i
IMPLEMENTATION OF MMI STRUCTURE FOR OPTICAL DEVICE USING
POLYMER MATERIAL
FARAH WAHEEDA BINTI AHMAD WAHIDDIN
A project report submitted in partial fulfillment of the
requirements for the award of the degree of
Master of Engineering (Electrical – Electronic & Telecommunication)
FACULTY OF ELECTRICAL ENGINEERING
UNIVERSITI TEKNOLOGI MALAYSIA
NOV 2007
iii
To all my loving family members,
especially to my beloved PARENTS….
iv
ACKNOWLEDGEMENT
In the name of Allah, the Most Beneficent and Most Merciful.
First and foremost, I would like to extend my highest gratitude and thanks to
my supervisor, Assoc. Prof. Dr. Norazan bin Mohd Kassim for his support,
comments and advice throughout the duration of my project.
The thanks also go to all my friends for their constant kind help and moral
support despite the hectic semester that we had to undergo.
Last but not least, my deepest appreciation to my dearest parents and family
members, for all their support, love and care… your fully support and
encouragement is gratefully appreciated.
v
ABSTRACT
Multimode interference (MMI) devices have been extensively studied and are
of considerable interest as key optical components in photonic integrated circuit
(PIC). The principle of the MMI devices is based on destructive/constructive
interferences occurring in the MMI area with a large number of multimodes. Because
of its unique properties, such as low insertion loss, large optical bandwidth,
compactness, low crosstalk and excellent fabrication tolerances, the MMI devices
has many potential applications such as couplers, splitters, combiners, filters and
routers. Compared with silica, recently, polymeric material has lately attracted
considerable attention for various waveguide devices, such as optical switches and
variable optical attenuators, especially for its simple fabrication process.
vi
ABSTRAK
Peralatan Gangguan Pelbagai Mod (MMI) telah dipelajari secara meluas dan
dianggap sebagai komponen kunci/penting kepada litar fotonik (PIC). Pada
umumnya, peralatan MMI adalah berdasarkan pada gangguan pemusnah/pembina
yang berlaku di dalam kawasan MMI dengan jumlah nombor gangguan yang banyak.
Disebabkan ciri-ciri unik seperti kehilangan penyelitan yang rendah, jalur optik yang
besar, kepadatan, dan toleran pembuatan yang amat tinggi, peralatan MMI adalah
berpotensi dalam aplikasi seperti pasangan, penggabung, penapis dan juga
pembahagi. Berbanding dengan silika, sejak akhir-akhir ini, bahan polimer telah
menarik minat ramai untuk digunakan dalam pelbagai peralatan waveguide, seperti
suis optik dan atenuator optic boleh laras, terutama sekali kerana proses
pembuatannya yang mudah.
vii
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
LIST OF CONTENTS
vii
LIST OF TABLES
ix
LIST OF FIGURES
x
LIST OF SYMBOLS
xii
LIST OF ABBREAVIATIONS
xiii
LIST OF APPENDICES
xiv
1 INTRODUCTION
1.1 Introduction
1
1.2 Challenges in Optical Networking
3
1.3 Objectives
5
1.4 Scope of Works & Methodology
5
1.5 Outline of Thesis
5
viii
2 OPTICAL WAVEGUIDE
2.1 Introduction
7
2.2 Optical Planar Waveguide
10
2.3 Maxwell Equation
11
2.4 Vector-wave Equation
12
2.5 Scalar Wave Equation
13
2.6 Field Components for Planar OpticalWaveguide
14
2.7 Effective Index Method (EIM)
17
3 MULTIMODE INTERFERENCE (MMI)
3.1 Introduction
18
3.2 MMI Theory
20
3.3 Performance Parameter
22
4 POLYMER BASED MULTIMODE INTERFERENCE DEVICES
4.1 Introduction
24
4.2 Properties of Polymers & Comparison
26
5 CONCLUSION & FUTURE WORKS
5.1 Conclusion
29
5.2 Future Works
30
REFERENCES
31
APPENDICES A
33
ix
LIST OF TABLES
TABLE
Table 4.1
:
DESCRIPTION
PAGE
Properties of key oprtical material systems
25
at 1550nm wavelength
Table 4.2
:
Typical properties of waveguides in popular
27
materials used in integrated optics.
Table 4.3
:
Funtions achieved to date in different optical
material systems.
28
x
LIST OF FIGURES
FIGURE
DESCRIPTION
PAGE
Figure 1.1
:
Internal reflection in optical fibre
1
Figure 1.2
:
Fiber optic communication system
2
Figure 2.1
:
Integrated Photonic Element
8
Figure 2.2
:
Planar Optical Waveguide
10
Figure 2.3
:
Transverse Electric Field Distribution,
16
Ey(x), for the first three modes of three-layer
symmetric planar optical waveguide with
n1 = n3 = 3.4 , n2 = 3.5 , and = 1.3 m .
Figure 2.4
:
3D model and effective 2D model of a
17
directional coupler.
Figure 3.2
:
Schematic configuration of the MMI coupler
with a lateral index profile of the multimode
waveguide.
19
xi
FIGURE
Figure 3.3
:
DESCRIPTION
PAGE
Simulation results of the MMI coupler: the
19
beam propagation profile and the coupling
efficiency to both the in/output waveguides
along the propagation direction
(z = 0 to 6000 m).
Figure 3.4
:
Schematic Diagram of 1 x 1 MMI Device
20
Figure 4.1
:
Structure of BCB (a) and PFCB (b)
27
xii
LIST OF SYMBOLS
-
Propagation Constant
λ
-
Free Space Wavelength
c
-
Speed of Light in free space
E
-
Electric Field
H
-
Magnetic Field
nc
-
Cladding refractive index
nf
-
Core refractive index
ω
-
Angular frequency
n
-
Refractive index
tg
-
Thickness of the waveguide
-
Permitivity of material
-
Permitivity of free space
-
Conductivity of material
-
Free charge density
-
Electric or Magnetic field
xiii
LIST OF ABBREVIATIONS
PIC
-
Photonic Integrated Circuit
MMI
-
Multimode Interference
TE
-
Transverse Electric
TM
-
Transverse Magnetic
EIM
-
Effective Index Method
MZI
-
Mach-Zehnder interferometer
SiO2
-
Silica
SOS
-
Silica on Silicon
GaAs
-
Gallium Arsenide
BCB
-
Benzocyclobutene
xiv
LIST OF APPENDICES
APPENDIX
A
TITLE
-
MATLAB code for longitudinal propagation constants,
using Newton-Raphson method
1
CHAPTER 1
INTRODUCTION
1.1
INTRODUCTION
Fiber optics is a relatively new technology that uses rays of light to send
information over hair-thin fibers at blinding speeds. These fibers are used as an
alternative to conventional copper wire in a variety of applications such as those
associated with security, telecommunications, instrumentation and control, broadcast
or audio/visual systems.
Figure 1.1 : Internal reflection in optical fibre
2
Figure 1.2 : Fiber optic communication system
One major reason for considering optical signal processing is its bandwidth
(speed) advantage over electronic processors. With the increase in the transmission
speed in modern optical communication systems, the application of optical signal
processing in optical communication systems has been an active area of research.
As more communication capacity is demanded, more electronic components
are being exchanged for optical components and many research efforts are going into
integrating optical components into planar waveguide devices and photonic
integrated circuit (PICs). PIC provides optical circuits connecting optical
components such as optical filter, optical switches and optical amplifier.
In future, demand for application for PIC surely increase and also increased
need of reducing the size of PIC. Thus, design and fabrication of ultra compact
multimode interference (MMI) devices has gained more interests because of their
importance in PIC.
Multi-mode interference (MMI) devices have been extensively studied and
are of considerable interest as key optical components in photonic integrated circuits
(PICs). The principle of the MMI devices is based on destructive/constructive
interferences occurring in the MMI area with a large number of multi-modes.
Because of its unique properties, such as low insertion loss, large optical bandwidths,
compactness, polarization insensitivity, low crosstalk, and excellent fabrication
tolerances, the MMI device has many potential applications such as couplers,
3
splitters, combiners, mode converters, filters, and routers. They can also be easily
fabricated in more complex PICs such as ring lasers, optical modulators, MZI
(Mach-Zehnder interferometer) switches, dense wavelength multiplexers, and
wavelength converters.
1.2
CHALLENGES IN OPTICAL NETWORKING
The increase need for intercommunication have resulted in the intense
demand for broadband services in the Internet. Currently, ongoing research is being
carried out to introduce more intelligence system in the control plane of the optical
transport systems, which will make them more reliable, flexible, controllable and
open for traffic engineering.
In future, the critical challenges of optical networking may generally be
classified into the following areas (i) Access Networks (ii) Core network
architectures (iii) Integrated device and network research (iv) Network management
& control (v) Robust and Secure optical networking and (vi) Application-driven
optical networks.
(i)
Access Networks
Efficient grooming, cross-connect and switching architectures for the optical
Metro networks that can meet different (and time-varying) traffic granularity
and QoS needs of users should be studied.
(ii)
Core Network Architectures
One of the key issues in the design of core network architectures is how to
transport data across a wide area in a cost-effective manner.
4
(iii)
Integrated device and network research
It is evident that network architectures guide device and component
technology development and at the same time, device and component
capabilities
influence
network
design.
Tools
for
the
design,
modeling/simulation, and evaluation of optical devices, components and
networks are of particular importance.
(iv)
Network management & control
Rapid bandwidth provisioning is achievable in the next-generation optical
network architectures. However, further research is required to develop the
control software, physical layer modulation and signaling protocols, and
mechanisms for monitoring, measurement, and fault-isolation.
(v)
Robustness and security
With increasing line speeds, protection/restoration at the optical layer is
clearly more attractive than restoration at higher layers in the event of fiber
cuts and/or node failures. Efficient failure-resilient and survivable network
architectures and protocols that take into consideration the interactions
between multiple layers to achieve fast and guaranteed recovery without
incurring excessive overhead should be investigated.
(vi)
Application-driven optical networks
Both applications and optical networking technologies should be redesigned
and existing protocols constantly improved to optimize for TCP/IP which is
and will likely to remain the prevailing transport/routing protocols.
5
1.3
OBJECTIVES
The objective of this project is to understand the theory of Multimode
Interference (MMI) structure, to identify the significant MMI structure easier to build
using polymer material compared to silicon structure and also to do simulation on
data measured.
1.4
SCOPE OF WORKS
The scope of works includes understanding the theory and concept of
Multimode Interference (MMI) devices, the polymer-based MMI, advantages and
disadvantages and also to justify the measured data.
1.5
OUTLINE OF THE THESIS
The thesis comprises of 5 chapters and the overviews of the chapter are as
below:
CHAPTER 1 :
This chapter provides the introduction, objective and scope of
work involved in accomplishing the project.
CHAPTER 2 :
The second chapter represents the literature review and
explains the optical waveguide.
6
CHAPTER 3 :
The third chapter is the overview and explanation of the
multimode Interference.
CHAPTER 4 :
The fourth chapter focus more on the polymer based
multimode interference devices and also comparison with
other material.
CHAPTER 5 :
The fifth chapter concludes the thesis and suggestion for future
works.
7
CHAPTER 2
OPTICAL WAVEGUIDE
2.1
INTRODUCTION
The most important feature in integrated optics is the optical waveguide as
they are the transportation pathways for light-waves. Optical waveguides are the
basic structures used in the design of integrated optical devices such as directional
couplers, multimode interference devices and Mach-Zehnder interferometers.
All the optical components in integrated photonics are constructed with three
building blocks. They are the straight waveguide, the bend waveguide and the power
splitter. Using these building blocks, several basic components have been developed
to perform basic optical functions. Figure 2.1 shows some basic functions common
in many integrated optical devices.
In order to investigate and develop integrated optical circuits, a thorough
understanding of the principles of lightwave propagation is required. In its general
form, a waveguide consists of a core having a refractive index n1, and a cladding, or
substrate surrounding the core, having a refractive index n0. The light will remain
8
confined inside the core of the waveguide if the condition for internal reflection is
satisfied, explicitly if n1>n0.
Figure 2.1 : Integrated Photonic Elements
9
Figure 2.1 : Integrated Photonic Elements (cont.)
10
2.2
OPTICAL PLANAR WAVEGUIDE
The simplest form of optical waveguide is as shown Fig. (2-1). An
understanding of this structure is important, because it forms the basis for the study
of more complex wave guiding structures.
Figure 2.2 : Planar Optical Waveguide
The above figure shows a 3-layer planar optical waveguide consists of a
dielectric core material of refractive index n2 surrounded on the top and bottom by
dielectric cladding materials of refractive indices n1 and n3, where the refractive
indices of the cladding materials are less than that of the core material. It is common
in optics to set up the coordinate system so that the z-axis is in the direction of
propagation of the optical signal.
The core/cladding interfaces are in the y-z plane, and occur at x = 0 and x =
tg, where tg is the thickness of the waveguide, and is on the order of one wavelength.
The cladding layers extend to infinity as does the y dimension of the waveguide.
Although planar optical waveguides can be made in any number of layers greater
than or equal to three, this thesis will only look at three-layer waveguides and hence,
three layers should always be assumed.
11
2.3
MAXWELL EQUATION
The Maxwell’s equations is used to modeling the waveguide
∇⋅D=ρ
(Gauss’ Law)
(2.1a)
∇ x E = - µ ( H/ t)
(Faraday’s Law)
(2.1b)
∇⋅H=0
∇x H = J + ( D/ t)
(2.1c)
(Ampere’s Law)
(2.1d)
Boldface represents a vector quantity, and E, H, and D =
E represents the
electric field, magnetic field, and electric displacement, respectively.
is the
permittivity of the material, which is a constant for isotropic media and a tensor of
rank two for anisotropic media.
In the present analysis the material is assumed to be non-magnetic, which
means that the permeability of the material is equal to the permeability of free-space,
or
=
o
.
density, where
is the free charge density, t is time, and J =
is the conductivity of the material.
E is the free current
12
2.4
VECTOR WAVE EQUATION
Applying the vector identity as follows
(2.2)
In to equations (2.1b,d) will produce
(2.3)
(2.3a)
Inserting equation (2-1d) into (2-3a), and (2-1b) into (2-3b) produces
(2.4a)
(2.4b)
Equations (2.4a,b) are the general electromagnetic wave equations. Assuming the
isotropic media with no free charge ( = 0) equations (2.4a,b) will become
(2.5)
where
represents either the electric or magnetic field. For a non-conducting
medium ( = 0) equation (2.5) reduces to
(2.6)
13
Equation (2.6) is the standard form of the wave equation for isotropic dielectric
media. The general solution to equation (2.6) for a monochromatic traveling wave
propagating in the z direction is
(2.7)
where i = −1 ,
is the propagation constant, and
=2
, where
is the optical
frequency. The velocity of the wave is given by
(2-8)
where c =
is the speed of light, is the free-space wavelength,
0
is the permittivity
of free-space, and n = √ r is defined as the refractive index of the medium.
2.5
SCALAR WAVE EQUATION
Inserting a scalar field with a harmonic time dependence
(2.9)
into the wave equation (2.6) and using the equality
(2.10)
14
where k = 2
is the free-space wave-number, yields
(2.11)
Equation (2.11) is Helmholtz equation or the time-independent scalar wave equation,
and is used to model the spatial dependence of the fields in optical waveguides.
2.6
FIELD COMPONENTS FOR PLANAR OPTICAL WAVEGUIDE
Analysis of planar optical waveguides requires the solution of the scalar wave
equation (2.11) and the application of boundary conditions in order to obtain the
eigenmodes for the given waveguide indices and thickness at a particular
wavelength. However, before obtaining this solution it is convenient to examine the
field components associated with the given modes.
This is accomplished by expanding the general solutions for the electric and
magnetic fields given in equation (2-7), where the z-dependence is assumed to be
contained entirely in the exponent due to the constant geometry of the waveguide in
the propagation direction.
(2-12a)
(2-12b)
Inserting equations (2-13a,b) into Faraday’s equation (2-1b) yields
15
(2-13)
Since the waveguide geometry is constant in the y direction, / y = 0 in equation (213). Equating the field components yields the following set of equations
(2-14a)
(2-14b)
(2-14c)
Inserting equations (2-14a,b) into the generalized form of Ampére’s equation (2-1d)
yields
(2-15)
Taking / y = 0 and equating the field components yields the following set of
equations
(2-16a)
(2-16b)
(2-16c)
16
reviewing of equations (2-15a,b,c) and (2-17a,b,c) it is evident that the field
components Ey, Hx, Hz are independent of the field components Ex, Ez, Hy. These two
situations refer to transverse electric (TE) modes, and transverse magnetic (TM)
modes, respectively, meaning that there is no component of the associated field in the
direction of propagation. It is also important to note that for the TE case there is only
one transverse electric field component, Ey, and for the TM case there is only one
transverse Magnetic field component, Hy.
Figure 2.3 : Transverse Electric Field Distribution, Ey(x), for the first three modes of
three-layer symmetric planar optical waveguide with n1 = n3 = 3.4 , n2 = 3.5 , and
= 1.3 m .
17
2.7
EFFECTIVE INDEX METHOD
In order to avoid the use of numerical analysis, various methods have been
developed to approximate the effective indices of this type of waveguide structure.
The simplest and most popular of these is the effective index method, which provides
reasonably accurate results.
Effective index method (EIM) is widely and successfully used in designs and
simulations of planar lightwave circuits (PLCs) for it can convert the original threedimension (3D) channel waveguides into effective two-dimension (2D) planar
waveguides. With EIM one can carry out design and simulation works, e.g., using
the beam propagation method (BPM) with the obtained effective 2D planar
waveguides.
This saves significant computation time. Several EIMs were recently
proposed to improve the accuracy .Most of these methods showed a satisfactory
accuracy for a single waveguide when V (normalized frequency of the waveguide) is
relatively large, which means a multimode waveguide. However, single mode
waveguides are mainly involved in practical PLCs.
Figure 2.4 : 3D model and effective 2D model of a directional coupler.
18
CHAPTER 3
MULTIMODE INTERFERENCE (MMI)
3.1
INTRODUCTION
The self-imaging phenomenon is a property of multimode waveguides by
which an input field profile is reproduced in single or multiple images at periodic
intervals along the propagation direction of the waveguide.
The multimode waveguide of the MMI coupler typically supports more than
three guided-modes, and access waveguides as the in/output waveguides are placed
at the beginning and the end of the multimode waveguide. Fig. 3.2 shows the
structure of the MMI coupler and the lateral index profile of the multimode
waveguide.
19
Figure 3.2 - Schematic configuration of the MMI coupler with a
lateral index profile of the multimode waveguide.
.
Figure 3.3 - Simulation results of the MMI coupler: the beam propagation profile and
the coupling efficiency to both the in/output waveguides along the propagation
direction (z = 0 to 6000 m).
20
3.2
MMI THEORY
The simple 1x1 rectangular shape MMI device is as shown in Figure 3.4. The
MMI device generally consists of three parts: input ports (or left ports), a MMI area
output ports (or right ports). The typical, practical MMI device is usually an M-inputand-N-output device with tapered functions. There are three kinds of MMI devices,
which allow different interferences.
Figure 3.4 – Schematic Diagram of 1 x 1 MMI Device
Here the guided-mode propagation method, one of the analytical methods, is
used to illustrate the self-imaging effect in the MMI device. In this approach, the
propagation constants βi (βi= 0, 1, 2, 3, …, N, where N is the number of guided
modes) of multi-modes in the MMI area are given in the paraxial approximation by:
(3-1)
where Lπ is defined as the beat length (or coupling length) between the fundamental
mode (i=0) and the first-order mode (i=1):
21
(3-2)
where λ is the free-space wavelength and We is the effective width of the MMI area:
(3-3)
where W is the physical width of the MMI area, nr and nc are the effective core index
and effective cladding index, respectively; and integer σ=0 for TE modes and σ=1
for TM modes.
According to the guided-mode propagation analysis, three different selfimage phenomena can be observed:
(i) 1xN symmetrical self-imaging: The coefficients of odd modes are zero when the
MMI area is fed by a single central port (D=0). According to Eq.(3-1), the self
imaging distance and N-fold image distance are ¾Lπ and ¾ Lπ/N.
(ii) 2xN restricted self-imaging: The coefficients of 2nd, 5th, 8th, etc is zero when
the MMI area is fed by one or two input ports at D=±We/6. According to Eq.(3-1),
the self-imaging distance, the mirror image distance, and N-fold image distance are
2Lπ, Lπ , and Lπ/N, respectively.
(iii) MxN general self-imaging: The coefficients of modes are non-zero when the
MMI area is fed by one or M input ports at the arbitrary position (-W/2<D<W/2).
According to Eq.(3-1), the self-imaging distance, the mirror image distance, and
Nfold image distance are 6Lπ , 3Lπ , and 3Lπ/N, respectively.
22
Therefore, the input field profile can be reproduced in single or multiple
images at periodic intervals along the propagation direction of the guide. As can be
seen in the above discussion, for the same width or beat length, the MMI device
based on symmetrical self-imaging is four times shorter than one based on general
self-imaging, and the MMI device based on restricted self-imaging is three time
shorter than one based on general self-imaging.
3.3
PERFORMANCE PARAMETERS
This section will discuss performance parameters more specifically related to
MMI-based devices. The excess loss Le (dB) of the device is defined by the
difference between the sum of the powers exciting the outputs and the power
entering the devices:
(3-4)
As a coupler, two performance parameters, the crosstalk and power
imbalance, should be evaluated. The crosstalk Lc (dB) is a ratio of the desired power
output (Pd) to unwanted outputs (Pu) and the power imbalance Lb (dB) is a ratio
between two the desired outputs.
(3-5)
(3-6)
where the crosstalk and the power imbalance of the coupler is also evaluated by the
extinction ratio (or contrast) and the coupling ratio, respectively.
23
One of the most critical issues in designing MMI devices is the design
tolerance, including width tolerance δW/W, length tolerance δL/L, and wavelength
tolerance δλ/λ, which are given by as:
(3-7)
where the width tolerance δW/W is calculated by:
(3-8)
where d is the mode width of the input port and Z(Le ) is a function depending on the
excess Le, which is expressed as:
(3-9)
where Le (dB) = −10log10 T. Fabrication tolerances such as the device width
variations δW/W are inversely proportional to the coupler length L. For the restricted
2x2 MMI 3dB coupler on InP (index n = 3.44) at 1.55 µm, where length L = Lπ / 2 ,
if W=12, d=3m, and the length L= 213 µm, the result is δW=0.08µm, δL=2.89 µm,
and δλ= 2.1 nm for 0.5 dB excess loss. Obviously, the wavelength tolerance δW
represents the most critical value. Note that tapered input and output ports of the
MMI devices relax the wavelength tolerance.
24
CHAPTER 4
POLYMER BASED MULTIMODE INTERFERENCE (MMI) DEVICES
4.1
INTRODUCTION
Recently, polymer waveguides has potentially a relatively low cost
alternative to electronics in communication systems. Polymers offer relatively simple
and economical fabrication when compared to conventional materials. Indium
Phosphide (InP) based waveguides are often a popular choice in the design and
production of integrated dielectric waveguides (DWG). However, the processing
involved is highly complex and the materials are exceptionally expensive.
Among other, the one that attract a lot of attention is the class of polymers.
Numerous polymer based waveguide devices have been made in the past, and great
progress is being made to develop waveguides suitable for communication and
sensing purposes. For communications wavelengths near 1550nm polymer
waveguides are attractive because they are relatively simple to process, cost effective
and demonstrate low optical loss.
25
Apart from this they offer a possibility to fabricate dense integrated circuits,
suitable for present requirements. There is a possibility of achieving high contrast
index, which makes the device smaller and reduces the bending losses.
Table 4.1 : Properties of key oprtical material systems at 1550nm wavelength
The table above shows the main properties of key material used in optical
communication. Taking example of silica (SiO2) fiber technology, it is the most
established optical guided-wave technology. The silica commonly used to produce
device such as lasers, amplifiers, couplers, filters, switches and attenuators. The
silica on silicon (SOS) technology is the most widely used planar technology. The
growth processes for SOS is lengthy that may take up a a few up to several days.
Because of that, the high level of stress due to deposited layers result in
misalignment between the waveguide.
Polymer however can use fast turn-around spin-and-expose technique. These
materials have an obvious advantage in turnaround time, producing between 10 and
1000 times faster than other planar technologies. Furthermore, this technology uses
low-cost material and low-cost processing equipments.
26
4.2
PROPERTIES OF POLYMERS AND COMPARISON
Polymers give the possibility to design materials with specific characteristics
for specific applications. In principle it is possible to achieve low optical loss (near
infrared), high thermal and environmental stability, high electro optic or thermo optic
effects, low thermal conductivity, good linkage to metals and silica, and refractive
index tailoring.
However, it is difficult to combine all these characteristics in a single
polymer and usually chemists and designers of integrated optical devices need to
work close together. As a result optical polymers are usually not commercially
available but restricted to small groups of researchers associated with certain
manufacturers.
Polymers which are commercially available are not specifically designed for
integrated optics. Some of them like PFCB, BCB display very desirable material
__
characteristics. Usage of these materials offers advantages like availability in large
quantities and guaranteed quality. As these materials are not designed for integrated
optics no core cladding refractive index combinations are available to realize weak
guiding waveguides. Optical polymers can be highly transparent, with absorption
loss around or below 0.1dB/cm at all key communication wavelengths (840nm,
1310nm and 1550nm). The polymers technology also can be designed to form stressfree layers regardless of the substrate and can be essentially free of polarization
dependence.
Despite their excellent properties these polymers have two major drawbacks.
First the relatively high losses of BCB at λ = 1550µm and second is the birefringence
due to the high glass temperature of both materials and the thermal curing. This
birefringence is also the reason to focus on digital optical devices which do not
depend on interferometric effects to avoid polarization dependence.
27
Then figure below shows the example structure of BCB and PFCB and table
4.2 presents the typical properties of waveguides in some of materials.
Figure 4.1 : Structure of BCB (a) and PFCB (b)
Table 4.2 : Typical properties of waveguides in popular materials used in integrated
optics.
Gallium arsenide (GaAs) is another semiconductor material that can be used
to fabricate both active and passive optical devices but in reality the uses is quite
limited because of manufacturability and very costly. It is however lest costly than
InP.
28
Table 4.3 : Funtions achieved to date in different optical material systems.
The table above represents the function for different materials that have been
achieved to date. Apparently, polymer material has become recent attraction. Mainly,
it is due to its more advantages despite of its drawback for optical device. Silicon has
been preferable for almost a few decade, however, polymer has become in more
favour in manufacturing of optical devices. The previous explanation has described
the superior quality of polymer for the devices.
29
CHAPTER 5
CONCLUSION & FUTURE WORKS
5.1
CONCLUSION
The aim of this project is to understand the multimode interference for optical
devices, and to study the significant advantages of the polymer material. The data
measured are to be simulated and justified. The introduction of the optical
networking and the outline of the thesis are briefly elaborated in chapter 1.
The details explanation of the optical waveguide is elaborated in Chapter 2. In
that chapter, explained the numerical method in achieving the mathematical model. It
is derived based on Maxwell Equations. Then, the planar waveguide wave equation
is solved. Hence, the number of modes can be determined and electrical field shall be
described.
The multimode interference (MMI) theory is elaborated in chapter 3. The
parameters’ and property for MMI device are discussed and described further. From
that explanation and justification, thus in chapter 4 the polymer based MMI devices
are describe in detail. By comparison with other material, it shows most of the
30
positive and significant advantages using polymer-based optical devices. Here, we
can see what polymer is in beneficial despite a few drawbacks.
The comparison which has explained in that chapter shows characteristic of
different materials for optical devices. From the given measured value, it shows that
polymer-based optical devices having better future in market. In general, the lowcost and ease of fabrication material on the other hand gives the outstanding
performance are definitely will be the choice to be fabricated for optical devices.
5.2
FUTURE WORKS
To do simulation on MMI devices for the different applications such as
splitter, combiner, multiplexer and filter.
31
REFERENCES
Andrew W Molloy “Adiabatic Coarse Wavelength De/Multiplexing for
Optical Systems, October 2004
Apollo Photonics, Multi-Mode Interference (MMI) Devices – Design, Simulation
and Layout, Issued date 2003
D.A.May-Arrioya, N. Bickel and P.Likamwa – Robust 2 X 2 Multimode interference
Optical Switch, Nov 2005
David C. Hutchings and John M. Arnold, University of Glasgow, Institute of
Physics, Fall 2004
Dominic F.G. Gallangher, Thomas P. Felici, Eigenmode Expansion Methods for
Simulation of Optical Propagation in Photonics, Photon design, Oxford
James J. Licari, Coating Materials for Electronic Application, 1999
Jong-Moo Lee, Joon Tae Ahn, Doo Hee Cho, Jung Jin Ju, Myung-Hyun Lee, and
Kyong Hon Kim, Vertical Coupling of Polymer Double-Layered Waveguides Using
a Stepped MMI Coupler, ETRI Journal, Volume 25, No.2, April 2003
Journal of Lightwave Technology “Optical Bandwidth and Fabrication Tolerances
of Multimode Interference Couplers”, 1994
32
Juerg Leuthold and Charles H. Joyner –Multimode Interference Couplers
Katsunari Okamoto, Fundamental of Optical Waveguide, Elsevier, 2006 Louise
Peterson Vassy, Optimization of Device Performance in 1x2 Symmetric Interference
Multimode Interference Devices, University of Cincinnati , May 2003
Louay Eldada, Optical Networking Components, Dupont Photonics Technologies
Ma Huilian, Yang Jianyi, Jiang Xiaoqing, Wang Minghua, Dept. of Information
Science and Electronics Engineers, Zhejiang University, Hangzhou, China “Compact
and Economical MMI Optical Power Splitter for Optical Communication”
Michael Fowler, Physics Department, UVa “Maxwell’s Equations and
Electromagnetic Waves”
Mohd Haniff Ibrahim, Norazan Mohd Kassim, Abu Bakar Mohammad & Mee-Koy
Chin, Design of Multimode Interference Optical Splitter Based on
BenzoCyclobutene (BCB 4024-40) Polymer, Regional Postgraduate Conference on
Engineering and Science, July 2006
Muhammad Taher, King Fahd University of Petroleum and Minerals “Large Signal
Analysis of the Mach-Zehnder Modulator with Variable BIAS”, Sept 2000
Optical Engineering – Society of Photo-Optical Instrumentation Engineers, March
2002
R. Hanfoug, L. M. Augustin, Y. Barbarin, J.J.G.M. van der Tol, E.A.J.M
Bente, F.Karouta, D. Rogers, Y.S. Oei, X.J.M. Leijtens and M.K. Smit “A
Multimode Interference Coupler With Low Reflections
Ralf Hauffe, Integrated Optical Switching Matrices Constructed from Digital Optical
Switches Based on Polymeric Rib Waveguides, May 2002
33
Appendix A
MATLAB Source code for longitudinal constant,
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Input:
%%%% nf,nc - Core and cladding effective indices,
respetively
%%%% lambda - Free space of light wavelength
%%%% w_mmi - Full width of multimode waveguide
%%%% w_sm - Full width of input waveguide
%%%%
%%%% Output:
%%%% BetaGuideS - Longitudinal propagation
%%%% constants of the symmetric guided modes of the
multimode
%%%% waveguide
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [BetaGuideS,BetaSM] =
GuidedModeSolve(nf,nc,lambda,w_sm,w_mmi)
while 1
clear, clf, clc
fprintf ('\n***************************************\n');
fprintf ('\n******CALCULATION OF GUIDED MODES******\n');
fprintf ('\n***************************************\n');
fprintf ('\nKey-in the followings values:-\n');
34
fprintf ('\n\n');
%%%%%%%%Input Waveguide Guided Mode%%%%%%%%%%%%%%%%
nf=input('Value of core refractive index, nf = ');
nc=input('Value of cladding refractive index, nc = ');
lambda=input('Value of Lambda (um) = ');
w_mmi1=input('Value of w_mmi (um) = ');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
um=1e-6;
lambda1=lambda*um;
w_mmi=w_mmi1*um;
k0=(2*pi)/lambda1;
k1=k0.*nf;
k2=nc.*k0;
Beta = real(k2):real((k1-k2))/1e5:real(k1);
Gamma = sqrt(k1^2 - Beta.^2);
Alpha = sqrt(Beta.^2 - k2^2);
%%%%%%Begin Newton-Raphson Method%%%%%%%%%%%%%%%%%
F=((Gamma./Alpha).*tan(Gamma.*(w_mmi/2))) - 1;
guess=[];
guess_count=1;
%%%%%%%%%%%%%%Look for change in sign of F(rough
estimate)%%%%
for counter = 1:length(Beta)-1
if(and(sign(F(counter))>sign(F(counter+1)),isfinite(F(cou
nter))==1))
35
guess(guess_count,1) = counter;
guess(guess_count,2) = Beta(counter);
guess(guess_count,3) = Beta(counter+1);
guess(guess_count,4) = F(counter);
guess_count = guess_count+1;
end
end
clear Beta;
clear Gamma;
clear Alpha;
clear F;
p_save = [];
%%%%%%%%%%%%Refine rough estimates%%%%%%%%%%%%%%%%%
for counter = 1:guess_count-1
p0 = guess(counter,2);
p1 = guess(counter,3);
for iter = 1:30
Gamma = sqrt(k1^2 - p0^2);
Alpha = sqrt(p0^2 - k2^2);
F = ((Gamma./Alpha).*tan(Gamma.*(w_mmi/2))) - 1;
Gamma1 = sqrt(k1^2 - p1^2);
Alpha1 = sqrt(p1^2 - k2^2);
F1 = ((Gamma1./Alpha1).*tan(Gamma1.*(w_mmi/2))) 1;
if (p1 == p0)
p_save(counter) = p0;
break;
36
end
F_prime = (F1 - F)/(p1 - p0);
p = p0 - (F/F_prime);
p1 = p0;
p0 = p;
end
end
BetaSM = p_save(length(p_save));
clear Beta;
clear Gamma;
clear Alpha;
clear F;
clear p0;
clear p1;
clear p;
clear p_save;
%%%%%%%%%%%%%End of Newton_Raphson Method%%%%%%%%%%%
%%%%%%%%%%%%%%%%%Symmetric Mode(s)%%%%%%%%%%%%%%
k0 = (2*pi)/lambda1;
k1 = k0.*nf;
k2 = nc.*k0;
Beta = k2:(k1 - k2)/1e5:k1;
Gamma = sqrt(k1^2 - Beta.^2);
Alpha = sqrt(Beta.^2 - k2^2);
F = ((Gamma./Alpha).*tan(Gamma.*(w_mmi/2))) - 1;
37
guess=[];
guess_count = 1;
for counter = 1:length(Beta)-1
if(and(sign(F(counter)) >
sign(F(counter+1)),isfinite(F(counter)) == 1))
guess(guess_count,1) = counter;
guess(guess_count,2) = Beta(counter);
guess(guess_count,3) = Beta(counter+1);
guess(guess_count,4) = F(counter);
guess_count = guess_count+1;
end
end
clear Beta;
clear Gamma;
clear Alpha;
clear F;
p_save1 = [];
for counter = 1:guess_count-1
p0 = guess(counter,2);
p1 = guess(counter,3);
for iter = 1:20
Gamma = sqrt(k1^2 - p0^2);
Alpha = sqrt(p0^2 - k2^2);
F = ((Gamma./Alpha).*tan(Gamma.*(w_mmi/2))) - 1;
Gamma1 = sqrt(k1^2 - p1^2);
Alpha1 = sqrt(p1^2 - k2^2);
F1 = ((Gamma1./Alpha1).*tan(Gamma1.*(w_mmi/2))) 1;
38
if (p1 == p0)
p_save1(counter) = p0;
break;
end
F_prime = (F1 - F)/(p1 - p0);
p = p0 - (F/F_prime);
p1 = p0;
p0 = p;
end
end
BetaGuideS0 = p_save1;
clear Beta;
clear Gamma;
clear Alpha;
clear F;
clear p0;
clear p1;
clear p;
clear p_save1;
clear Beta;
clear Gamma;
clear Alpha;
clear F;
p_save = [];
for counter = 1:guess_count-1
p0 = guess(counter,2);
39
p1 = guess(counter,3);
for iter = 1:20
Gamma = sqrt(k1^2 - p0^2);
Alpha = sqrt(p0^2 - k2^2);
F = ((Gamma./Alpha).*tan(Gamma.*(w_mmi/2))) - ((1
+ exp(Alpha.*(w_mmi - w_box)))./(1 - exp(Alpha.*(w_mmi w_box))));
Gamma1 = sqrt(k1^2 - p1^2);
Alpha1 = sqrt(p1^2 - k2^2);
F1 = ((Gamma1./Alpha1).*tan(Gamma1.*(w_mmi/2))) ((1 + exp(Alpha1.*(w_mmi - w_box)))./(1 exp(Alpha1.*(w_mmi - w_box))));
if (p1 == p0)
p_save(counter) = p0;
break;
end
F_prime = (F1 - F)/(p1 - p0);
p = p0 - (F/F_prime);
p1 = p0;
p0 = p;
end
end
BetaGuideS = p_save;
clear Beta;
clear Gamma;
clear Alpha;
clear F;
40
clear p0;
clear p1;
clear p;
clear p_save;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fprintf ('\n===============RESULTS=================\n');
fprintf ('\nThe values of BetaGuideS = %6.6,BetaGuideS);
BetaGuideS = fliplr(unique((nonzeros(BetaGuideS))'));
fprintf
('\n******************************************\n');
fprintf ('\n\n');
cont1 = input('Type 1 to continue, or 0 to stop.');
if cont1 == 0, return;