coordinate
w
-
Rib Width
wc
-
y
-
Power at the Output Port
Cutoff Width
Spatial Coordinate
yi
-
z
-
Upper Bound of Layer i
Spatial Coordinate
xvii
α
-
Full Intersection Angle of Waveguides
β
-
Propagation Constant
β eff
-
∆φ
-
Phase Difference
∆β
-
Propagation Constant Difference
ε
-
Dielectricity
ε0
-
εr
-
γ
-
Linear Thermal Expansion Coeficient
λ
-
Wavelength
µ
-
Mode Order
Effective Propagation Constant
Dielectricity of Free Space
Relative Dielectricity
Weighting Functions
w1 , w2 η
-
Phase Correction for Gaussian Beams
θ
-
Angular Range
ξ
-
Polarizability per Scatterer
xviii
LIST OF ABREVIATIONS
ADI
-
Alternating Direction Implicit
Al
-
Alluminium
Ar
-
Argon
AWG
-
Arrayed Waveguide Grating
BCB
-
Benzocyclobutene
BPM
-
Beam Propagation Method
CAD
-
Computer Aided Design
CIF
-
Caltech Intermediate Format
CT
-
Cross Talk
FBG
-
Fiber Bragg Grating
FD
-
Finite Differences
FFT
-
Fast Fourier Transform
GaAs
-
Galium-Arsenid
HeCd
-
HeliumCadmium
HF
-
Hydrofluoric Acid
HNO3
-
Nitric Acid
H 2O
-
Water
H 3 PO4
-
Ortho-PhosphoricAcid
IL
-
Insertion Loss
InGaAsP
-
Indium-Galium-Arsenid-Phosphid
LiNbO3
-
Lithiumniobat
MEMS
-
Micro ElectroMechanical System
xix
LIST OF APPENDICIES
APPENDIX
A
TITLE
BPM Diffused Waveguides
PAGE
85
CHAPTER 1
PROJECT OVERVIEW
1.1
Introduction
Future telecommunication network will be largely based optical fiber as the
transmission medium. With the proliferation of fiber in May parts of
telecommunication network, it becomes increasingly apparent that photonic
switching and optical signal processing, including optical multiplexing, will play
important role in the network evolution into all photonic networks.
The external sources such as voltage, current or thermal have been used to
change the optical propagation characteristics, the basis of optical switching. For
example a rearrange able no blocking polymer wavelength thermo-optic 4x4
switching matrix with low power consumption at 1550 nm has been worked out by
using thermal to control the 4x4 switches. Recently, low power compact 2x2 thermo
optic silica-on-silicon waveguide switch with fast response has been successfully
shown by using MZI.
Thermal effect was used to activate the MZI. High performance wavelength
multiplexing and demultiplexing optical channels spaced 100GHz apart (0.8nm
spacing at 1550nm) has been shown by the device based on Mach-Zehnder
interferometer.
Active wavelength switching technology is one of the latest approach in fiber
optical communication in order to make wavelength division multiplexing (WDM)
2
becoming a better choice for switching technology, knowing that WDM can exploit
the huge bandwidths of optical fiber. In this project we report the results of a
simulation study on the dependence of wavelength using beam propagation method
(BPM) on LiNbO3 directional coupler (DC) switch. The variation of the output
splitting ratio is the major outcome from the simulation.
This directional coupler switch, which we call as WDM switch, is also having
the same behavior as a passive directional coupler but with variable coupling
efficiencies when under an external field. By applying an external voltage of less
than 10V, the change of coupling efficiency of each optical wavelength between.
1.10µm and 1.55µm can be observed.
1.2
Objective
¾ Define the material of Mach-Zehnder switch.
¾ Simulation using BPM-CAD.
¾ Optimization of Mach-Zehnder switch.
1.3
Scope of Project
¾ To understand the concepts and operational principles of different types of
optical devices used as optical switching.
¾ Investigation some of the parameters ( β, Refractive index, Width, Length,
size, material ) that are used for designing an optimum optical switch.
¾ Designing an optical switch by using MZI technique by using BPM CAD
software.
¾ Analysis on Mach-Zehnder in terms of light coupling efficiency.
3
1.4
Problem Statement
¾ Using optical-electrical conversion switches results in expensive and nonreliable systems due to large coupling loss.
¾ By designing optical-optical switches, the performance of the system is
proved much better.
1.5
Methodology
1.5.1 Case Study
This part covered a study case about different types of coupler for example,
Fused fiber coupler, waveguide coupler, Mach-Zehnder interferometer.
1.5.2
Literature Review
This covered titanium diffusion in lithium niobate process upon the literature
review through materials for design this choice was based on that it has low loss and
switching voltage need to be applied is small which is normally below 10v, Further
more, silicon based substrate normally acts passively to electric field. In designed
electro-optic switch, material is the best choice due to its electro-optic and piezoelectric characteristics.
1.5.3
Optical Switch Design
Initially, the switch be design using Mach-Zehnder interferometer as a
beginning, 2x2 switches be designed.
4
1.5.4
Simulation
The simulation will be done by using BPM_CAD. This simulation will show
the propagation in the switch.
1.6
Thesis Structure.
This thesis consists of main chapters. The first chapter consists of a general
introduction, the scope and objective of the project and also the flow of this thesis.
Chapter 2 is an introduction about Waveguide and Fiber-to-the-home. The
chapter discusses in detail about the waveguide analysis and WDM system
performance.
Chapter 3 studies about the optical switches and waveguide coupler and fiber
coupler and Mach-Zehnder.
Chapter 4 in this chapter has simulation results and discuses the results.
Chapter 5 is a conclusion for this project. The chapter also has future works
CHAPTER 2
OPTICAL WAVEGUIDE ANALYSIS
2.1
Waveguide
Consider two closely spaced infinite parallel planes defining the interfaces
between a medium (the ‘core’) of refractive index n1 between the planes and
a surrounding medium (the ‘cladding’) of index n2. When n1 > n2 this defines
the symmetrical slab waveguide in which light may be confined by total
reflection boundaries but is unconfined in the plane as shown in figure 2.1 at the
two The definition of the system is encompassed in the following diagram
Figure 2.1 Rays propagating by total reflection in a slab waveguide, H x Component
of the Magnetical Field, H z Component of the Magnetical Field, E y Component of
the Electrical Field
6
As shown, light propagates along Z with its electric field polarised in the y
direction. This is the transverse electric, TE case. However, we could also depict
the magnetic field polarized along ‘y’ to depict the transverse magnetic, TM, case.
We are interested in defining the propagation characteristics of this field and in
determining its amplitude distribution in the transverse (x) direction. We start with
the vector wave equation for electric field.
r
r
∇ 2 E − µ 0εδ 2 E / σ 2t = 0
(1.1)
And reduce it to the following scalar wave equation as follows by applying the
restrictions of the problem at hand (note that in this slab waveguide, δ 2 E y / δy 2 = 0 )
δ 2 E y / δx 2 + δ 2 E y / δz 2 − µ 0εδ 2 E y / δt 2 = 0
(1.2)
Where the permittivity, e, is equated with refractive index through
ε = n 2ε 0 . Taking the z and t variations in the field first, we use the propagating
wave form
E y ( z , t ) = A exp i ( k z z − ω t )
(1.3)
Carrying out the differentiation w.r.t. z and t gives the scalar wave equation
for this case as
δ 2 E y / δx 2 − E y (k z2 − µ 0εω 2 ) = 0
(1.4)
Now we seek solutions to this equation for the x variation in the field in the
core layer. A general solution for E y ( −t / 2〈 x〉 t / 2) i.e. in the slab is
E y ( x) = B cos(α1 x) + C sin(α 1 x)
(1.5)
7
Provided that –
α 12 = ( µ 0ε 1ω 2 − k z2 )
(1.6)
We also seek solutions to C4 in the regions outside the slab i.e. 2 t x > and 2 t
x − < , i.e. in the region of the evanescent field.
As we have shown, under conditions of total reflection the x variation of this
field is an exponentially decaying function. We thus choose the following solutions.
E y ( −t / 2〉 x ) = E exp(α 2 x )
(1.7)
Whereupon substitution into (4) (changing e1 to e2) is allowed provided that
α 22 = (k z2 − µ 0ε 2ω 2 )
(1.8)
With these solutions (1.5) and (1.7) and (1.8) to the wave equation (1.4) we
can proceed to define appropriate boundary conditions pertinent to the problem and
then to derive the eigenvalue equations for the slab waveguide TE modes. The
constants B, C, D and E in the above will be eliminated in this process.
2.2
Optical link of fiber-to-the-home (FTTH)
Cable television modems (CTMs) and digital subscriber line (DSLs) are
leading in the race to deploy residential broadband. But we know the eventual winner
will be fiber-to-the-home. Fiber-to-the-home is an efficient network in sending voice,
video and high speed internet data to the home over a fully optical network. Fiber-tothe-home has always been an attractive option since it has all the benefits of fiber. It
provides a future-proof network in that we do not have to go through the hassles of
upgrading from ADSL to XDSL to digital co-ax digital wireless. It doesn’t have to
8
contend with electromagnetic interference problems. It doesn’t need electric
powering and is immune to lighting and other transients shown in figure 2.2. Benefits
of fiber-to-the-home are.
¾
Better communication
o Within the community, between homes and employers, worldwide.
o Better quality as well as quantity 100% ON, 100% FAST
¾
New ways to work
o Telecommunicating, even for high-bandwidth tasks
o Internet-based businesses can be started in any home with fiber-to-thehome
o Disabled or home-bound residents can work from home
Figure 2.2 Fiber to the home
¾
Unparalleled bandwidth and a great value
o Fiber costs are similar to lower speed services
o Very fast
o Symmetric bandwidth inherent, eventual choice of ISP
9
The wavelength used in the system is 1.55µm for downlink and 1.31µm for
uplink. These two wavelengths are chosen because lowest attenuation occurs at these
two wavelengths as shown in figure 2.3.
Figure 2.3 Attenuation spectrums for an ultra-low-loss single mode fiber
2.3
Optical Fiber Communication System
Since the beginning of the 1970’s optical networking is available as an
alternative for the electronic data networks, thanks to the invention of lasers
[Mai60]and glass fibers with an acceptable optical loss of (at that time) 20 dB/km.
The optical frequencies applied in these networks are such that a much larger signal
bandwidth is possible in optical communication networks, as compared to their
electrical counterparts, making them very suitable for satisfying the ever-increasing
demand for bandwidth.
In the last two decennia large amounts of fiber links with low attenuation
have been deployed. At first these were digital links consisting of 34 Mb/s voice
lines for trucking of telephone links. Later on much higher bit rates and more
complex transmission techniques have been realized.
10
To reduce the numbers of expensive repeaters and amplifiers in optical
networks, the attenuation of the optical signal in these networks must be small. Since
the lowest fiber attenuation is obtained at wavelengths around 1550 nm (0.15
dB/cm), the 1550 nm wave-length window is preferred above the conventional zero
dispersion 1300 nm window. The availability of the Erbium Doped Fiber Amplifier
(EDFA) for signal amplification between 1530 nm and 1560 nm is another advantage
of using the 1550 nm window.
The wavelength window of the EDFA has a bandwidth of about 4 GHz,
which implies that a single optical carrier at 1550 nm has a theoretical maximum
transmission capacity of 8Tb/s. The 1550 nm wavelength window, which is wider
than the EDFA window, has a theoretical maximum transmission capacity even six
times large (~ 50 Tb/s) before fiber losses would limit the transmission.
However, in present-day optical devices these extremely high bit rates are
impossible to achieve, since almost all currently used optical devices, like
modulators and detectors, have bandwidths smaller than 20 GHz. One way of using
the available bandwidth of the optical network as much as possible with current
devices is achieved by utilizing multi-plexing methods.
Figure 2.4 Two multiplexing techniques for increasing the transmission capacity of
optical networks. (a) Time division multiplexing and (b) wavelength division
multiplexing. The modulated signal provides the time frames available for each
logical state (0 or 1).
11
2.3.1
Multiplexing Methods in Optical Networks
The transmission capacity of an optical network could be extended in a
simple way by installing additional fibbers (space division multiplexing or SDM).
Since this is very expensive, methods have been developed for a more efficient use
of the available bandwidth in the existing fiber network. A first solution is to increase
the bit rate in the network, which requires higher-speed electronics at the nodes of
the network. Many lower-speed data streams can be multiplexed into one high-speed
stream by means of time division multiplexing (TDM), such that each input channel
transmits its data in an assigned time slot. The assignment is performed by a fast
multiplexer switch (mux). The routing of different data streams at the end of the
TDM link is performed by a demultiplexer switch (demux). The interleaving can be
carried out on a bit-by-bit basis, like shown in Fig. 2.5a, or on a packet-by-packet
basis. As data speeds become higher and higher, it becomes more difficult for the
electronic parts (switches) in the system to handle the data properly. This problem
can be overcome by routing the data through the optical domain, which is denoted as
optical time division multiplexing (OTDM). The speed of the present day
experimental OTDM systems is in the order of 100 Gb/s (single channel), and is
mostly limited by the speed of the non-linear elements and the influence of physical
effects like chromatic dispersion on the optical pulses in the employed fibers.
Figure 2.5 Three network topologies. (a) Star (broadcast and select network)
(b) Ring and (c) bus.
12
Despite the high bit rates that are obtained with the OTDM technique, only a
limited part of the available bandwidth in the 1550 nm telecommunication window is
used by the OTDM channel. If, together with the data in this single channel,
additional data are transmitted at different carrier wavelengths over a fiber, a better
use of the huge fiber bandwidth is obtained. The maximum number of channels in
these wavelength division multiplexed (WDM) systems is determined by the
performance (channel spacing, signal to- noise ratio) of the band pass filters, which
are employed at both sides of the WDM-connection and, again, the effect of nonlinear ties in fibers.
WDM networks are greatly improved by employing a wavelength routing
architecture nstead of the broadcast and select system. The routing is performed in
the nodes of the network which are capable of routing the different wavelengths at a
specific input port to one of the various outputs. The wavelength routing in these
networks is performed by add-drop multiplexers and (optical) cross connects. The
first are used for adding one wave-length channel to, as well as for removing one of
the wavelength channels from, a WDM Line; the latter are used for the transfer of
data streams from e.g. one ring network to another (see Fig. 2.5b). In the case of a
simple (reconfigurable) cross connect configuration, they consist of space switches
and (de)multiplexers (Fig. 2.6), in which case only an exchange of data streams is
possible. If one data stream at a carrier wavelength λ1 needs to be transferred from
one network to an other in which carrier wavelength λ1 is already occupied, this
simple cross connect configuration is insufficient and wavelength converters need to
be added. In this way different wavelengths can be assigned to an optical information
path such that a more efficient use of the available wavelengths in the total network
is obtained. Depending on the required functionality of the cross connect extra
components, like opto-electronic regenerators, can be added to the cross connect
configuration. To obtain a reliable network, special attention needs to be paid to
failure prevention. In the available protection techniques routing devices (switches)
are employed for rerouting the traffic in case of a failure. The allowed restoration
time is in the millisecond range. In case packet-switching is employed in optical
networks, much faster space switches are required with switching speeds in the order
of 1 ns..
13
Figure 2.6 Typical structure of a (optical) cross connect which is used for
interchanging the three wavelength channels in the three inputs of the OXC.
2.4
WDM System Performance
In a high-quality digital system the physical layer, the medium that
determines the required bandwidth, must ensure a reliable transmission of the bits
from their source to larger than the power penalty related to the improvement, has as
no effect on the performance of the system or even decreases it. Crosstalk reduction
in switches, to which attention is paid, can be obtained with methods that entail an
increase of the switch loss. To know if such a method really improves the
performance of the network, the relation between the obtained crosstalk reduction
and the allowed loss increase needs to be considered. The mentioned relation is
found when the power penalty as a function of the crosstalk level of a network
element (e.g. a switch) is calculated, which is performed with the use of a system
calculation. The results of these calculations depend strongly on the configuration of
the system (e.g. the source and receiver type and the length of the employed fiber)
and the mathematical models used for the different components and effects in the
system. Since an evaluation of all possible configurations and the accompanying
14
detailed calculations are beyond the scope of this investigation, the power penalty
due to (coherent) crosstalk in a network is only calculated for a simple and general
network. In Figure.2.7 this power penalty is plotted as a function of the intra channel
crosstalk power for 1, 10 and 100 crosstalk sources, for a single crosstalk introducing
element the required (intra channel) crosstalk level for a power penalty of 1 dB,
which is its standard magnitude in most networks, is -26 dB. When the number of
crosstalk introducing elements is increased in the calculation, the required inter
channel crosstalk levels for a power penalty of 1 dB rise rapidly. According to our
model, if only 10 identical crosstalk elements are used in a network, their intra
channel crosstalk level must be lower than -36 dB. This observation is confirmed by
measurements.
Figure 2.7 the intra channel crosstalk penalties for 1, 10 and 100 crosstalk
introducing elements, as functions of the crosstalk level of each element in the
network for a BER of 10-9. All elements are assumed to produce crosstalk at equal
powers.
Important application of switches is that of protection switching. Here, the
switches are used for rerouting a data stream via a secondary fiber, in case the
primary fiber fails. Since these switches are only used in case of failure, switching
speeds in the order of a microsecond to hundred microseconds are sufficient. Packet
switching imposes the most severe requirements on the switching time of the routers
in an optical network. The packets are switched separately by the routing devices in
15
such a way that the switching time is much smaller than packet duration. A packet
consisting of bytes at 10 Gb/s has a time duration of 42 ns and requires a switching
time in the order of 1 ns for an efficient operation. In future networks this packet
switching in combination with the WDM technology is expected to play an important
role. Most of the optical network components are usually fabricated in the form of
photonic integrated circuits (PIC’s), which are much smaller than their electrical
counterparts [Joh96, Her98a]; this simplifies their implementation. An additional
advantage of these PIC’s is the possibility to integrate the different components onto
a single chip, in which way complicated interconnections can be avoided and small
and relatively cheap complex circuits can be constructed. The required integrability
of a component depends on its (onchip) size and the number of additional
components that can be realised on the employed PIC-material. Since switching
devices are expected to have a large number of in and outputs, scalability of
elementary switches is an important property. For a good functioning of the
components in optical networks a high bit rate transparency and low power
consumption are required. Relaxed fabrication tolerances and good manufacturability
guarantee an easy fabrication of the various components with a high yield.
CHAPTER 3
OPTICAL SWITCHING CONCEPTS AND DEVICES
3.1
PIC Space Switches
In the course of time many types of PIC space switches have been developed,
which can be distinguished by their geometry and the type of material they have been
built from. For a considerable part the switch geometry is determined by the physical
effect that is used for the switching. The application of the different switches
depends strongly on the properties of the particular type of switch e.g., the switching
speed. In the following subsections a description is given of the main switch types.
3.1.1
Mechanical witches
In mechanical switches the required manipulation of the light is obtained by
the displacement of a fiber/waveguide or by the rearrangement of a mirror which is
positioned in a free-space light beam. Most promising for commercial application is
the MOEMS switch MOEMS: micro (opto-electro mechanical system) [Lin98,
Bis99], which uses electrical actuators for the mirror rotation. Mechanical switches
feature a low crosstalk level (< -50 dB) and low (polarization index- pendent) loss
17
The main disadvantages are their low speed (~ 10 ms), sensitivity to vibrations,
mechanical wear and bad integrability with other optical components.
Many different (integrated optical) switch architectures have been developed
in the past years. Some of these are designed for a specific application, other
architectures are more generally applicable. In this subsection the basic functionality
of the latter types (shown in Fig. 3.1a - d) will be treated.
These switches are fabricated on silicon with the use of micro machining
technology. Large switching structures, utilising fiber switches and a rearrangement
time in the order of 1 minute have already experimentally been demonstrated. The
ear-lier mentioned MOEMS switch is also suitable for employment in larger
switching struc-tures due to its low loss property. The dimensions of these switches
are limited by beam divergence and alignment issues.
18
Total internal reflection switch
Y-branch or digital optical switch
SOA-gate switch
Figure 3.1 The wave guiding structures of the most commonly used switch
architectures. In (a), (b), (c) and (d) switches are depicted which employ a refractive
index change for the switching property, the switch in (e) is based on the
functionality of a semiconductor optical amplifier (SOA). The grey areas represent
the parts with adjustable effective refractive indices.
The total internal reflection switch consists of a waveguide crossing, in part
of which the effective refractive index can be controlled. The light, applied to the
(single) input, can be switched from one output to the other by changing this
effective refractive index such that the light is reflected or transmitted at the crossing.
In this way a polarization and wave-length independent switch is obtained with two
19
states above the switching voltage and at zero bias (digital response), respectively.
Usually current injection is used for the high effective refractive index change
that is required in this switch, which is a disadvantage due to the resulting heating
and low switching speed. An additional disadvantage is the high fabrication precision
that is required for the switching area and the angle between the waveguides.
The Y-branch or digital optical switch (DOS) makes use of adiabatic mode
evolution for switching, by changing the effective refractive index of one of the Ybranches. The required refractive index change, which is higher than in e.g. a MZIbased switch, can be obtained by reverse bias or current injection. The switch has a
digital response which is polarisation and wavelength independent. The main
disadvantages of this switch type are the high refractive index change needed for
switching and the accuracy that is required for the fabrication of the angle between
the waveguides and the sharpness of the vertex.
3.2
LiNbO3 Directional Coupler
For our directional couplers, the design parameters, such as refractive index,
waveguide spacing, and lateral diffusion distance were based on Ti-diffused LiNb03.
It was chosen because of its attractive characteristics such as low loss, small
operating voltage and easy fabrication.
The coupling efficiency can be controlled by external voltage level applied
through the electrode as shown in Figure 3.2. The applied voltage will determine the
amount of optical power transmitted to a particular output port.
20
Figure 3.2 A Directional coupler designed by BPM-CAD for 2x2 DC switch
3.3
Coupling Efficiency
When the guides in Figure 3.3 are identical, then their respective refractive
indices n1 = n2 and propagation constant β1 = β 2 , where subscript 1 refers to
waveguide 1 and subscript 2 refers to the other waveguide. In the phase matched
mode, the power exchange is simply.
P1 ( z ) = P1 (0 ) cos 2 l z
(3.1)
P2 ( z ) = P1 (0)sin 2 l z
(3.2)
Where P1 (0 ) and P2 (0 ) are the input power of the coupler propagating in zdirection of guide 1 and guide 2 respectively.
distance z = L0 =
π
2l
l
is the coupling coefficient. At
.
The power is transferred completely from guide 1 to guide 2. In phase
mismatch cases, β1 ≠ β 2 , power transfer ratio is ℑ =
P2 (L0 )
which depends on the
P1 (0 )
phase mismatch
Parameter, ∆ β L0 .
1
⎧
⎫
2
∆
L
β
1
⎪ ⎡
0 2⎤ ⎪
ℑ = ⎜ ⎟ sin c 2 ⎨ ⎢1 + (
) ⎥ ⎬
π
⎝2⎠
⎦ ⎪
⎪⎩ 2 ⎣
⎭
⎛π ⎞
2
For efficiency from 100% to 0%, the value of
to 3π . At ∆ β L0 =
(3.3)
∆ β L0 must change from 0
3π ; the optical power is not transferred to waveguide 2.
21
Figure 3.3 Relationship between coupling ratio and phase-mismatch parameter
Another method of controlling the mismatch
∆ β L0 is by changing ∆ β by
the use of electro-optical effects. By applying a voltage, V, an electric field will be
generated, E =
V
d
One line goes downward at one waveguide and upward at the other. This will
cause the refractive index of the first waveguide to increase and the refractive index
of the second waveguide to decrease. The dependence of the coupling efficiency on
the applied voltage, can be observed by taking into account the net refractive index
⎛V ⎞
difference 2∆n = − n 3 r ⎜ ⎟ , then the ratio is given by,
⎝d⎠
1
⎧
⎫
V 2⎤2 ⎪
⎛π ⎞
2 ⎪1 ⎡
ℑ = ⎜ ⎟ sin c ⎨ ⎢1 + 3( ) ⎥ ⎬
Vs ⎦ ⎪
⎝2⎠
⎪2 ⎣
⎩
⎭
2
(3.4)
Where r is the Pockets coefficient and Vs is the switching voltage.
The dependence of the coupling efficiency on the applied voltage is shown in
figure 3.4, when V = 0 all of the optical power is transferred from guide one to guide
two When Vs = V all of the power remains in guide one.
22
Figure 3.4 Relationship between coupling Efficiency and applied voltage
3.4
Types of Optical Switching
Optical switching can be performed either passively or actively. Optical
switching is an operation in passing or blocking light (ON/OFF) or changing the
output port of propagating light. It is very useful in sending information of different
wavelengths from central office to the subscribers in the optical network of fiber-tothe-home. Optical switching can be performed either passively.
A passive switch can be made of number of directional couplers as shown in
figure 3.5. As coupler is the basic component in making optical switch. In the figure
shown above, the input wavelengths λ1 and λ2 can be switched into two different
output channels which is Pout1 and Pout 2 , this design is named as passive switch
because the input wavelengths are de-multiplexed into fixed output channel. The user
can't change the output into any other output channel.
23
Figure 3.5 4x4 Active optical switches
An actively using same design, the designer can de-multiplex or switch input
wavelength λ2 preferred output channel. This can be done by applying electrooptical effect to each element of the coupler. The design shown in figure 3.6 is called
active switch. By applying electro-optical effect to the coupler, changes will occur in
the refractive index of the coupler. This will cause the changes in transferring optical
power into output 1 or 2 of the coupler. This will lead to full coupling or no coupling
states of light source.
Figure 3.6 4x4 Active optical switch
The light source from input A, B, C or D can be diverted into output 1, 2, 3 or
4. This can be done by changing the voltage state in V1 , V2 , V3 and V4 .
24
3.5
Passive Optical Sitching Device and Operational Principles
Optical switching can be performed using passive or active devices. Several
types of device used to switch optical signal are discussed in the following section..
Passive optical switch device operate in the optical domain to switch light streams.
They include NxN fiber couplers with N>2, NxN waveguide couplers with N>2,
Mach-Zehnder interferometer and so on. These components can be fabricated either
from optical fiber or by means of planar optical waveguides using material such as
lithium nio ate LiNbO3 or InP.
The tree fundamental technologies for making passive optical switches are
based on optical fibers, integrated optical waveguides, and bulk micro-optics.
Researchers have examined many different component designs using these
techniques. Couplers using micro-optic designs aren't widely used because the strict
tolerances required in the fabrication and alignment processes affect their cost,
performance, and robustness.
3.6
Fiber Coupler
The N x M coupler is simple fundamental device that will be used here to
demonstrate the operational principles in switching optical signals. A common
construction is the fused-fiber coupler. This is fabricated by twisting together,
melting, and pulling two single mode fibers so they get fused together over a uniform
section of length W, as shown in figure 3.7.
Figure 3.7 Fiber coupler
25
Each input and output fiber has a long tapered section of length L, since the
transverse dimensions are gradually reduced down to that of the coupling region
when the fibers are pulled during the fusion process. The total draw length is L+W.
here,
P0 is the input power, P1 is the throughout power, and P2 is the power coupled
into the second fiber. The parameters P3 and P4 are extremely low signal levels
resulting from backward reflections and scattering due to bending in and packing of
the device.
As the input light P0 propagates along the taper in fiber 1 an into the
coupling region W, there is a significant decrease in the V number owing to the
reduction in the ratio r , where r is the reduced fiber radius. Consequently, as the
λ
signal enters the coupling region, an increasingly larger portion of the input field
now propagates outside the core of fiber. Depending on the dimensioning of the
coupling region, any desired fraction of this decoupled filed can be recouped into the
other fiber. By making the tapers very gradual, only a negligible fraction of the
incoming optical power is reflected back into either of the input ports. Thus, these
devices are also known as directional couplers.
The optical power coupled from one fiber to another can be varied through
three parameter, the axial length of the coupling region over which the fields from
the two fibers interact, the size of the reduced radius r in the coupling region, and
∆r , the difference in the radii of two fibers in the coupling region. In making a fused
fiber coupler, the coupling length W is normally fixed by the with of the heating
flame, so that only L and r change as the coupler is elongated. Typical values for W
and L are few millimeters, the exact values depending on the coupling ratios are
∆r
desired for a specific wavelength, and
r
are around 0.015. Assuming that the
coupler is lossless, the expression for the power P2 coupled from one fiber to
another over an axial distance is P2 = P0 sin 2 k where k is the coupling coefficient
describing the interaction between the fields in the two fibers, by conservation of
[
]
power, for identical-core fiber, P1 = P0 − P2 = P0 1 − sin 2 k = P0 cos 2 k .
26
This shows that the phase of the driven fiber always lags 90° behind the
phase of the driving fiber, as figure 3.8.
Figure 3.8 Normalized coupled powers P2 / P1 and P1 / P0 as a function of the coupler
draw length for a 1300nm power level P0 launched into fiber 1
Figure 3.9 Dependence on wavelength of the coupled powers in completed 15mm
long coupler
Thus, when power is launched into fiber 1, at z=0 the phase in fiber 2 lags
90° behind that in fiber 1. this lagging phase relationship continues for increasing z,
until at a distance that satisfies kz = π
2
, all of the power has been transferred from
fiber 1 to fiber 2, now fiber 2 becomes the driving fiber, so that for π
2
≤ kz ≤ π the
27
phase in fiber 1 lags behind that in fiber 2, and so on. As a result f this phase
relationship, the 2x2 coupler is a directional coupler. That is, no energy can be
coupled into a wave traveling backward in the negative –z direction in the driven
waveguide. Figure 3.9 shows how k varies with wavelength for the final 15 mm
parameters. Thus, different performance couplers can be made by varying the
parameters W, L, r and ∆r for a specific wavelength λ .
In specifying the performance of an optical coupler, one usually indicates the
percentage division of optical power between the output ports by means of the
splitting ratio or coupling ratio.
⎧ P ⎫
Splitting ratio = ⎨ 2 ⎬ ×100%
⎩ P1 + P2 ⎭
(3.5)
By adjusting the parameters so that power is divided evenly, with half of the
input power going to output, one creates a 3dB coupler. In the above analysis, the
device is assumed lossless, however, in any practical coupler there is always some
light that is lost when a signal goes through it. The two basic losses are excess loss
and insertion loss. The excess loss is defined as the ratio of the input power to the
total output power. Thus, in decibels, the excess loss for a 2x2 coupler is
⎧ P ⎫
Excess loss = 10 log⎨ 0 ⎬
⎩ P1 + P2 ⎭
(3.6)
The insertion loss refers to the loss for a particular port-to-port path.
⎧⎪ P ⎫⎪
Insertion loss = 10 log ⎨ i ⎬
⎪⎩ Pj ⎪⎭
(3.7)
Another performance parameter is crosstalk, which measures the degree of
isolation between the input at one port and the optical power scattered or reflected
back into the other input port, which is measure of optical power level P3 .
28
⎧P ⎫
Cross talk= 10 log ⎨ 3 ⎬
⎩ P0 ⎭
(3.8)
A 2x2 guided wave coupler as a four terminal device that has two inputs and
two outputs. Either all fiber or integrated optics device can be analyzed in terms of
the scattering matrix S, which defines the relationship between the two input filed
strength b1 and b2 by definition,
b = Sa, where
⎡b ⎤
b = ⎢ 1 ⎥,
⎣b2 ⎦
⎡a ⎤
a = ⎢ 1 ⎥,
⎣a 2 ⎦
and
⎡S
⎢ 11
S=⎢
⎢ S 21
⎣
S12 ⎤
⎥
⎥
S 22 ⎥
⎦
(3.9)
Here, S ij = S ij exp( jφ ij ) represents the coupling coefficient of optical power
transfer from input port i to output port j , with S ij being the magnitude of S ij and
φ ij being its phase at port j relative to port i . For an actual physical device, two
restrictions apply to the scattering matrix S . One is result of the reciprocity condition
arising from the fact that Maxwell’s equations are invariant for time inversion; that
is, they have two solutions in opposite propagating directions thought the device,
assuming single-mode operation shown figure 3.10. The other restriction arises from
energy-conservation principles under the assumption that the device is lossless. From
the first condition, it follows S12 = S 21 .
Figure 3.10 Generic 2x2 guided- wave coupler
From the second restriction, if the device is lossless, the sum of the sum of
the output intensities to must equal the sum of the input intensities I i
29
I 0 = b1 ∗ b1 + b2 ∗ b2 = I i = a1 ∗ a1 + a 2 ∗ a 2
(3.10)
Where the superscript ∗ means the complex conjugate and the superscript
+
indicates the transpose conjugate.
S11 ∗ S11 + S12 ∗ S12 = 1
(3.11)
S11 ∗ S12 + S12 ∗ S 22 = 0
(3.12)
S 22 ∗ S 22 + S12 ∗ S12 = 1
(3.13)
If we now assume that the coupler has been constructed so that fraction
(1 − ε ) of the optical power from input 1 appears at output 1, with the remainder ε
going to port 2, than we have S11 = 1 − ε , which is a real number between 0 and 1,
here, we have assumed, without loss of generality, that the electric field at output 1
has zero phase shift relative to the input at port 1; that is φ11 = 0 . Since we are
interested in the phase change that occurs when the coupled optical power input 1
emerges from port 2, we make the simplifying assumption that the coupler is
symmetric.
Then, analogous to the effect at port 1, we have S 22 = 1 − ε with φ 22 = 0 .
Using these expressions, we can determine the phase φ12 of the coupled outputs
relative to the input signals and find the constraints on the composite outputs when
both input ports are receiving singles. Inserting the expressions for S11 and S 22 into
(3.12) and letting S12 = S12 exp( jφ12 ) where S12 is the magnitude of S12 and φ12 is
its phase, we have exp( jφ12 ) = −1 which holds when,
φ12 = (2n + 1)
π
2
Where n=0, 1, 2 …..
(3.14)
So that the scattering matrix from (3.9)becomes
⎡ 1− ε
⎢
S=⎢
⎢j ε
⎣
⎤
⎥
⎥
1− ε ⎥
⎦
j ε
(3.15)
30
When we want a large portion of the input power from, say, port 1 to emerge
from output 1, we need ε to be small. From there, optical single can be switch to the
output that desired.
3.7
Waveguide Coupler
More versatile 2x2 couplers are possible with waveguide-type device in
switching optical signal. Figure 3.6 shows two types of 2x2 waveguide couples. The
uniformly symmetric device has two identical parallel guides in the coupling region,
whereas the uniformly asymmetric coupler has one guide wider than the other,
analogous to fused-fiber couplers, waveguide device have than an intrinsic
wavelength dependence in coupling region, and the degree of interaction between the
guides can be varied through the guide width w , the gap s between the guides, and
the refractive index n1 between the guides. In figure 3.11, the z direction lies along
the coupler length and the y axis lies in the coupler plane transverse to the two
waveguides, let us first consider the symmetric coupler.
Figure3.11 An uniformly asymmetric directional waveguide coupler in which one
guide has a narrower width in coupling region.
31
In real waveguides, with absorption and scatting losses, the propagation
constant, β z is a complex number given by β z = β r + j
α
2
.
Where, β r is real part of the propagation constant and α is the optical loss
coefficient in guide. Hence, the total power contained in both guide decreases by a
factor exp( −αz ) along their length.. Example, losses in semiconductor waveguide
device fall in the 0.05〈α 〈 0.3cm −1 range, which is substantially higher than the
nominal 0.1-dB/km losses in fused-fiber couples.
The transmission characteristics of the symmetric coupler can be expressed through
the coupled-mode theory approach to yield,
P2 = P0 sin 2 (α )e −α
(3.16)
Where the coupling coefficient is
k=
2β y2 qe − qs
β z w(q 2 + β y2 )
(3.17)
This is a function of the waveguide propagation constant β r and β z , the gap
width and separation, and the extinction coefficient q in the y direction outside the
waveguide, which is,
q 2 = β y2 − k12
(3.18)
The theoretical power distribution s a function of the guide length is as shown
in figure3.12, where we have used k = 0.6mm −1 and α = 0.02 mm −1 . Analogous to
the fused-fiber coupler, complete, complete power transfer to the second guide
occurs when guide length L is
L=
π
2k
( m + 1)
(3.19)
32
Since k is found to be almost monotonically proportional to wavelength, the
coupling ratio P2
P0
rises and falls sinus dally from 0 to 100 percent as a function of
wavelength, as figure 3.8 illustrates generically.
When the two guides do not have the same widths, as shown in figure 3.11(b)
the amplitude of the coupled power is dependent on the wavelength, and the coupling
ratio becomes.
P2
P0
=
k2
sin 2 ( gz )e −α
2
g
(3.20)
Where
⎛ ∆β ⎞
g = k +⎜
⎟
⎝ 2 ⎠
2
2
2
(3.21)
Figure3.12 Theoretical through-path and coupled power distribution as a function of
the guide length in a symmetric 2x2 guided-wave coupler with k = 0.6mm −1
and α = 0.02 mm −1 .
33
Figure3.13 wavelength response of the coupled power P2 / P0
With
∆β being the phase difference between the two guides in the z
direction. With this type of configuration, device that have a flattened response can
be fabricated in which the coupling ratio is less than 100 percent in a specific desired
wavelength range. The main cause of the wave-flattened response at the lower
2
wavelength results from suppression by the amplitude tem k
g2
. This asymmetric
characteristic can be used in a device where only a fraction of power from a specific
wavelength should be tapped off. When ∆β = 0 ,(3.21) reduces to the symmetric
case given by (3.13).
More complex structures are readily fabricated in which the widths of the
guides are tapered. These non-symmetric structures can be used to flatten the
wavelength response over a particular spectral range. The above analysis based on
the coupled-mode theory holds when the indices of the two waveguide are identical,
but a more complex analytical treatment is needed for different indices.
3.8
Mach-Zehnder Interferometer
Wavelength-dependent switches can also be made using Mach-Zehnder
anemometry techniques. This device can be either active or passive. Passive switches
based on Mach-Zehnder interferometer is discussed here. Figure 3.14 illustrates the
34
constituents of a individual Mach-Zehnder interferometer. This 2x2 Mach-Zehnder
interferometer consists of three stages: an initial 3-dB directional coupler which
splits the input signals, a central section where one of the waveguides is longer by
∆L to give a wavelength-dependent phase shift between the two arms, and another
3dB coupler which recombines the signals at the output. In the following derivation,
the function of this in one of the paths, the recombined signals will interfere
constructively at one output and destructively at the other. The signals then finally
emerge from only one output port. For simplicity, waveguide material losses or bend
losses in the following analysis is not taken into account.
The propagation matrix M coupler for a coupler of length d is
⎡cos kd
⎢
M coupler ⎢
⎢ j sin kd
⎣
j sin kd ⎤
⎥
⎥
cos kd ⎥
⎦
(3.22)
Where k is the coupling coefficient? Since 3dB couples which divide the
power equally is considered, then 2kd = π
M coupler
⎡1
1 ⎢
=
⎢
2 ⎢j
⎣
2
, so that
j⎤
⎥
⎥
1⎥
⎦
(2.23)
In the central region, when the signals in the two arms come from the same light
source, the outputs from these two guides have a phase difference ∆φ give by
∆φ =
2πn1
λ
L−
2πn2
λ
( L + ∆L) .
35
Figure 3.14 2x2 Mach-Zehnder interferometer
This phase difference can arise either from a different path length or through
a refractive index difference if n1 = n2 = neff (The effective refractive index in the
waveguide).
Than we can rewrite last Equation, ∆φ = k∆L , Where k =
2πneff
λ
. For a give
phase difference ∆φ , the propagation matrix M ∆φ for the phase shifter is:
M ∆φ
⎡ jk∆L
⎢e 2
=⎢
⎢
⎢ 0
⎢⎣
⎤
⎥
⎥
− jk∆L ⎥
e 2 ⎥
⎥⎦
0
(3.24)
The optical fields E out ,1 and E out , 2 from the two central arms can be related to
the input fields Ein ,1 and Ein ,1 by
⎡ Eout ,1 ⎤
⎡ Ein ,1 ⎤
=
M
⎢
⎥
⎢
⎥
⎣ Eout , 2 ⎦
⎣ Ein , 2 ⎦
(3.25)
36
M = M couples . M ∆φ
k∆L
⎡
⎢sin( 2 )
= j⎢
⎢cos( k∆L )
⎢⎣
2
k∆L ⎤
)
2 ⎥
⎥
k∆L ⎥
)
− sin(
2 ⎥⎦
cos(
(3.26)
An optical switch can be modified to become an optical multiplexer, where
inputs to the MZI at different wavelengths are needed; that is Ein ,1 is at λ1 and E in , 2 is
at λ2 .
Then
k ∆L
k ∆L ⎤
⎡
Eout ,1 = j ⎢ Ein ,1 (λ1 ) sin( 1 ) + Ein , 2 (λ2 ) cos( 2 ⎥
2
2 ⎦
⎣
(3.27)
k ∆L
k ∆L ⎤
⎡
Eout , 2 = j ⎢ Ein ,1 (λ1 ) cos( 1 ) + Ein , 2 (λ2 ) sin( 2 )⎥
2
2 ⎦
⎣
(3.28)
Where k j =
2πneff
λi
. The output powers are than found from the light
intensity, which is square of the field strengths, thus,
*
2
Pout ,1 = Eout ,1 .Eout
,1 = sin (
k1∆L
k ∆L
) Pin ,1 + cos 2 ( 2 ) Pin , 2
2
2
*
2
Pout , 2 = Eout , 2 .Eout
, 2 = cos (
k1∆L
k ∆L
) Pin ,1 + sin 2 ( 2 ) Pin , 2
2
2
(3.29)
(3.30)
2
Where Pin , j = Ein , j = Ein , j .Ein , j . Deriving for last two equations, the cross
terms are dropped because their frequency, which is twice the optical carrier
frequency, is beyond the response capability of the photo detector.
And from last two equation, if all power from both inputs leave the same output
port, k 1 ∆ L = π and
2
k 2 ∆L π
= are needed,
2
2
37
⎛1 1 ⎞
(k1 − k 2 )∆L = 2πneff ⎜⎜ − ⎟⎟∆L = π
⎝ λ1 λ2 ⎠
(3.31)
Hence, the length difference in the interferometer arms should be
⎡
⎛ 1 1 ⎞⎤
∆L = ⎢2neff ⎜⎜ − ⎟⎟⎥
⎝ λ1 λ2 ⎠⎦
⎣
−1
=
c
2neff ∆v
(3.32)
Where ∆v is the frequency separation of two wavelengths.
Using basic 2x2 Mach-Zehnder interferometer, any size NxN optical switch
can be constructed. Figure 3.15, gives an example for 4x4 multiplexer, the inputs to
MZI1 are v and v + 2∆v , and the inputs to MZI 2 are v + ∆v and v + 3∆v . Since the
signals in both interferometers of the first stage are separated by 2∆v , the path
differences satisfy the condition.
∆L1 = ∆L2 =
c
2neff (2∆v)
(3.33)
In the next stage, the input are separated by ∆v consequently,
∆L3 =
c
= 2∆L1
2neff (2∆v)
(3.34)
Figure 3.15 Four channel wavelength multiplexer there 2x2 MZI elements
38
When these conditions are satisfied, all four input power will emerge from
port C. It means all four input powers can be switched or multiplexed into the same
output port using combination of Mach-Zehnder interferometer.
From this design example, an N-to-1 Mach-Zehnder interferometer
multiplexer can be deduced that, where N = 2 n with the integer n ≥ 1 , the number of
multiplexer stages is n and the number of Mach-Zehnder interferometer in stags j
is 2 n − j . The path difference in an interferometer element of stage j is thus
∆Lstage j =
2
n− j
c
neff ∆v
(3.35)
The N-to-1 Mach-Zehnder interferometer multiplexer can also be used as 1to-N demultiplexer by reversing the light-propagation. For a real Mach-Zehnder
interferometer, the ideal case given in these examples needs to be modified to have a
slight difference in ∆L1 and ∆L2 .
This design example, an N-to-1 Mach-Zehnder interferometer multiplexer
can be deduced that, where N = 2 n with the integer n ≥ 1 , the number of multiplexer
stages is n and the number of Mach-Zehnder interferometer in stage j is 2 n− j . The
path difference in an interferometer element of stage j is thus:
∆Lstage j =
2
n− j
C
neff ∆v
(3.36)
The N-to-1 Mach-Zehnder multiplexer can also be used as 1-to-N
demultiplexer by reversing the light-propagation direction. For real Mach-Zehnder
interferometer, the ideal case given in these examples needs to be modified to have a
slight difference in ∆L1 and ∆L2 .
39
3.9
Application of Integrated Optics in The Evolution of Optical Switching
Technology
The multitude of potential application areas for optical fiber communications
coupled with the tremendous advances in the filed have over recent years stimulated
a resurgence of interest in the area of integrated optics (IO) especially in the
application of optical switching. The concept of IO involves the realization of optical
and electro-optical elements which may be integrated in large numbers on to a single
substrate. Hence, IO seeks to provide an alternative to the conversion of an optical
signal back into the electrical regime prior to signal processing by allowing such
processing to be performed on the optical signal. Thin transparent dielectric on
planar substrates which act as optical waveguides are used in IO to produce
miniature optical components and circuits.
Developments in IO have now reached the stage where simple signal
processing and logic junctions may be physically realized. Furthermore, such devices
may form the building blocks for future digital optical computers. Nevertheless, at
present, these advances are closely linked with development in light wave
communication employing optical fiber. A major factor in the development of
integrated optics is that it is essentially based on single-mode optical waveguides and
therefore tends to be incompatible with multimode fiber systems. Hence IO did not
make a significant contribution to first and second generation optical fiber systems.
The advent, however, of single-mode transmission technology has further
stimulated work in IO in order to provide devices and circuits for these more
advanced third generation systems. It is apparent that the continued expansion of
single-mode optical fiber communication will create a growing market for such IO
components.
Furthermore, it is predicted that the next generation of optical fiber
communication systems employing coherent transmission will lean heavily on IO
techniques for their implementation especially in optical switching.
40
The proposals for IO device and circuits which in many cases involve
reinventions of electronic device and circuits exhibits major advantages other than
solely a compatibility with optical fiber communications. Electronic circuits have
practical limitation on speed of operation at a frequency of around 101° Hz resulting
from their use of metallic conductors to transport electronic charges and build-up
signals. The large transmission bandwidths (over 1 Ghz) currently under
investigation for optical fiber communication are already causing difficulties for
electronic signal processing within the terminal equipment. The use of light with its
property as an electromagnetic wave of extremely high frequency ( 1014 to 1015 Hz)
offers the possibility of high speed operation around 1014 times faster than that
conceivable employing electronic circuit. Interaction of light with materials such as
semiconductors or transparent dielectrics occurs at speed in the range 1012 pico to
approaching 1015 seconds, thus providing a basis for subpicosecond optical
switching.
The other major attribute provided by optical signals interacting within a
responsive medium is the ability to utilize light waves of different frequencies (or
wavelengths) within the same guided wave channel or device. Such frequency
division multiplexing allows an information transfer capacity far superiors to
anything offered by electronics. Moreover, in signal processing terms it facilitates
parallel access to information points within an optical system. The possibility for
powerful parallel signals processing coupled with ultrahigh speed operation offers
tremendous potential for applications within both communications and computing.
The devices of interest in IO are often the counterparts of microwave or bulk optical
device. These include junctions and directional couplers, switches and modulators,
filters and wavelength multiplexers, laser and amplifier, detectors and bitable
elements. It is envisaged that developments in this technology will provide the basis
for the fourth generation systems where full monolithic integration may be achieved.
It also gives a large contribution in the field of optical switching.
41
3.10
Planar waveguide Integrated optical in optical switching
These use circular dielectric waveguide structures for confining light is
universally utilized within optical fiber communication. IO involves an extension of
this guided wave optical technology through the use of planar optical waveguides to
confine and guide the light in guided wave devices and circuits and thus perform
switching of light. In fact the simplest dielectric waveguide structure is the planar
slab guide shown in figure 3.16 It comprises a planar film of refractive index n ,
sandwiched between a substrate of refractive index
n2 , and a cover layer of
refractive index n3 where n1 〉 n2 〉 n3 . Often the cover layer consists of air where
n3 = n0 = 1 , and it exhibits a substantially lower refractive index than the two layers.
In this case the film has layers of different refractive index above and below the
guiding layer and hence performs as an asymmetric waveguide.
When the dimensions of the guide are reduced so are the number of
propagating modes. Eventually the waveguide dimensions are such that only a
single-mode propagates, and if the dimensions are reduced further this single-mode
still continues to propagate. Hence there id no cutoff for the fundamental mode in a
symmetric guide.
Figure 3.16 A planar slab waveguide. The film with h refractive index n1 acts as the
guiding layer and the cover layer is usually air where n3 = n0 = 1
This is not the case for an asymmetric guide where the dimensions may be
reduced until the structure cannot support any mode and even the fundamental is
42
cutoff. If the thickness or height of the guide layer pf a planar asymmetric guide is h,
then the guide can support a mode of order m with a waveguide λ when
( m + 1 )λ
2
h≥
2
2(n1 − n22 ) 0.5
(3.37)
Which assumes, n 2 〉 n3 defines the limits of the single-mode region for
h between values when m = 0 and m = 1 . An additional consideration of equal
importance is the degree of confinement of the guiding layer. The light is not
exclusively confined to the guiding region and evanescent fields penetrate into the
substrate and cover. An effective guide layer thickness heff may be expressed as
heff = h + x 2 + x3
Where
(3.38)
x 2 and x3 are the evanescent field penetration depths for the
substrate and cover regions respectively. Furthermore, normalized effective thickness
H for an asymmetric slab guide is
H = kheff (n12 − n22 ) 0.5
Where k is the free space propagation constant equal to 2π
(3.39)
λ . The
normalized frequency for the planar slab guide is
H = kh(n12 − n 22 ) 0.5
(3.40)
An indication of the degree of confinement for the asymmetric waveguide
may be observed by plotting the normalized effective thickness the normalized
frequency for the TE modes. A series of such plots is show in figure 3.17 for various
values of the parameter which indicates the asymmetry of the guide, and is as defined
as
a=
n 22 − n32
n12 − n22
(3.41)
43
Figure 3.17 A planar slab waveguide. The film with h refractive index n1 acts as the
guiding layer and the cover layer is usually air where n3 = n0 = 1 the normalized
effective thickness H as a function of the normalized frequency V for a waveguide
with various degrees of asymmetry
The planar waveguide for IO may be fabricated from glasses and other
isotropic materials such as silicon dioxide and polymers. Although these materials
are used to produce the simplest integrated optical components, their properties
cannot be controlled by external energy source and hence they are of limited interest.
In order to provide external control of entrapped light to optical switching, active
device employing alternative material must be utilized. A allow the local refractive
index to be varied by application of either electrical, magnetic or acoustic energy.
To date, interest has centered on the exploitation of the electro-optical effect
due to the ease of controlling electric field through the use of electrodes together
with the generally superior performance of electro-optical device. Acousto-optic
device have, however, found a lesser role, primarily in the area of beam deflection.
Magneto-optic device utilizing the Faraday Effect are not widely used, as in general,
electric field are easier to generate than magnetic field.
44
A variety of electro-optical and acousto-optical materials have employed
materials have been employed in the fabrication of photonics switching device. Two
basic groups can be distinguished by their refractive indices. These are materials with
a refractive index near 2( LiNbO3 , LitaO3 , NbO5 , ZnS
and
ZnO ) and materials
with a refractive index greater than 3( GaAs, InP and compounds of Ga and in with
elements of AI, as and Sb).
Planar waveguide structures are produced using several different techniques
which have in large part been part been derived from the microelectronic industry.
For example, passive device may be fabricated by radio frequency sputtering to
deposit thin films of glass onto glass substrates. Alternatively, active device are often
produced by titanium (Ti) diffusion into lithium niobate ( LiNbO3 ) or by ion
implantation into gallium arsenide.
The planar slab waveguide show in figure 3.16 confines light in only one
direction, allowing it to spread across the guided layer. In many instances it is useful
to confine the light in two dimensions to a particular path on the surface of the
substrate. This is achieved by defining the light index guiding region as a thin strip
(strip guide) where total internal reflection will prevent the spread of the light beam
across the substrate. In addition the strips can be curved or branched as required.
Figure 3.18 cross section of some strip waveguide structures structure
(a) Ridge guide
(b) diffused channel
(c) rib guide
Examples of such strip waveguide structures are shown in figure3.16. They
may be formed as either a ridge on surface of substrate or by diffusion to provide a
region of higher refractive index below the substrate, or as rib of increased thickness
within a thin planar slab. Techniques employed to obtain the strip the pattern include
45
electron and laser beam lithography as well as photolithography. The rectangular
waveguide configuration illustrated in figure 3.18 prove very suitable for as use with
electro-optic deflectors and modulators giving a reduction in voltage required to
achieve a particular field strength. In addition they allow a number of optical paths to
be provided on a given substrate.
A trade-off exists between the minimum radius of curvature which is required
for high density integration and the ease of fabrication, which the waveguide
dimensions are dependent upon the refractive index change. When the change is
large, the dimensions of waveguide may be reduced, even though the scattering
losses become larger. As the maximum confinement of single-mode guide occurs
when it is operated near to the cutoff of the second order mode, then when the
refractive index change is large, the radius of curvature of the waveguide can also be
made very small. It is therefore necessary to find a compromise for the waveguide
material used.
Titanium in diffusion of ( LiNbO3 ) gives rise to refractive index increases in
the order of 0.01 to 0.02 which dictates a bend radius of the order of a few
centimeters for negligible losses. It is, however, possible to use a proton exchange
techniques to increase the refractive index change up to 0.15. By contrast,
semiconductor III-V alloy waveguide based on compositional modification of the
crystal give an index change of around 0.1 or more. Therefore, bend radii of the
order of 1mm or less may be obtained using these compounds. Moreover, although
the effects of interest in IO are usually exhibited over short distances of around one
waveguide, efficient device require relatively long interaction lengths, the effects
being cumulative. Hence, typical optical switching device lengths range from 0.5 to
10mm.
Optical connections to and from optical switching device are normally made
by optical fiber. The overall insertion loss for device therefore comprises a
waveguide fiber coupling loss as well as the waveguide optical propagation loss.
46
Careful fabrication of Ti : LiNbO3 waveguides have gone below 0.2dBcm −1 ,
with excess bend losses being maintained below 0.1dB per bend. By contract
propagation losses in semiconductor waveguide around 1dBcm −1 are obtained when
operating at wavelength corresponding to the bandgap energy. Much lower losses of
approximately 0.2dBcm −1 , however, have to be achieved at operating wavelengths
far below the bandgap energy.
3.11
Active optical switching devices and operational principles
Here, some examples of active optical switching devices in today’s
technology together with their salient features are considered. However, the
numerous developments in this field exclude any attempt to provide other than
general examples in the major areas of investigation which are pertinent to optical
fiber communication. The requirement for multichannel communication within the
various systems demands the combination from separate channels, transmission of
the combined signals over a single optical fiber link, and separation of the individual
channels at the receiver prior to routing to their individual destinations. Hence the
application of IO in this areca is to proved optical methods for switching.
3.12
Electro-optic Mach Zehnder Interferometer
Mach Zehnder Interferometer can be used as active optical switch if a voltage
is applied. The limitation imposed by direct current modulation of semiconductor
injection lasers currently restricts the maximum achievable modulation frequencies
to few gigahertzes. Furthermore, with most injection lasers high speed current
modulation also creates undesirable wavelength modulation which imposes problems
for systems employing wavelength division multiplexing. Thus to extend the
bandwidth capability of signal-mode fiber systems there is a requirement for high
speed modulation which can be provided by integrated optical waveguide intensity
47
modulation. Simple on/off modulation may be based be based on the techniques
utilized for the active beam splitters and switches. In addition a large variety of
predominantly electro-optical modulation have been reported which exhibit good
characteristics. For example, an important waveguide modulator is based upon a Ybranch interferometer which employs optical phases shifting produced by the electrooptic effect.
The change in refractive index exhibited by an electro-optic material with the
application of an electric field given by δn = ±0.5n13 rE also provides a phase change
for light propagation in the material. This phase change δφ is accumulative over a
distance L within the material
δφ =
2π
λ
δnL
(3.42)
When the electric field is applied transversely to the direction of optical
propagation we may substitute for δn from δn = ±0.5n13 rE giving
δφ =
π 3
n1 rEL
λ
(3.43)
Furthermore taking E equal to V
d
, where V is the applied voltage and d is the
distance between electrodes gives
δφ =
π 3 VL
n1 r
λ
d
(3.44)
It may be noted from δφ =
π 3 VL
that in order to reduce the applied
n1 r
λ
d
voltage V required to provide a particular phases change, the ratio L
d
must be made
as large as possible.
A simple phase modulator may therefore be realized on a strip waveguide in
which the ratio L
d
is large as shown in figure 3.19. These devices when, for
48
example, fabricated by diffusion of Nb into LiNbO3 , provide a change of π radians
with an applied voltage in the range 5 to 10V, hence provides optical switching.
Figure 3.19 A simple strip waveguide phase modulator
The consequence of these no uniform fields can be incorporated into an
overlap integral a, having a value between 0 and 1 which gives a measure of overlap
between the electrical and optical and optical fields. The electro-optic refractive
index change of δn = ±0.5n13 rE therefore becomes
± an13 r V
δφ =
2 d
(3.45)
Where the factor a represent the efficiency of the electro-optical interaction
relative to an idealized parallel plate capacitor with the same distance between the
electrodes.
The electro-optic property can be employed in an interferometer intensity
modulator. Such a Mach Zehnder type interferometer is shown in figure 3.16. The
device comprises two Y-junctions which give an equal division of the input optical
power. With no potential applied to electrodes, the input optical power is split into
the two arms at the first Y-junction and arrives at the second Y-junction in phase
giving an intensity maximum at the waveguide output. This condition corresponds to
the “no” state. Alternatively when a potential is applied to the electrodes, which
operate in a push-pull mode on the two arms of the interferometer, a differential
phase change is created between the signals in the arms. The subsequent
recombination of the signals gives rise to constructive or destructive interference in
the output waveguide. Hence the process has the effect of converting the phase
49
modulation into intensity modulation. A phase shift of a between the two arms gives
the “off” state for the device.
High speed interferometer modulators have been demonstrated with titanium
doped lithium niobate waveguide. A 1.1 GHz modulation bandwidth has been
reported for a 6mm interferometer employing a 3.8V on/off voltage across a 0.9µm
gap. Similar devices incorporating electrodes on one arm only may be utilized as
switching and are generally referred to as balanced bridge interferometric switches.
Figure 3.20 A Y-junction interferometric modulator based on the Mach Zehnder
interferometer
CHAPTER 4
DESIGNING OPTICAL SWITCH
In this chapter, analysis on Mach Zehnder interferometer is done theoretically
in terms of its light coupling efficiency for use of optical switching. Waveguiding
and medium used in designing switch are analyzed in detailed. Titanium diffused
lithium niobate or the Ti : LiNbO3 waveguide is used as the waveguide medium in the
optical switch design. Titanium diffusion in lithium niobate process and its electrooptic effect are discussed. A Mach Zehnder interferometer is designed for use of
switching optical signal. In designing an optimum optical switch in terms of its
coupling efficiency, many parameters are analyzed. From the analysis, efficiency of
optical signal coupling is found effected by wavelength of light source, refractive
index of medium, with of electrode, and separation distance between waveguides.
The design and simulation of optical switch is carried out step stay by step using
BPM for diffused waveguides of BPM_CAD. Flow chart of optical switch design is
shown in figure 5.1.
51
Figure 4.1 Flow chat of optical switch design
52
4.1
Titanium Diffusion in Lithium Niobate Process
The material that I choose in my optical switch design is titanium diffused
lithium niobate Ti : LiNbO3 . The reason that I choose this material is it has very low
loss and switching voltage need to applied is small which is normally below 10V.
Further more, silicon based substrate normally acts passively to electric-optic,
Ti : LiNbO3 material is best choice due to its electro-optic and piezo-electric
characteristics.
The titanium diffused waveguides in lithium niobate, or the Ti : LiNbO3
waveguides, are formed by the in diffusion of titanium dopant into the lithium
niobate host. To form a waveguide, a stripe of titanium is deposited on the LiNbO3
substrate. For a given stripe width, which is identified with the waveguide with the
waveguide with, the amount of titanium is characterized by the stripe thickness
before diffusion. The titanium lithium niobate sample is heated for a few hours at
temperature that range from hundred degrees Celsius. The titanium ions penetrate the
host substrate and form a graded index waveguide. The graded waveguide has a bellshaped refractive index distribution in the lateral and in-depth directions. The index
distribution can be characterized phenomenologically by diffusion lengths or, as an
alternative, by diffusion constants, diffusion constants, diffusion temperature and a
diffusion temperature coefficient, by diffusion constants, diffusion temperature and a
diffusion temperature coefficient. Moreover, since the lithium niobate crystal is
anisotropic, the refractive index depends on the crystal cut and light polarization.
Referring to the anisotropy, we distinguish between ordinary and extraordinary
parameters. The material chromatic dispersion is also taken into account. The
chromatic factor is different for ordinary and extraordinary cases, the graded
refractive index n1 is a sum of the bulk crystal index ni0 and the diffusion-induced
index change ∆n1 ,
n1 (λ , x, y ) = ni0 (λ ) + ∆ni (λ , x, y )
(4.1)
i = o, e
53
Where, depending on the crystal cut and light polarization, we consider the
ordinary (O) or extraordinary (e) index distributions. Due to the chromatic
dispersion, the graded index also depends on the wavelength λ .
The chromatic of the ordinary and extraordinary bulk index is computed
using the Sellmeier dispersions equations.
( no0 ) 2 = 4.9048 −
(no0 ) 2 = 4.582 −
[
]
(4.2)
[
]
(4.3)
0.11768
− 0.027169 µm 2
2
2
0.0475 − λ µn
[ ]
0.099169
− 0.02195 µm 2
2
2
0.044432 − λ µn
[ ]
That is valid for wavelengths ranging from 0.43584 to 3.3913 microns. The
diffusion-induced index change is described by the product of the dispersion factor
d i (λ ) and the distribution function hi ( x, y ) ,
n1 (λ , x, y ) = d i (λ )hi (λ , x, y )
i = o, e
(4.4)
Where the dispersion factor is different for the ordinary and extraordinary
cases
d o (λ ) =
0.67λ2
λ2 − 0.13
(4.5)
d e (λ ) =
0.839λ2
λ2 − 0.0645
(4.6)
And the wavelength is measured in microns. In turn, the diffusion-induced
distribution function is a combination of the distribution constant
Fi the dopant
concentration profile c ( x, y ) and the distribution power factor γ i ,
h( x, y ) = [Fi c( x, y)] i
γ
i = o, e
(4.7)
54
Where then distribution constants
Fo = 1.3 × 10 −25 cm 3
Fe = 1.2 × 10 −23 cm 3
And the distribution power factors
γ o = 0.55 , γ e = 1 .
The differences between the ordinary and extraordinary cases are fitted from
published experimental data. The concentration profile can be derived following the
classical diffusion theory. The profile has a bell-shaped form
⎧ ⎡ w
c( x, y ) = co ⎨erf ⎢
⎩ ⎣ 2 Dx
⎡ w
⎛ 2 x ⎞⎤
⎜1 +
⎟⎥ + erf ⎢
w ⎠⎦
⎝
⎣ 2 Dx
⎛ y2 ⎞
⎛ 2 x ⎞⎤ ⎫
⎟
⎜−
−
1
.
exp
⎜
⎟⎥ ⎬
⎜ D2 ⎟
w ⎠⎦ ⎭
⎝
y
⎠
⎝
(4.8)
In the lateral direction, that is horizontal to the crystal surface, the profile is
characterized by the combination of error function. In the crystal in-depth direction,
that is vertical to the crystal surface, it has a Gaussian shape. The profile parameters
include the profile constant co , the dopant stripe width before diffusion w , the lateral
diffusion length Dx and the diffusion length in depth D y . In the BPM diffused
waveguide program, the dopant stripe width before diffusion is identified with the
waveguide with provided by the layout. In the literature, the above lateral diffusion
length and the diffusion length in depth are also called the horizontal and vertical
lengths, with a reference to the crystal surface. The lateral diffusion length
DH = 2 tDoH exp(
− To
T
)
DH = D x
(4.9)
And the diffusion length in depth
DV = 2 tDoV exp(
(4.10)
− To
T
)
DV = D y
55
Are exponential functions of the diffusion time t and the diffusion
To
temperature T . The temperature coefficient
and the diffusion constants DoH and
D oV are specific for the titanium niobate.
In the program, I enter the lateral diffusion length and diffusion length in
depth (option called group I). The concentration profile constant is a combination of
the stripe thickness before diffusion
length in depth
C0 = τ
τ,
the dopant constant
Cm
and the diffusion
CV ,
τCm
( π DV )
(4.11)
Where the dopant constant
Cm =
ρ
M at
(4.12)
A
Is material parameter determined by dopant density ρ , atomic weight
and
the
Avogadro
assume ρ = 4.52g
4.2
3
cm
number
, Mat = 49.7
g
A.
for
the
molthat gives
titanium
dopant
material,
Mat
we
Cm = 5.67×1022cm−3 .
Electro-Optic Effect
Electro-optic material like lithium niobate has refractive indices that can be
altered by an applied electric field. Many waveguide modulators or switches employ
metallic electrodes deposited on top of optical waveguide to serve the purpose of
applying the electric filed. An intermediate buffer layer with la low dielectric
constant id often deposited between the electrodes and the substrate to reduce the
losses that are due to the metallic cover of the waveguide. The efficiency of the
56
device depends on overlap between the electric field and the optical filed. By
changing electrode parameters the optical switch designed can be optimized.
Usually, the electrode in electro-optic devices is plated to a thickness of 2-3 microns
in order to reduce its ohmic losses while the electrode width can be as small as
10microns and the gap between electrodes is typically 5microns.
In BPM_CAD, I lay out rectangular electrodes using the electrodes region
tool. Than, a multiple of electrode sets per region are entered. An electrode set can
have up to three electrodes, with each electrode characterized by the width and
applied voltage. The separation between the electrodes and their common thickness
are adjusted. A buffer layer is also applied characterized by its thickness, horizontal
region is not limited.
From the electro-optic effect perspective, lithium niobate is a tridiagonal
crystal with the point group 3m. The matrix of the electro-optic or Pockels
coefficient for the group 3m crystal is
⎡0
⎢
⎢
⎢0
⎢
⎢
⎢0
⎢
⎢0
⎢
⎢
⎢ r 51
⎢
⎢
⎢ − r 22
⎣
− r 22
r 22
0
r 51
0
0
r13 ⎤
⎥
⎥
r13 ⎥
⎥
⎥
r 33 ⎥
⎥
0 ⎥
⎥
⎥
0 ⎥
⎥
⎥
0
⎥
⎦
(4.13)
In the materials and process dialog box the values of the electro-optic
coefficient are entered, however, published data are proposed as the program
defaults. The crystal coordinate system ( X , Y , Z ) is aligned with the principal axes of
the crystal. Referring to the crystal coordinates; the program offers calculations with
different crystal cuts, propagation directions and the choice of the TE or TM
polarization.
57
The ( X , Y , Z ) crystal system is not the same as the device layout coordinate
system ( X , Y , Z ) . In the layout coordinates, it is assumed that the z-direction is the
propagation direction. The electrodes filed are referred to the layout coordinates. The
crystal cut direction is conventionally assumed as perpendicular to the crystal wafer
surface. Electrode sets produce static electrical fields that can be either horizontal or
vertical to the crystal surface. The optical field, being the principal electrical
component of the electromagnetic field, can oscillate horizontally, TE polarization,
or vertically, TM polarization, to the surface.
In the absence of electrode fields the refractive index ellipsoid, or indicatrix,
is of the following form
X2 Y2 Z2
+
+
=1
no2 no2 ne2
(4.14)
Where no and ne are the ordinary and extraordinary refractive indices,
respectively. If the electrode field is assumed in the X direction of the crystal, then
the equation for the new indicatrix is
X2 Y2 Z2
+
+
+ 2r51 ⋅ E x ⋅ Z − 2r22 ⋅ E x ⋅ X ⋅ Y = 1
no2 no2 ne2
(4.15)
Assuming that the electrode field is in the Y-direction of the crystal, the indicatrix is
⎛ 1
⎞
⎛ 1
⎞
⎛ 1
⎞
⎜⎜ 2 − r22 E z ⎟⎟ X 2 + ⎜⎜ 2 + r13 E z ⎟⎟Y 2 + ⎜⎜ 2 + r33 E z ⎟⎟ Z 2 = 1
⎝ no
⎠
⎝ no
⎠
⎝ no
⎠
(4.16)
In different cases of the cut, propagation and polarization, and the electrode
filed direction, different electro-optic coefficient rii are used in the simulation
program. Table 5.1 and table 5.2 give a reference in entering electro-optic
coefficients for TE polarization and TM polarization. It is noticed that whether the
electrode field is considered horizontal or vertical depends on the electrode
58
configuration, voltage and the waveguide position. Intuitively, the electrostatic field
lines between electrodes are assumed follow patterns familiar from electrostatics.
Table 4.1 Electro-optic coefficients for TE polarization
Crystal cut, propagation direction
Horizontal electrode field
Vertical electrode field
X-cut, Y-propag
r33
0
Y-cut, X-propag
r33
0
r22
r13
0
r13
Y-cut, Z-propag
0
− r22
X-cut, Z-propag
r22
0
Z-cut, X-propag
Z-cut, Y-propag
Table 4.2 Electro-optic coefficients for TM polarization
Crystal cut, propagation direction
Horizontal electrode field
Vertical electrode field
X-cut, Y-propag
r13
0
Y-cut, X-propag
r13
r22
r22
r33
0
r33
0
r22
Z-cut, X-propag
Z-cut, Y-propag
Y-cut, Z-propag
X-cut, Z-propag
4.3
0
Optical Switching Using Electro-Optic Effect
Mach-Zehnder interferometer consists of a pair of waveguides which are
parallel of each other and separated by a separation distance. Input of optical signal
into one of the waveguide of MZI is coupled into one of the output over a evanescent
coupling. Coupling power is proportional to the separation of waveguides and size of
the waveguiding mode depends on the wavelength used. If two of the waveguides are
the same, then full coupling between them occurs over a certain separation which
depends on the coupling power. With locating electrode on the waveguides of the
59
optical switch designed, input optical signal can be coupled into desired output by
applying certain over the electrode.
With applying electric field, the refractive index of the electro-optic material
like lithium niobate can be changed. Optical switches or modulators use electrode
plate which located on the coupling region to couple the input optical signal. A
buffer layer with low dielectric constant is added between the electrode and the
substrate to reduce loss due to the electrode plate. Coupling efficiency of the optical
switch designed depends largely on the overlapping of the optical field and electric
field. With changing the electrode parameters, the coupling efficiency of the optical
switch designed can be optimized. Normally, the thickness of the electrode is 2 to
4µm to reduce loss and the inter-electrode gap is 5 to 6µm.
The applied voltage produce a electric field,
E =V
d
where the electric field
lines direct to the bottom of one of the waveguide and direct to the top of the another
waveguide. Due to this, the refractive index increases in one waveguide and
decreases in another waveguide. One important application for the electro-optic
effect is in controlling the coupling of waveguide in integrated optical switch. With
the electro-optic effect, coupling of optical signal to a certain output can be done.
The coupling process of the optical switch depends on two parameters, which
are the coupling constant, C (depends on the dimension, wavelength and refractive
index) and propagation constant difference, ∆β = β 1 − β 2 =
2n∆β
. ∆n Is the
λ0
difference between the refractive index of the waveguides. If two the waveguides are
similar where ∆β = 0 and the optical signal is in the first input of the switch, then at
a distance Z = L0 = 2π
2ζ
which is called the coupling length, the optical signal
power is fully coupled from first input to second output. For a waveguide with
coupling length L0 and ∆β ≠ 0 the ratio of power transfer is ℑ =
P2 ( L0 )
P1 (0)
where
P2 ( L0 ) the optical power is at second output and P1 (0) is the optical power at first
input and it is a function related to the phase mismatch of the waveguides.
60
4.4
Phase Mismatch
The ratio of optical power transfer ℑ =
P2 ( L0 )
P1 (0)
can be written as a
function of phase mismatch ∆β
2 0.5 ⎫
2
⎧ ⎡
⎤ ⎪
∆
β
L
1
⎛
⎞
⎪
⎛π ⎞
o
ℑ = ⎜ ⎟ sin c 2 ⎨ ⎢1 + ⎜
⎟ ⎥ ⎬
⎝2⎠
⎪⎩ 2 ⎢⎣ ⎝ π ⎠ ⎥⎦ ⎪⎭
(4.17)
Figure 5.1 shows that the ratio of optical power transfer, ℑ , depends on phase
mismatch
∆βLo .
This
ratio, ℑ ,
has
a
maximum
value
of
1
when ∆βLo = 0 ,decreasewhen ∆βLo increase and become zero when ∆βLo = 3π .
Figure 4.2 dependency of optical power transfer ratio, ℑ , on phase mismatch ∆βLo
Dependency of optical power transfer ratio, ℑ , on phase mismatch ∆βLo can
be used to produce a optical switch is which is activated electro-optically. If phase
mismatch ∆βLo is changed from 0 and 3π , the optical signal can be transferred
from second output to first output if the input is at first input. Electro-optic control of
optical signal can be done since the material used is electro-optic material, LiNbO3 .
61
When an electric field, E is applied on a waveguide, change of refractive index
occurs due to the electro-optic effect.
1
∆n E 0 = − (n 3 rE )
2
(4.18)
Where r: the electro-optic coefficient. The change of propagation constant is
∆β = k∆n E 0 = −
π 3
n rE
λ0
(4.19)
For modulation the phase is
∆φ E 0 = L∆β = −
π 3
n rEL
λ0
(4.20)
Where L is the length of the modulator in the direction of propagation Z.
figure 5.1 shows the ratio of optical power transfer, ℑ , has maximum value 1 when
∆βLo = 0 and
decrease
when
∆βLo increase.
The
ratio ℑ
becomes
zero
when ∆βLo = 3π where in this situation; the optical power is not transferred to
second output. V0 Is the switching voltage and V is the total voltage to the coupling
region of the optical switch.
4.5
Switching Voltage
Dependency of power coupled on phase mismatch is the key to produce
Mach-Zehnder interferometer which can be activated by electric field. If the
mismatch ∆β Lo is changed from 0 to 3π , the optical signal in input 1 is coupled
into output 1. Electric field control on ∆β is achieved with using electro-optic effect.
An electric field E is applied on one of the waveguide of the optical switch to change
62
1
the refractive index ∆n = − n 3 ΓE where Γ Pockets constant. This produces a phase
2
change,
⎛ L ⎞
⎛π ⎞
∆βL0 = ∆n⎜⎜ 2π 0 ⎟⎟ = −⎜⎜ ⎟⎟n 3 ΓL0 E
⎝ λ0 ⎠
⎝ λ0 ⎠
(4.21)
A Mach-Zehnder interferometer can be realized as a 2x2 electro-optic switch
with the electro-optic effect. A geometry 2x2 electro-optic switch based MachZehnder interferometer is shown in figure 4.3.
Figure 4.3 A design of 2x2 electro-optic switch based Mach-Zehnder interferometer
From figure 4.3 the electrode is placed on two waveguide. The separation
between two waveguides P1 and P2 is d .A voltage, V , is applied to yield a electric
field, E = V
d
in one waveguide and E = − V
d
in another one, where d is the
effective distance determined by solving the electrostatic problem. The refractive
index increases in one waveguide and decreases in another waveguide. The results is
3
a summation of the refractive index difference, 2∆n = − n ΓV
d
, which is matched is
L
matched with a phase mismatch factor, ∆βLo = −⎛⎜ 2π ⎞⎟n 3 Γ⎛⎜ o ⎞⎟V , which is
λ
o⎠
⎝
⎝ d⎠
proportional to the voltage applied, V.
63
The voltage, Vo needed to be applied to coupled the optical into same
waveguide for the situation, where, ∆β Lo = 3π , is
Vo = 3
d λo
Lo 2n 3 Γ
(4.22)
Where, the switching voltage is Vo . The phase mismatch then becomes
∆β Lo = 3π
V
Vo
(4.23)
It gives the ratio of optical power transfer or the coupling efficiency as
⎧ ⎡
2
⎛V
⎛π ⎞
2 ⎪1
ℑ = ⎜ ⎟ sin c ⎨ ⎢1 + 3⎜⎜
⎝2⎠
⎝ Vo
⎪⎩ 2 ⎢⎣
⎞
⎟⎟
⎠
2
⎤
⎥
⎥⎦
0.5
⎫
⎪
⎬
⎪⎭
(4.24)
The coupling power ratio as a function of voltage applied. A Mach-Zehnder
interferometer acts as an electro-optical switch and can be used to switch optical
signal to desired output with applying 0 volt or switching voltage. If 0 volt is applied,
the optical signal is coupled into another waveguide and if switching voltage, Vo , is
applied, the optical signal is coupled into the same waveguide.
4.6
Coupling Efficiency Control of 2x2 Optical Switch
64
It is noticed that the coupling efficiency of a 2x2 optical switch based MachZehnder interferometer depends on the voltage applied in the coupling region. To
design a 2x2 optical switch, several parameters need to be determined to produce an
optimum design. Parameters needed in designing an optimum optical switching is the
refractive index of the waveguide (n) , waveguide of optical signal (λo ) , separation
between waveguides in coupling region (d ) , and the length of electrode ( Lo ) . Figure
4.3 shows a design of 2x2 optical switch based Mach-Zehnder interferometer and the
related design parameter.
Equation 4.22 explains the relationship between the switching voltage, Vo and
other parameters such as d , Lo , λ o and n . It is noticed that d and λ o are directly
proportional to the change of Vo . While Lo and n are inversely proportional to the
change of Vo . In overall, the change of voltage applied and switching voltage, Vo give
change for the coupling efficiency.
The 2x2 optical switching based Mach-Zehnder interferometer is designed as
an integrated device with titanium diffused lithium material. The switching voltage
Vo normally is less than 10 volt and the speed of operation might greater than
10GHz.
Generally, a 2x2 optical switch based Mach-Zehnder interferometer is built
using optimum parameters to give full coupling. This means, when a optical signal
enters at Pin 2 , the optical signal is coupled into Pout 2 . This occurs due to the
overlapping of field from waveguides placed closed to each other and thus yields full
coupling process. External effect which is the electro-optic effect can be used to
control the coupling of optical signal. Switching voltage, V0 applied to the coupling
region of the 2x2 optical switch will cause no coupling occurs. This means, when
optical signal enters at Pin1 , the light will exit at Pout1 . If the optical signal enters at
Pin 2 , it then will exit at Pin 2 .
65
Effects of changing d , L0 , and λ 0 on the coupling efficiency of a 2x2 optical
switch is analyzed theoretically.
4.7
Analysis on Effect of Changing Separation Distance between Waveguides
(d)
When the separation distance between waveguides in the coupling region is
changed, the switching voltage needed also changes. This is because the change of
separation distance between waveguides d is directly proportional to the switching
voltage V0 . From equation 4.24, if the voltage applied, V , is same, then the coupling
efficiency will change due to the change of switching voltage. Table 5.3 shows the
needed switching voltage V0 when d is changed to a certain distance. Figure 5.4
shows that the coupling efficiency also changes due to the change of d .
This result is obtained using theoretical analysis from equation 4.24. From the
graph plotted shown in figure 4.3, it is noticed that for d = 24 µm , the coupling
efficiency is zero when 12volt is applied in the electrode region.
This means no coupling occurs when 12volt is applied since switching
voltage V0 is 12 volt calculated from equation 4.22. The other parameters are fixed
like electrode region length L0 = 10000µm , refractive index of waveguide
n = 2.1389 and wavelength of optical signal λ0 = 1300nm .
66
Table 4.3 Effect of changing separation distance, d
Separation
between
waveguides
dµm
Electrode
region length
L0 µm
Refractive
n index
Wavelength
λ0 (nm)
Switching
voltage
V0 (volt )
Voltage
Coupling
applied
efficiency
V (volt )
ζ
24
10000
2.1389
1300
12
12
0
34
10000
2.1389
1300
14.8125
12
0.1509
44
10000
2.1389
1300
17.625
12
0.3648
54
10000
2.1389
1300
20.4375
12
0.5274
64
10000
2.1389
1300
23.25
12
0.641
74
10000
2.1389
1300
26.0625
12
0.7203
84
10000
2.1389
1300
28.875
12
0.777
94
10000
2.1389
1300
31.6875
12
0.8185
104
10000
2.1389
1300
34.5
12
0.8497
114
10000
2.1389
1300
37.3125
12
0.8236
124
10000
2.1389
1300
40.125
12
0.8924
134
10000
2.1389
1300
42.9375
12
0.9072
144
10000
2.1389
1300
45.75
12
0.9193
154
10000
2.1389
1300
48.5625
12
0.9291
164
10000
2.1389
1300
51.375
12
0.9373
174
10000
2.1389
1300
54.1875
12
0.9442
184
10000
2.1389
1300
57
12
0.9499
194
10000
2.1389
1300
59.8125
12
0.9549
204
10000
2.1389
1300
62.625
12
0.9591
214
10000
2.1389
1300
65.4375
12
0.9628
224
10000
2.1389
1300
68.25
12
0.966
234
10000
2.1389
1300
71.0625
12
0.9688
67
Figure 4.4 Effect of changing separation distance, d, at V=12
4.8
Analysis on Effect of Changing Wavelength (λ0 )
Wavelength from 1300nm to 1700nm is analyzed in terms of their coupling
efficiency. From equation 4.22 and 4.25, it is noticed that the change of the
wavelength is directly proportional to the switching voltage, V0 .
In this theoretical analysis, the fixed parameters are separation distance
between waveguides d = 24 µm , length of electrode L = 10000 µm , refractive index of
waveguide n = 2.1389 and voltage applied to the electrode region V = 12 volt.
From the graph plotted in figure 4.4, we can that wavelength λ0 = 1300nm
needs 12 volt as its switching voltage. When 12 volt is applied on the coupling
region, no coupling occurs for this wavelength.
68
Table 4.4 Effects of changing wavelength, λ 0
Separation
between
waveguides
dµm
Electrode
region length
L0 µm
Refractive
n index
Wavelength
λ0 (nm)
Switching
Voltage
Coupling
voltage
applied
efficiency
V0 (volt )
V (volt )
ζ
24
10000
2.1389
1300
12
12
0
24
10000
2.1389
1320
12.1038
12
0.0003
24
10000
2.1389
1340
12.2076
12
0.0013
24
10000
2.1389
1360
12.3114
12
0.0028
24
10000
2.1389
1380
12.4152
12
0.005
24
10000
2.1389
1400
12.519
12
0.0077
24
10000
2.1389
1420
12.6228
12
0.0109
24
10000
2.1389
1440
12.7266
12
0.0146
24
10000
2.1389
1460
12.8304
12
0.0187
24
10000
2.1389
1480
12.9342
12
0.233
24
10000
2.1389
1500
13.038
12
0.0283
24
10000
2.1389
1520
13.1418
12
0.0337
24
10000
2.1389
1540
13.2456
12
0.0394
24
10000
2.1389
1560
13.3494
12
0.0454
24
10000
2.1389
1580
13.4532
12
0.0517
24
10000
2.1389
1600
13.557
12
0.0582
24
10000
2.1389
1620
13.6608
12
0.0651
24
10000
2.1389
1640
13.7646
12
0.0721
24
10000
2.1389
1660
13.8684
12
0.0793
24
10000
2.1389
1680
13.9722
12
24
10000
2.1389
1700
14.076
12
Figure 4.5 Effect of changing separation distance, λ 0 at V=12
0.0867
0.0943
69
4.9
Design 2x2 Optical Switch using Mach-Zehnder Interferometer
In this project, effect of changing parameters are analyzed through theoretical
analysis as mentioned above, such as changing separation distance between
waveguide, L0 . From the theoretical analysis, the optimum parameters of separation
distance between waveguides, wavelength used and length of electrode are
determined in designing an optimum2x2 optical switch which has coupling
efficiency of 100% when voltage is 0 volt and 0% when voltage applied is 12volt.
The separation distance between waveguides used is 24µm, wavelength used is
1300nm, and length of electrode is 10000µm.
Design of 2x2 optical switch based on Mach-Zehnder interferometer without
electrode region is shown in figure 4.8, with an electrode region, the coupling
behavior of a 2x2 optical switch can be controlled. The optimum parameter for the
design of a 2x2 optical switch based on Mach-Zehnder interferometer are obtained
by repeating simulations using different parameters. Comparisons of the design
parameters with the theoretical optimum parameters are also made. The design
parameters used to design a 2x2 optical switch based on Mach-Zehnder
interferometer is shown in table 4.5.
Table 4.5 Optimum design parameters for 2x2 Optical switch operating in
wavelength 1300nm
Parameter
Length of electrode,
L0
Value
10000µm
Wafer length
3300
Waveguide start width
8µm
Wafer width
100 µm
70
Refractive index of substrate
LiNbO3 , n 2
Refractive index of waveguide
1.47
Ti : LiNbO3 , n1
Separation between waveguide in coupling region,
2.1389
d
24µm
Cladding thickness
2µm
Substrate thickness
10 µm
4.9.1
First Design of Mach-Zehnder 2x2 optical switch
71
Figure 4.6 First Design a 2x2 optical switch of Mach-Zehnder interferometer
without electrode region
Figure 5.7 First Design a 2x2 optical switch of Mach-Zehnder interferometer
4.9.2
Second Design of Mach-Zehnder 2x2 Optical Switch
72
Figure 4.8 Design a 2x2 optical switch based on Mach-Zehnder interferometer
without electrode region
Figure 4.9 Design a 2x2 optical switch based on Mach-Zehnder interferometer with
electrode region
4.10
Configuration of BPM_CAD for Diffused Waveguide in BPM_CAD
73
There are many parameters which are necessary to be identified in order to
obtain satisfied simulation results. Identification of the simulation parameters in
designing 2x2 optical switch based on Mach-Zehnder interferometer are discussed in
this section. Table 4.6 shows the simulation parameters used in simulating the 2x2
optical switch designed. The identification of simulation parameters before
simulation is carried out.
Table 4.6 Simulation parameter for 2x2 optical switch
Parameter
Value
Starting field
Mode
Boundary
Simple TBC
Number of display
50
Wavelength
1300µm
Propagation step
2µm
Propagation direction
Y
Strip thickness before diffusion
0.05µm
Lateral diffusion length
DH
3.5µm
Lateral diffusion length
DV
4.2µm
Buffer layer
-Thickness =0.3µm
Electrode region properties
-Horizontal permittivity=4
-Vertical permittivity=4
-Refractive index=1.47
Electrode thickness=4µm
Electrode 1 = 50µm
Electrode width
Electrode 2 = 26µm
Electrode 3 = 50µm
Interelectrode gap
4.11
6µm
Simulation Results of First Design of Mach-Zehnder 2x2 Optical Switch
Zero Voltage
When voltage applied is 0 volt, full coupling occurs to the input optical
signal. The optical signal at the input Pin 1 is fully coupled into Pout 2 at the output.
The simulation results are shown in figure 4.10. But it has field about 10% at Pout1.
74
Figure 4.10 Simulation results of a 2x2 optical switch when V2 = 0 volt Optical
signal is fully coupled from Pin1 to Pout 2 .
75
Figure 4.11 Simulation results of a 2x2 optical switch when V2 = 0 volt
Optical field and effective refractive index at the output
4.11.1 Simulation Results of First Design of Mach-Zehnder 2x2 Optical Switch
with Switching Voltage
When voltage applied is the switching voltage, 12 volt, no coupling occurs to
the input optical signal. The optical signal at the input Pin1 is switched into Pout 1 at
76
the output. This is matched to theoretical analysis. The simulation results are shown
in figure 4.12.
Figure 4.12 simulation results of a 2x2 optical switch when V2 = 12 volt Optical
signal is fully coupled from Pin 1 to Pout 1 .
4.12
Simulation Results of 2x2 Optical Switch with Zero Voltage
When voltage applied is 0 volt, full coupling occurs to the input optical
signal. The optical signal at the input Pin 2 is fully coupled into Pout1 at the output. The
simulation results are shown in figure 4.13.
77
Figure 4.13 simulation results of a 2x2 optical switch when V2 = 0 volt Optical
signal is fully coupled from Pin 2 to Pout1 .
78
Figure 4.14 Simulation results of a 2x2 optical switch when V2 = 0 volt
Optical field and effective refractive index at the output
4.12.1 Simulation results of 2x2 Optical Switch with Switching Voltage
When voltage applied is the switching voltage, 12 volt, no coupling occurs to
the input optical signal. The optical signal at the input Pin 2 is switched into Pout 2 at
79
the output. This is matched to theoretical analysis. The simulation results are shown
in figure 5.22 .
Figure 4.15 Simulation results of a 2x2 optical switch when V2 = 12 Volt
Optical signal is switched from Pin 2 to Pout 2
80
Figure 4.16 Simulation results of a 2x2 optical switch when V2 = 12 Volt
Optical filed and effective refractive index at the output
CHAPTER 5
CONCLUSIONS AND RECOMMENDATION
5.1
Conclusions
An optimum 2x2 optical switch based on Mach-Zehnder interferometer was
successfully designed using BPM diffused waveguide in BPM_CAD for switching
optical signal with waveguide 1300nm. The coupling efficiency of the 2x2 optical
switch designed can be controlled by changing the voltage applied to the electrode
region. When no voltage is applied, the switch acts as a passive optical switch in
which the coupling efficiency is 100%. When switching voltage is applied to the
electrode region of the 2x2 optical switch, on coupling occurs where the optical
signal is switched to the same output waveguide. With this electro-optic effect, the
2x2 optical switch can act as an electro-optic switch to switch optical signal to
desired output port.
Figure 5.1 shows the next generation system architecture of fiber-to-the-home
(FTTH). In order to increase the bandwidth achievable of the system, wavelength
division multiplexing (WDM) is used to extend the wavelength usage. In order to
extend the coverage of the system, higher splitting ration will be used up to 1:2048,
for future work, I recommend development of WDM switch and higher splitting ratio
splitter should be emphasized.
82
Figure 5.1 Fiber-To-The-Home system architecture
83
REFERENCES
[1]
J.M senior(1992).”Optial Fiber Communicaton: Principle and Practice.”2nd
edition. U.K: Prentic Hall.
[2]
M.J adams (1981).”An introduction to Optical waveguides.
[3]
Jinguji, K., N. Takato, A. Sugita,and M. Kawachi,”Mach-zehnder
Interferometer, Type Optical Waveguide Coupler With Wavelenth-falttened
Coupling Ratio.”Electron.Lett., Vol.26, 1990, p.1326.
[4]
Schauweeker, B,:Arnold, M;przyrembel, G;kuhlow, B; Radehaus, C,;
“optical waveguide components with high refractive index difference in siliconoxynitride for application in integrated optopelectronice”, opt. Eng 41(1), p237-243
(2002 ).
[5]
Verbeek,
B.H.;Henry,
C.H.;Olsson,N
A.;Orlowsky,
K.J.
;Kazarinov,
R.F.;Johnson, B.H.: integrated four-channel Mach-zehnder multi/demultipexer
fabricated with phosphorous-doped SiO2 waveguides on Si “journal of light wave
Technology 6(6), p.1011-1015 (1988 ).
[6]
a
Chunling Zhou and Yuanyuan Yang, “Wide-Sense Nonblocking Multicast in
Class
of
Regular
Optical
WDM
Networks”,
IEEE
Transactions
On
Communactions, 50, No. 1, Jan., pp. 126-134(2002).
[7]
Chong Siew Kuang and Sahbudin Shaari, Member, IEEE Photonics
Technology Laboratory Institute of Micro Engineering and Nanoelectronics (IMEN)
Universiti Kebangsaan Malaysia (2004).
84
[8]
Q.Lai, W.Hunziker and H.Melchior, "Low-Power Compact 2x2 Thenno-optic
Silica- On Silica Waveguide Switch with Fast Response ", IEEE Photon. Technol.
Lett.,Vol. 10, No. 5, pp. 681, May 1998.
[9]
D.Personick, “Photonic switching: technology and applications and
applications. “IEEE Commun.Mag.,25(5),pp.5-8,1987.
[10]
Gerd Keiser(2000). “Optical Fiber Communication.” 3rd ed. USA:McGraw-
Hill.
[11]
Masanori Konshiba(1992). “ Optical Waveguide Analysis.” Japan:McGraw-
Hill, Inc.
85
APPENDICX A
BPM Diffused Waveguides
File formats
Data file formats
BPM_CAD used the next data format for saving the simulation results and reading
user defined and inde distributions
Real Data 2D File format: BCF2DPC
Real Data 3D File format: BCF3DPC
Real Data 2D File format: BCF2DC
Complex Data 3D File format: BCF3DC
User Refractive Index Distribution File format
Function Defined Waveguide Reference
Formulas in function Defined Waveguide
Formulas are specified using standard notation and precedence rules. The operation
in order of decreasing precedence are:
∗ / -- multiplication and division
+ - -- addition subtraction
Operations of equal precedence are evaluated from left to right. Parentheses may be
used to override precedence o to clarify.
See also:
Function Defined Waveguide layout command
Function Defined Waveguide layout dialog bo
Function Definition layout dialog bo
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Function in Function Defined Waveguide
The following functions for real argument x and integer argument m and n are
supported.
Sin(x)- sine
Cos(x)- cosine
Tan(x)-tangent
Cot(x)-cotangent
Sec(x)-secant
Csc(x)-cosecant
arcsin(x)-arc sine
arcos(x)-arc cosine
arctan(x)-arc tangent
Sinc(x)-sin(x)/
deg(x)-radians to degrees
rad(x)-degrees to radians
Hyperbolic function
Sinh(x)- Hyperbolic sine
Cosh(x)- Hyperbolic cosine
Tanh(x)- Hyperbolic tangent
Coth(x)- Hyperbolic cotangent
Sech(x)- Hyperbolic secant
Csch(x)- Hyperbolic cosecant
arcsinh(x)- arc Hyperbolic sine
arcsinh(x)-arc Hyperbolic sine
arccosh(x)-arc Hyperbolic cosine
arctanh(x)-arc Hyperbolic tangent
Exponential and Logarithmic Functions
exp(x)-exponent
Gauss(x:c)-Gaussion function centered at (x:c)
log(x)-logarithm in base 10
ln(x)-logarithm in based e
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lg(x,b)-logarithm in base b
Special Functions
besseljn(n,x)-bassel function Jn(x)
besseljn(n,x)-bassel function Yn(x)
besseljn(n,x)-modified Bassel function ln(x)
besseljn(n,x)-modidied bassel function Kn(x)
Jinc(x)-returns J1(x)/x
beta(x1,x2)-beta function of x1 and x2
erf(x)-error function erf(x)
gamma(x)-gamma function (x)
Orthogonal polynomials
hermite(n,x)-Hermite polynomial of order n
laguerre(n,x)-Laguerre polynomial of order n
legendre(n,x)-legendre polynomial of order n
tcheby(n,x)-Chebyshev polynomial of order n
Square and Square Root Functions
Sqr(x)-x*
Sqrt(x)-square root
Hypot(x,y)-hypotenuse, that is sqrt(x*x+y*y)
Sign and absolute value
Sign(x)-+1 or -1 according to the sign of
abs(x)-absolute value of x, that is, x
Integer part and fractional part
int(x)-integer part of
frc(x)-fractional part of
Floor(x)-nearest integer less than x
Ceiling(x)-nearest integer greater than x
Miscellaneous Functions
Gcd(a,b)-greatest common division
88
lcm(a,b)-largest common multiple between a and b
Fact(x)-factorial of x, that is, x!
Random(integer)-random number number between 0 and the integer argument
See also:
Function Defined Waveguide layout command
Function Defined Waveguide layout dialog bo
Function Defined Waveguide dialog bo