OPTICAL Y-JUNCTION POWER SPLITTER
ALIYA ASHRAF
UNIVERSITI TEKNOLOGI MALAYSIA
To my beloved family and friends.
.."Only those who dare to fail greatly, can ever achieve success greatly."
iii
ACKNOWLEDGEMENT
First and foremost, I thank God the Almighty for giving me strength to finish this
thesis. I wish to express my sincere appreciation to my supervisor, Dr. Abu Sahmah bin
Mohd Supa’at for encouragement, guidance, critics and friendship. His mentorship style,
guiding rather than leading, has allowed me to strengthen my intellectual wings and
tackle problems on my own. When I needed it,he was always ready with a helpful
suggestion as well as explanations. I am very thankful to my family members for all
their support and love even though they were not around. I am also very grateful for the
encouragement provided by my friends who have provided assistance and support at
various occasions.
iv
ABSTRACT
In terms of performance, communication by optical fiber is potentially the most
rewarding of all communications. It has been suggested that if the full potential of fiber
optic communication is realized, a single fiber would be sufficient to serve the needs of
telecommunication users (heavy data traffic demands) throughout the world. Fiber optics
is the channeled transmission of light through hair thin glass. The explosive growth of
optical networks has brought forward an increased need for guided wave optical
components for the sake of multiplexing and routing. Beam splitters are a basic element
of many optical fiber communication systems often providing a Y-junction by which
signals separate sources can be combined, or the received power divided between two
channels. The purpose of this project is to investigate how an asymmetric Y-junction
behaves as a power splitter using switching function called Thermo Optic Effect. The
focus is made on the polymers used for making various layers of waveguide, geometry
and design parameters of waveguide which make it better than other Y-splitters.
Polymers are relatively cheap starting material and can be processed from solution,
which offers additional potential for cost savings compared to other technologies and
also have the advantage of having large thermo optic coefficient range. The polymers
used are polyurethane (thermal coefficient: -3.3 x 10-4 K-1, thermal conductivity: -0.19
W m-1K-1) and PMMA (thermal coefficient: -1.2 x 10-4 K-1, thermal conductivity: -0.17
W m-1K-1). The 2D thermal analysis is made on buried type waveguide. The analysis is
based on how heating of one of the arms change its refractive index leading to low
crosstalk, insertion loss, low driving power, coupling length and optimum switching
characteristics. All simulations are done using BPM (Beam Propagation Method) and
FEMLAB (Finite Element Method) software. The results from this project is a structure
of Y-junction Power Splitter which is compact in size, less power consumption, low
crosstalk and insertion loss by varying various parameters like branching angle, spacing
between the two arms of Y-junction, refractive index change of one of the arms by
means of heating phenomenon and switching temperature.
v
ABSTRAK
Dari segi prestasi, komunikasi melalui fiber optik berpotensi memberikan ganjaran yang
paling memuaskan untuk semua komunikasi. Cadangan pernah diutarakan sekiranya
potensi fiber optik direalisasikan sepenuhnya, satu fiber mungkin sudah cukup untuk
menampung keperluan pengguna telekomunikasi (permintaan trafik terhadap data yang
padat) ke seluruh dunia. Fiber optik adalah saluran yang menghantar cahaya melalui
kaca yang nipis. Ledakan pembangunan rangkaian fiber telah membawa kepada
peningkatan terhadap penggunaan komponen optikal gelombang terpandu untuk
permultipleks dan laluan (routing). Pecahan cahaya adalah elemen asas dalam
kebanyakan sistem komunikasi fiber optik yang menjadikan penghubung-Y boleh
berfungsi menyatukan isyarat yang datang dari sumber yang berasingan atau berupaya
membahagikan kuasa yang diterima antara dua saluran. Tujuan projek ini adalah untuk
mengkaji bagaimana penghubung-Y bertindak sebagai pecahan kuasa dengan
menggunakan fungsi pensuisan yang dikenali sebagai Kesan Kepanasan Optik.
Penekanan diberikan kepada penggunaan polimer dalam penghasilan kepelbagaian
lapisan gelombang pandu, serta geometri dan parameter rekabentuk gelombang pandu
yang mana menjadikan ia lebih baik berbanding penghubung-Y yang lain. Polimer
merupakan material pengasas yang murah, yang mana berpotensi dalam penjimatan kos
berbanding teknologi yang lain, dan juga memberikan kelebihan dengan mempunyai had
pekali kepanasan optic yang besar. Polimer yang digunakan adalah poliureten (pekali
kepanasan: -3.3 x 10-4 K-1, kealiran kepanasan: -0.19 W m-1K-1) dan PMMA (pekali
kepanasan: -1.2 x 10-4 K-1, kealiran kepanasan: -0.17 W m-1K-1). Analisis kepanasan 2D
akan dilaksanakan ke atas gelombang pandu yang tersembunyi. Analisis ini dibuat
berdasarkan kepada bagaimana pemanasan pada satu lengan mengubah indeks
pembiasan yang kemudiannya membawa kepada perbicaraan bersilang yang rendah,
kehilangan penyisipan yang rendah, kuasa terpandu yang rendah, panjang perangkai dan
ciri-ciri pensuisan optimum. Semua simulasi dilakukan menggunanakan perisian BPM
(kaedah penyebaran cahaya) and FEMLAB (Keadah Elemen Terhad ).
vi
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE NO
TITLE PAGE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF FIGURES
xi
LIST OF TABLES
xv
LIST OF SYMBOLS
xvi
INTRODUCTION
1
1.1 Objective of this Project
1
1.2 Scope of this Project
3
1.3 Problem Statement
4
1.4 Project Background
5
vii
2
3
4
1.5 Overview of this Project
8
OPTICAL WAVEGUIDES
9
2.1 Optical Fiber transmission
9
2.1.1 Ray Theory
10
2.1.2 Electromagnetic Mode theory
14
2.1.3 Maxwell Equations
14
2.2 Optical waveguide structure
17
2.3 Polymer Waveguides
19
2.3.1 Material Thermal Propagation
20
ASYMMETRIC Y-JUNCTION POWER
SPLITTER
22
3.1 Integrated Optics
22
3.2 Literature Review
24
3.3 Operational Principle
26
3.3.1 Geometry of Y-junction
31
MODELING AND DESIGN OF
WAVEGUIDE
33
4.1 Numerical methods
33
4.1.1 Finite Difference Method
4.1.1.1 Crank Nicolson Method
4.1.2 Finite Element Method
34
36
37
viii
5
4.2 Heat Transfer Equation
40
4.3 Simulation Guide
42
4.3.1 Setting up the model
42
4.3.2 Options and settings
44
4.3.3 Draw Mode
45
4.3.4 Boundary Mode
46
4.3.5 Sub Domain Mode
48
4.3.6 Mesh Mode
49
RESULTS AND DISCUSSION
51
5.1 Project Methodology
51
5.2 Propagation of light through device
54
5.2.1 Light through parallel arms
54
5.2.2 Light through the S-bends
56
5.3 Electric field generated
58
5.4 Thermal Distribution
62
5.5 Optimum Configuration of Y-junction
66
5.5.1 Mode Conversion factor and
Refractive index
66
5.5.2 Crosstalk and Mode Conversion
Factor
68
5.5.3 Attenuation in S-bend and
Heating power
69
ix
5.5.4 Crosstalk and Heating
Power(Coupling Efficiency)
6
70
FUTURE WORK AND CONCLUSION
71
6.1 Thermal Analysis Model
71
6.2 Thermal Coupling Model
72
6.3 Future Work
73
6.3.1 Variable Optical Attenuator
73
6.3.2 Double Digital Optical Switch
(DDOS)
REFERENCES
75
76
x
LIST OF FIGURES
FIGURE NO.
TITLE
2.1
Cross section of a planar waveguide
2.2
Zigzag ray picture for light waves in planar wave
guiding structure showing radiation mode
2.3
11
12
Vector triangle describing the relationship
between β, k and ҝ
2.5a
10
Zigzag ray picture for light waves in a planar wave
guiding structure showing guided modes
2.4
PAGE NO.
13
Typical dielectric waveguides: a)Strip Loaded
waveguide structure. b) Ridge waveguide structure.
c)Air-clad-rib waveguide structure d) Buried type
waveguide structure .e) Embedded
waveguide structure
3.1
18
All of the light couples with the wider channel and
very less light couples with narrower asymmetric
channel.
3.2
28
An electrode used on channel 1 to change its
refractive index leading to thermo coupling.
29
xi
3.3
The vertical cross section through a DOS
4.1
Finite Difference mesh for modeling of a rib
Waveguide
4.2
35
Modeling of a buried waveguide using a
Finite Element mesh
4.5
34
Locating nodes (a) on centre of a mesh cell, or
(b) on mesh points
4.4
31
37
The buried type waveguide is divided into sub
domain region, which are triangles
38
4.6
Model Navigator showing five tabbed pages
42
4.7
Model Navigator showing application modes
43
4.8
Add/Edit Constant dialog box
44
4.9
Axes/Grid settings
45
4.10
Draw Mode for buried type waveguide structure
46
4.11
Boundary settings
47
4.12
Insulated boundaries and uninsulated
boundary (red)
47
4.13
Sub domain settings
48
4.14
Sub domain settings showing the selected domain
(heater in red)
49
4.15
Mesh mode settings
50
5.1
Flowchart defining the procedural work done in
this project
52
xii
5.2
5.3
5.4a)
The top view of the buried type Y-junction power
splitter (using BPM)
54
Simulation for Y-junction
55
The top view of the S-bend of buried type Yjunction power splitter (using BPM)
56
5.4b)
Simulation for parallel arms.
57
5.5a)
The transverse normalized mode field distribution
5.5b)
of mode0 at Ld =2.5mm,Ld is length of the device
.
Mode1 at Ld=4.5mm,X=10µm
5.5c)
The fundamental exclusively excited in the non
heated arm.
5.6
59
60
61
2D thermal distribution with core dimension
2.5µm× 5µm and H= 2.5µm, at heater temperature
300K using FEMLAB 2.0
5.7a)
Temperature profile plot at z=4mm with fixed
heater distance, H=2.5m.
5.7b)
62
63
Graph plotted shows waveguide temperature versus
boundaries of the core (S-bend at z=4mm) with
fixed heater distance, H=2.5m.
5.8a)
64
Temperature profile plot at the gap between two
parallel arms of the waveguide) with fixed heater
distance, H=2.5m.
65
xiii
5.8b)
Graph plotted shows waveguide temperature versus
boundaries of the core (gap between two parallel
arms of the waveguide) with fixed heater distance
, H=2.5m.
5.9a)
Mode conversion factor And Refractive index
Change
5.9b)
68
Plot showing relation between Attenuation in Sbend And Heating Power
5.9d)
67
Plot showing relationship between Crosstalk and
Mode conversion factor
5.9c)
65
69
Plot showing the relationship between Crosstalk
and Heating Power(Coupling Efficiency)
70
6.1
Top view of DOS with S-bend VOA
74
6.2
Evolution from DOS to DDOS
75
xiv
LIST OF TABLES
TABLE NO.
1.1
TITLE
PAGE NO.
The typical properties of waveguide material
used in integrated optics is mentioned in the
tabulated form.
7
3.1
The coupling ratio related to insertion loss
28
5.1
Opto-thermal parameters for utilized
materials (Data Sheet, Technology Evaluation
Report for Optical Interconnections and
Enabling Technologies)
5.2
53
Numerical values for the design parameters of
designed DOS.
53
xv
LIST OF SYMBOLS
A
-
contact area
C
-
heat capacity
d
-
waveguide arm spacing
K
-
thermal coupling estimation
k
-
thermal conductivity
H
-
distance from heater to waveguide core
h
-
thickness of core arm
L
-
Length of device
η
-
refractive index
Q
-
rate of heat flow
t
-
thickness of the substrate
W
-
Heater width
w
-
Core arm width
β
-
propagation constant
µ
-
relative permittivity
∆
-
temperature ratio difference
Φ
-
change in polarizabilty with temperature
xvi
Θ
-
incident angle
λ
-
wavelength
ρ
-
density capacity
ε
-
relative capacity
γ
-
coefficient of volume expansion
Ld
-
Distance of symmetry in waveguide
xvii
1
CHAPTER 1
INTRODUCTION
1.1 Objective Of This Project
Today, optical network is developing rapidly as growing capacity demand in
telecommunication system is increasing. Optical transmission systems are typically
running at data rates of 2.5Gbits/s or 10Gbits/s per channel. There are many advantages
for designing switching elements using optical components. These advantages include
decreased switching time (less than 1/10 of a pico second (1012)), less cross talk and
interference, increased reliability, increased fault tolerance, enhanced transmission
capacity, economical broadband transport network construction, enhanced cross-connect
node throughput, and flexible service provisioning.
There exists a demand of combining information 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 integrated optics in this area is to provide optical methods for
2
multiplexing, modulation and routing. More recently, interest has grown in these devices
to divide or combine optical signals for application within optical fiber information
system including data buses, local area networks, computer network links and
telecommunication access networks. These functions may be performed with a
combination of optical beam splitters, switches, modulators, filters, sources and
detectors.
Beam splitters are a basic element of many optical fiber communication systems
often providing a Y-junction by which signals from separate sources can be combined,
or the received power divided between two or more channels. The objectives of this
project are, therefore:
¾ Model formulation of Y-junction which involves study of Y-junction geometry,
which makes it better than other beam splitters. To study how the length of
switch effects the operation and behavioral characteristics of switch.
¾ Generation of Electric field modes within the waveguide.
¾ Simulation of propagation of light through Y-junction.
¾ Other optimum configurations like:
•
Branching /Opening angle formed exactly at the junction of Y-channel.
•
Switching characteristics like switching temperature, switching power,
switching functions(Thermo optic effect, Acoustic optic effect, magneto
optic effect, electro optic effect etc)
•
Power consumption meaning how much power is required for thermal
3
coupling to occur.
•
Low crosstalk in Y-junction for lossless transmission through it.
1.2 Scope Of This Project
The aim of this project is twofold. Firstly, to study the effect of temperature on
the refractive index of the thermo-optic waveguide. The waveguide is heated by means
of a thin electrode which is placed on one of the channels of Y-junction. The electrode
leads to heating of one of the channels of Y- junction, in turn changing the density of
polymer, increasing the polarizability and variation in optical path from one channel to
other of Y-junction. In this project, the buried waveguide is considered and the
phenomenon of thermo coupling will be studied seriously.
The second investigation is to gain insight of the various design parameters of
the Y-channel power splitter. Here, we would determine how by varying he
opening/branching angle between to arms of Y-channel
•
Effect the total length of the power splitter.
•
Effect the power transmission in two channels of Y-junction.
The efforts will be made to keep the size of Y-junction power splitter small.
However, very short switch can lead to worst cases of crosstalk of about 2.25dB (which
in turn indicates the influence of interferometer effects on the device).All simulations are
done by means of software named MATLAB and BPM.
4
1.3 Problem Statement
The use of visible optical carrier waves or light for communication has been
common for many years. Simple systems like signal fibers, reflecting mirrors and
signaling lamps have provided successful information transfer. The communication
using optical carrier wave guided along a glass fiber has a number of extremely
attractive features, several of which were apparent when the technique was originally
conceived. These features include enormous potential bandwidth, small size, and weight,
electrical isolation, low transmission loss, signal security, reliability, flexibility, potential
low cost etc.
Due to these enormous features of Optical fiber communication in comparison to
conventional electrical communication, there is seen an increase in the complexity of
Optical modules. So, the demand of time is to provide structure that have below
mentioned features.
Firstly, Optical device with simple compact structure meaning small in size and
less in weight. The industry will need to more to new technologies, such as flip chip
instead of wire bond and multi chip modules to reduce package size. Secondly, there
exists a need to keep the excess loss associated to Optical module very low so that the
obtained output power is approximately equal to the input power. Next is the demand to
manufacture Optical structures with less polarization dependence. However, this can be
achieved by making using of an appropriate switching function like thermo-optic effect
which is polarization insensitive and can be easily implemented by usage of electrically
driven by micro heaters. Finally, the Optical module should be such which can provide
NxN structure for power splitting and combining if required. Sometimes a switching unit
does not provide the desired value of some parameter; the Optical module must be such
that by cascading it into various stages, the problem is overcome. For instance, if the
5
crosstalk of a single 1x2 switching unit(for example, a DOS) is not sufficient, it can be
improved by cascading several of these devices and thereby multiplying the crosstalk(in
dB) by the number of cascaded stages.
This project use polymer material to build Optical waveguide. Since polymer
has large range of thermo- optic coefficient, we will apply the thermo optic effect to
overcome the above stated problem statement.
1.4 Project Background
The term Integrated Optics came into being since 1969 and was first discovered
by Miller. The concept of Integrated Optics involves the realization of optical and
electro-optical elements which may be integrated in large numbers on to a single
substrate. The need of Integrated Optics is there because most of the equipments today
are still based on electronic signals meaning that optical signal has to be converted first
into electrical signal, amplified, regenerated or switched and then reconverted to optical
signals. It is called Optical-to-Electronics-to-Optical (OEO) conversion. This is well
explained in Chapter 3.
There are two major kinds of Integrated Optical Switch namely, Interferometer
switch like Directional Coupler, Mach Zehnder etc and Digital Optical switch. For the
concern of this project we consider DOS because of it’s low polarization and wavelength
insensitivity. Also unlike Interferometer switches, DOS doesn’t require tight control of
biasing condition and less sensitive to heat.
6
With the beginning of Integrated Optics many waveguide fabrication techniques
have been proposed and used to form various optical waveguides on a variety of
substrates. The great variety of potential applications for integrated optical devices have
spurred intensive investigation of a large number of waveguide as well as substrate
materials over the past two decades. Initially, semi conductive substrates were studied
in the hope of facilitating easy interface with microelectronic or optoelectronic
components. Glass substrates were investigated with intended applications as advance
passive fiber-optical components. Electro-optical crystal substrates were explored for the
development of optical switches, modulators, and optical signal –processing devices.
Non linear optical materials were studied in the attempts to make high efficiency optical
harmonic generators. But none of them fulfill all desirable criteria at the same time. An
interesting alternative is polymers which offer some unique advantages.
Polymers are a relatively cheap starting material and can be processed from
solution, which offers additional potential for cost savings compared to other
technologies. Besides this polymers have wide range of refractive index from (-1 x 10-4
K-1 to -4x 10-4 K-1) which leads to power efficient dynamic components. Waveguide can
be designed with very large or very small index contrast between core and cladding
(0%-35%). Polymer can also have very low optical loss<0.1dB/cm at the
telecommunication wavelengths 1310nm and 1550 nm(John M. Senior, 1992).At present
polymers find their application widely in optical communication devices like switches,
couplers, filters, attenuators, polarization, controllers, dispersion compensators,
modulators, laser and amplifiers. Polymer materials have proved to have satisfactory
light-guiding characteristics. In principle, it is possible to achieve low optical
loss(infrared), high thermal and environmental stability, high thermo optic effects, low
thermal conductivity, good adhesion to metals and silica, and refractive index tailoring.
Furthermore modifying the chemical structure or doping the polymers with guest
molecules can tune the physical properties far simpler than in the case of semiconductors
7
or dielectrics. Polymers with different functionalities can be integrated on the same chip
and offer a versatile platform. Additionally, the processing of polymers is usually
compatible with semiconductors or dielectrics, which allow hybrid integration.
Table 1.Some of the typical properties of waveguide material used in integrated optics is
mentioned in the tabulated form.
Propagation
Refractive Index
Loss(dB/cm) Index
T/O
Max.
Contrast(ηcor
Coef.
Modulation
ηclad)/(ηcor)
dn/dt
Freq.
Birefringence
-1
[K ]
Silica
0.1
1.5
0-1.5%
10-4-10-2
10-5
1kHz(TO)
Silicon
0.1
3.5
70%
10-4-10-2
1.8x10-4
1kHz(TO)
Polymers
0.1
1.3-1.7
0-35%
10-6-10-2
-1x10-4
1kHz(TO)
- 4x 10
Lithium
-4
0.5
2.2
0-0.5%
10-2-10-1
10-5
40GHz(EO)
3
3.1
0-3%
10-3
0.8x10-4
40GHz(EO)
Niobate
Indium
Phosphide
Furthermore modifying the chemical structure or doping the polymers with guest
molecules can tune the physical properties far simpler than in the case of semiconductors
or dielectrics. Polymers with different functionalities can be integrated on the same chip
and offer a versatile platform. Additionally, the processing of polymers is usually
compatible with semiconductors or dielectrics, which allow hybrid integration. Polymer
materials have proved to satisfy specific applications and are thus of wide interest
nowadays.
8
In this project we consider Polyurethane as core material (η1= 1.573) and
Polymethylmethacrylate as cladding (η3 = 1.49 to 1.56). The Thermo optic effect will be
studied over the refractive index of core in this project and also Thermo coupling of
power in the two channels of Y-channel.
1.5 Overview Of This Project
This part of Introduction provides the work frame of Project 1. This report
consists of four Chapters including the Introduction.
Chapter2 holds the discussion about the phenomenon of light traveling through a
waveguide. Here, the propagation of light wave is expressed in terms of Maxwell
Equations. The various types of Optical waveguides are discussed. However, for this
project we consider buried type waveguide.
Chapter3 involves the methodology of the project. Here, the Operational
principle of thermo-optic waveguide is discussed. There are certain numerical methods
(formulas) which describe the relationship between many light propagation parameters
and further used for simulation purpose.
Chapter 4 is about the design and geometry of Optical Y-junction power splitter.
Chapter 5 holds the simulations for this project. All the results are produced using
FEMLAB and BPM software. Future work for this project is discussed in Chapter 6.
9
CHAPTER 2
OPTICAL WAVEGUIDES
This chapter deals with light propagation in Optical fibers using the Ray theory
and Electromagnetic mode theory developed for planar waveguides. Various waveguide
structures used for light propagation are described. This chapter also holds derivation of
the characteristic equation for uniform planar waveguide using Maxwell Equations.
2.1 Optical Fiber Transmission Mechanisms.
Fiber Optics refers to Optical devices for conveying light through a particular
configuration of glass or plastic fibers. An optical fiber waveguide is basically a light
guidance system and relies upon modal transmission to transmit light along its axial
length. Light enters one end of the fiber and emerges from the opposite end with only
minimal loss. There exist two theories to describe propagation of light through Optical
fibers:
10
•
Ray theory
•
Electromagnetic mode theory
2.1.1 Ray Theory
This theory states that when an incident ray of light falls on the interface between
two dielectrics of differing relative indices, it gets refracted. The simplest dielectric
waveguide is the planar guide shown in Fig.2.1, where a film of refractive index n2 is
sandwiched between a substrate and a cover material with lower refractive indices n3
and n1, respectively. Often the cover material is air,n1= 1.
Fig 2.1 Cross section of a planar waveguide
Using Snell’s law, the angles of incidence, Ø1 and angle of refraction, Ø2 can be related
as given below in Fig 2.2.
η1Sinθ1 = η 2 Sinθ 2
Sinθ1 η1
=
Sinθ 2 η 2
(2.1)
(2.2)
11
Sinθ c =
η1
η2
(2.3)
Where η 2 > η1 and θ c is the critical angle.
⎛ η1 ⎞
⎟⎟
⎝ η2 ⎠
θ c = Sin −1 ⎜⎜
(2.4)
η2
θc
η1
η2
Fig2.2 Zigzag ray picture for light waves in planar wave guiding structure showing radiation mode
Due to total internal reflection at the film-substrate and film-cover interfaces,
light can be confined in the film layer as guided optical waves. There exists a limiting
case when angle of incidence becomes greater than critical angle, Øc and the light is
reflected back into the originating medium (total internal reflection) with high efficiency
Further increases in the ray incidence angle beyond the critical angle at the filmsubstrate interface can cause the total internal reflection to occur at both the interfaces as
shown in Fig2.3
12
θc
.
Fig 2.3 Zigzag ray picture for light waves in a planar wave guiding structure showing guided modes
Such rays can only propagate in the zigzag manner within the film region as
guided light. The zigzag rays may be considered as two superimposed plane wave
components with wave normal that follow the zigzag directions and are totally affected
at the film boundaries. These waves are coherent and monochromatic with wavelength λ,
and usually propagate in modes (set of guided electromagnetic waves).In wave Optics;
modes are generally characterized by propagation constants, although they are classified
by their incident angle in ray Optics. For a guided mode of planar waveguide, the zigzag
model predicts propagation constant, denoted by β. The relationship between β and k
(known as wave vector), described by
k=
2π
λ
(2.5)
where λ is the wavelength) is best described by triangle (C.K.Madsen and Jian
H.Zhao) in Fig2.4. As evident from the Fig 2.4, the additional vector, namely ҝ is called
the transverse wave vector.
13
Fig 2.4 Vector triangle describing the relationship between β, k and ҝ
The relationship between the incident angle, θ and the propagation constants along x and
z directions are
k x = k0η 2Cosθ
(2.6)
k z = k0η 2 Sinθ
(2.7)
This gives the propagation of the wave vector of the plane waves, k0n2 ,in the direction of
the wave guiding film. However, only a discrete set of angles that allow the reflected
plane waves to interfere constructively will lead to acceptable guided modes. There,
effective indices N of modes can be defined as
β = k0 N
(2.8)
N = η 2 Sinθ
(2.9)
Therefore for a planar slab dielectric waveguide with n2>n3>n1, the propagation
constant can be expressed as
k0η3 < β < k0η 2
(2.10)
14
In terms of an effective waveguide index, it can be expressed as
n3 < N < n2
(2.11)
2.1.2 Electromagnetic mode theory
Optics deal with light waves which are electromagnetic waves. In order to obtain
an improved model for the propagation of light in an optical fiber, electromagnetic wave
theory is considered. Electromagnetic waves include not only light waves, but also
ordinary alternating current at 60Hz, radio waves, microwaves, X-rays etc.
Electromagnetic waves obey Maxwell’s equations treats the electromagnetic wave
equation followed by the plane wave solution.
2.1.3 Maxwell Equations
The electromagnetic wave propagation is provided by Maxwell’s equations. For
a medium with zero conductivity the vector relationships are written in terms of electric
field E, magnetic field H, electric flux density D and magnetic flux density B as the curl
equations:
∇× E = −
∂B
∂t
(2.12)
∇× H = −
∂D
∂t
(2.13)
15
And the divergence conditions:
∇.D = 0 (no free charges)
(2.14)
∇.B = 0 (no free charges)
(2.15)
where ∇ is a vector operator.
The four field vectors are related by the relations:
D = εE
(2.16)
B = µH
(2.17)
where ε is the dielectric permittivity and µ is the magnetic permeability of the medium.
The dielectric permittivity is further defined as ε = ε0εr, where εr is the relative
permittivity or dielectric constant of the medium and ε0 the free space permittivity. The
magnetic field is defined similarly as µ=µ0µr , but in the context of this project nonmagnetic materials are considered, µr =1, and thus only the free space permeability , µ0 ,
is used in equation.
Substituting for D and B and taking the curl of a equations 2.12 and 2.13 gives
∂2E
∂t 2
(2.18)
∂2H
∇ × (∇ × H ) = − µε 2
∂t
(2.19)
∇ × (∇ × E ) = − µε
Then using the divergence conditions of equation (2.16) and (2.17) with vector identity
∇ × (∇ × Y ) = (∇.Y ) − ∇ 2 (Y )
we obtain the non dispersive wave equations:
(2.20)
16
∂2E
∇ E = µε 2
∂t
(2.21)
∂2E
∇ H = µε 2
∂t
(2.22)
2
2
Equation 2.18 can be rewritten as
∇ × ∇ × E = k 2E
(2.23)
where the local plane wave propagation constant or wave number k, is given by
k =ω
(µε ) = ω µ0ε 0 ε r
(2.24)
and λ is the free space wavelength. Using the identities
∇ × ∇ × ∇ = ∇∇ − ∇ 2
(2.25)
∇.(η 2 E ) = η 2∇.E + E∇η 2 = 0
(2.26)
The general vector wave equation for the electric field is obtained as under
⎛ E.∇k 2 ⎞
⎟⎟ + k 2 E = 0
∇.E + ⎜⎜
2
⎝ k ⎠
(2.27)
As evident from Fig 2.1 there are three regions in planar waveguide air(cover),
substrate(cladding) and film (core) with refractive indices being n1<n3<n2.
∂ 2 E ( x, y )
2
+ k 2η1 − β 2 E (x, y ) = 0
2
∂t
(
)
(2.28)
17
∂2
2
E ( x, y ) + (k1η 2 − β 2 ) E ( x, y ) = 0
2
∂t
(
)
∂2
2
E ( x, y ) + k2η3 − β 2 E ( x, y ) = 0
2
∂t
(2.29)
(2.30)
These equations help to study the phenomenon of light propagation core, how light
remains confined to the core of fiber.
2.2 Optical Waveguide Structure
Integrated Optical waveguides are simply structures that confine and guide
Optical waves due to an induced refractive index increases in the guiding region with
respect to the surrounding regions. Such waveguides are typically formed at or near the
surface of the substrate material by a variety of fabrication techniques. Channel
waveguides confine the light in three dimensions, two transverse and on longitudinal, in
contrast with the more general form of planar waveguides in which the light is confined
in two directions, one transverse and one longitudinal. A planar waveguide is typically a
thin, flat layer whose refractive index is higher than the two regions that come into
immediate contact with it. These regions typically comprise the substrate material and a
cover layer, which is often air, but could be any layer of lower refractive index. The five
basic structures of integrated Optics channel waveguides are shown below in Fig 2.5(ae).
18
(a)
(b)
(c)
η1
η2
(d)
(e)
Fig 2.5 Typical dielectric waveguides (a)strip loaded waveguide,
(b)ridge waveguide, (c)air –clad rib waveguide, (d) buried waveguide,
(e)embedded waveguide.
19
Fig 2.5a shows strip- loaded waveguide consisting of a planar film deposited on
a substrate of lower index. Fig2.5b shows ridge waveguide which is a narrow film
deposited on a substrate of lower refractive index, with air covering the top.. Fig 2.5c is
a rib waveguide formed by depositing a planar film layer of higher index than the
substrate and then removing part of the film on both sides of a narrow channel.
Finally fig 2.5d shows the buried waveguide which we will consider in this
Project. It is formed when the channel area of higher index is driven into the substrate
and is therefore surrounded symmetrically by regions of the same refractive index. For
buried strip waveguide the refractive index difference between core and cladding needs
to be small to allow for fiber mode matched single mode geometries. The involved
materials to create the core and cladding need to be carefully chosen or manufactured to
ensure this small refractive index difference. The main advantage of this type of channel
waveguide is that it provides propagation loss of about 1dB/cm with a smooth guide
surface.
Fig2.5e shows an embedded channel waveguide which is formed by diffusing
impurities into substrate such that the index in the diffused region is higher than the
substrate, thus forming a channel guide bound by the substrate on three sides and by air
on the fourth.
2.3 Polymer Waveguide
Polymer materials for telecommunication component manufacturing have
attracted attention because of the satisfactory light –guiding characteristics. In addition,
20
polymer materials have the advantages of a large thermo-optic (TO) coefficient and
nonlinear electro-optic coefficients(L. Eldada and L.W. Shaklette, 2000). In principle it
is possible to achieve low optical loss(near infrared), high thermal and environmental
stability, high thermo optic effects,low thermal conductivity,good adhesion to metals
and silica, and refractive index tailoring. Usage of these materials offer advantages like
availability in large qualities and guaranteed quality.
The simulation is done considering polyurethane(PUR) as a core and
Poymethylmethacrylate (PMMA) as a cladding.
2.3.1 Material Thermal Properties
The change in refractive index of a material is due to a combination of the
physical expansion of the material and the change of the index of refraction with
temperature, T . The thermo-optic coefficient can be expressed as(H. S njezana
Tomljenovic,2003):
⎛ ∂n ⎞ ⎛ ∂n ⎞ ⎛ ∂ρ ⎞ ⎛ ∂n ⎞
⎟
⎟+⎜
⎟ = ⎜⎜ ⎟⎟ ⎜
⎜
⎝ ∂T ⎠ ⎝ ∂ρ ⎠T ⎝ ∂T ⎠ ⎝ ∂T ⎠ ρ
(2.27)
where η is the refractive index, ρ is density.
When the coefficient of volume expansion, γ is used, then above equation becomes:
⎛ ∂n ⎞
⎛ ∂n ⎞
⎛ ∂n ⎞
⎟
⎟ γ +⎜
⎟ = −⎜ ρ
⎜
⎝ ∂T ⎠ ρ
⎝ ∂T ⎠T
⎝ ∂T ⎠
(2.28)
21
In most silica based integrated-optic materials the second term in above equation is the
more significant and its value is of order:
⎛ ∂n ⎞ ⎛ ∂n ⎞
−5 0
⎟ ρ ≈ 10 / C
⎟≈⎜
⎜
⎝ ∂T ⎠ ⎝ ∂T ⎠
(2.29)
On the other hand, for polymers the physical expansion of the material will be dominant
factor when the temperature change occurs. The first term for these materials is of the
(M.N.J.Diemeer,1998) order:
⎛ ∂n ⎞
⎛ ∂n ⎞
−4 0
⎜
⎟ ≈ −⎜ ρ
⎟ γ ≈ −10 / C
⎝ ∂T ⎠
⎝ ∂T ⎠T
(2.30)
If this result is compared with that for silica based materials in equation, the conclusion
is that the thermo-optic coefficient is a polymer is, in absolute value, an order of
magnitude larger than silica. There is also a difference in the sign, so with an increase in
temperature, the refractive index of polymer decreases, whereas for silica it increases.
Taking into account the difference, both in conductivity and thermo-optic
coefficient, it takes about two orders of magnitude more power to induce the same
refractive index change in silica-on-silicon than in polymers(K.Okamoto,2000).
22
CHAPTER 3
ASYMMETRIC Y-JUNCTION POWER SPLITTER
This chapter deals with project background in detail like integrated optics,
optical switching, thermal coupling and thermo optic polymers. The literature review
will cover the asymmetric configuration of Y-junction and Operational principle of light
propagating through the Y-junction power splitter.
3.1 Integrated Optics:
With the increasing complexity of Optical modules, there is a need for
integrating various active and passive devices on a single substrate to increase the
functionality of Optical chips. The multitude of potential applications areas for optical
fiber communications coupled with the tremendous advances in the field have over
recent years stimulated a resurgence of interest in the area of integrated optics(IO).The
concept of Integrated Optics involves the realization of optical and electro-optical
23
elements which may be integrated in large numbers on to a single substrate. Hence,
Integrated Optics 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.
The birth of Integrated Optics may be traced back to basic ideas outlined by
Anderson in 1966. He suggested that a micro fabrication technology could be developed
for single-mode optical devices with semiconductor and dielectric materials in a similar
manner to that which had taken place with electronic circuits.
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. It is apparent that the continued expansion of a single mode
optical fiber communications will create a growing market for such Integrated Optics
components.
Developments in integrated optics 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. At present,
these advances are closely linked with developments in light wave communication
employing optical fibers. It is predicted that the next generation of Optical fiber
communication systems employing coherent transmission will lean heavily on IO
techniques for their implementation.
24
3.2 literature review:
Most networking equipment today is still based on electronic-signals meaning
that the optical signals have to be converted to electrical ones, to be amplified,
regenerated or switched, and then reconverted to optical signals. This is generally
referred to as an ‘optical –to –electronic-to optical’ (OEO) conversion and is a
significant bottleneck in transmission. High amounts of information traveling around an
optical network needs to be switched through various points know as nodes.
Information arriving at anode will be forwarded on towards its final destination
via the best possible path, which may be determined by such factors as distance, cost,
and the reliability of specific routes. The conventional way to switch the information is
to detect the light from the input optical fibers, convert it to an electrical signal, and then
convert that back to a laser light signal, which is then sent down the fiber we want the
information to go back out on.
The basic premise of Optical switching is that by replacing existing electronic
network switches with optical ones, the need for OEO conversions is removed. Clearly,
the advantages of being able to avoid the OEO conversion stage are significant.
Thermo-optic
(TO)
switches
are
attractive
devices
for
fiber-optic
communications for applications like protection switching and optical routing. Taking
advantage of two different material systems – silica with ultra-low optical loss and
specially designed polymers with high Thermo Optic-coefficient and low thermal
conductivity –it’s realized a new hybrid polymer/silica concept, in which the planar SiO2
waveguide is used as an optical transport layer only, whereas the planar polymer
waveguide is used for the Thermo Optic-switching function. Moreover, the operation of
25
these devices is based on the thermo-optic effect. It consists in the variation of the
refractive index of a dielectric material, due to temperature variation of the material
itself. There are two categories of thermo –optic switches:
¾ Interferometric switches
¾ Digital Optical switches
The former need a particular value of driving voltage to achieve the switching of
signals, the latter are characterized by a threshold value of the driving voltage and a
step- like response. For the concern of this project we consider Digital Optical switch.
Digital Optical switch is a type of refractive index modulated optical switches. These are
integrated optical devices generally made of silica on silicon. The switch is composed of
two interacting waveguide arms through which light propagates. It does not use
interferometric effect, but exploits the adiabatic adaptation of fundamental mode in
waveguide.
A slightly higher index, modulation is usually required than interferometric
devices. That means high power consumption is needed in Digital Optical switches.
However, the DOS has switching characteristics remaining unchanged state after
applying further biasing voltage. This means that the DOS is less sensitive to the bias
voltage or heat variation than interferometric devices. The insensitivity to the
polarization is of high interest for the Digital Optical switch. The phase error between
the beams at the two arms determines the output port. The compromise between
branching angle and index change is needed for adiabatic mode evolution and low
crosstalk in Digital Optical switch (DOS).
26
3.3 Operational Principle:
The fundamental switching unit in this work is the 1x2 digital optical switch
which is sometimes called ‘Adiabatic switch’. In principle any physical effect that
changes the refractive index of a material (accousto optic, electro optic, magneto optic,
thermo optic etc.). The thermo optic effect that is employed in this project has the
advantage to be polarization insensitive, to reach quite high values in polymers, and to
be easily implemented by usage of electrically driven micro heaters. By using the
thermo optic (TO), the interaction between heat and light will cause the change in
refractive index. The change of refractive index with temperature depends on two
counteracting effects:
(1) The change in density caused by positive or negative coefficient of thermal
expansion (CTE).
(2) The increase in polarizabiliy with temperature (Robert Blum,2003).
In principle the DOS is just a y-splitting of waveguides with a very small
opening angle to minimize mode coupling between the local system modes. If the device
is perfectly symmetric the fundamental mode is perfectly even and the second mode is
perfectly uneven with respect to the midpoint between the waveguides. Power coming
from the in coupling single mode waveguide will only excite the fundamental
mode(neglecting losses to radiation modes) along the whole structure resulting 3dB
power splitting in the output ports independent of the device length.
A term known as mode conversion factor or the measure of switching
characteristics of Y-junction power splitter determines whether the junction is
27
symmetric or asymmetric. If⎮MCF⎮<<0.43 the Y-junction acts as a symmetric power
splitter. For ⎮MCF⎮>>0.43 the Y-Junction acts as asymmetric power splitter. Since we
consider asymmetric Y-junction in this project, so we expect width of one of the
branches of Y-junction channels to be more than the other. Due to asymmetry, power
incoming from the input port excite both modes- fundamental/zeroth order mode and the
second mode. So there exist two ways in which a Y-junction can act as power splitter, as
mentioned below:
¾ By varying the width of two channels of Y-junction.
¾ By varying the refractive index of one of the channels of Y-junction.
In first case it is observed that if one of the channels is much wider than the
other, the power in the former one is much more than the latter one, as shown in
Fig.3.1.This figure shows clearly that the width for broader arm,w2 is larger than the
width of narrower arm,w3 The total length of the device is denoted by Ld. However the
linear waveguide width being W1.
This further means that whole power will be in the fundamental mode. If
asymmetry of Y-junction is reduced by varying the width channels i.e. by increasing the
width of narrow channel and decreasing the width of wider channel, it is seen that the
power in wider channel starts decreasing from 100% to 50% and that in narrow channel
starts increasing from 50% to 100%. The splitting behavior of power of such a junction
is dominated by mode conversion factor. Once MCF equals to 0.4 such a junction acts as
a 50/50 or 3dB power splitter and is even known as mode splitter.
28
Fundamental mode
Incoming light
W2,
Wider
Channel
W1
Second mode
Ld
W3,
Narrow
Channel
Fig. 3.1 shows how almost all of the light couples with the wider channel and very less light
couples with narrower asymmetric channel.
However the insertion loss being 3.6dB the lowest for 50/50 coupling ratio and
increases with increase in coupling or splitting ratio. Using wavelength 1310-1440 nm
and 1480-1590 nm, for coupling ratio the corresponding insertion loss values are as
shown below.
Table3.1 Table showing the coupling ratio related to insertion loss.
Coupling Ratio (%)
Insertion Loss[dB]
50/50
3.6
45/55
4.2/3.2
40/60
4.7/2.7
35/65
5.4/2.3
30/70
6/1.9
25/75
6.95/1.7
20/80
7.9/1.4
15/85
9.6/1
10/90
11/0.7
29
In second case, asymmetric Y-junction is considered as previously and refractive
index is varied using thermo optic effect. Under certain conditions a fundamental mode
is launched in the input channel of Y-junction, where it gradually transforms itself to the
fundamental mode of combined branches. In a thermo optic digital switch the difference
in effective index between the two branches is achieved through thermo optic coefficient
of the wave guiding material, by heating up one of the branches. This heating is
achieved by an electrode of few micrometers in width placed alongside the branch, as
shown in Fig.3.2.
Fig.3.2shows an electrode used on channel 1 to change its refractive index leading to thermo
coupling.
As the temperature is raised, the refractive index (η2) of channel 1 starts
decreasing and the effective index contrast (η1 - η2) between the channels will increase.
From total internal reflection phenomenon, if dielectric on the other side of interface has
a refractive index (η2) which is less than (η1) the light is reflected back into the dielectric
medium of higher refractive index. Hence in this case, causing gradual shift of power
from channel 1 to channel 2. The effect gets stronger with increasing refractive index
30
difference and increasing waveguide separation until the modes are almost exclusively
localized in opposite arms. The purpose of forcing the fundamental system mode into
the non heated channel 2 is that all the power remains in the fundamental mode
guaranteeing very low crosstalk in the heated arm and lowest excess loss.
Qualitatively mode coupling can be described by the mode conversion factor or
coupling coefficient and the phase relation between the two modes. The division of the
modal power over the two channels is related to the DOS angle( opening/branching
angle) α and the effective indices of the output branches. This relationship is
conveniently described with the so- called Mode Conversion Factor (MCF):
MCF =
η1 − η 2
tan α η 2 − η3
2
(3.1)
In equation (3.1) η1 and η2 are the effective indices of the output channels 2 and
1 respectively, η is the average effective index of both output channels and η3 is the
effective index of the surrounding medium(cladding). Additionally the opening angle α
between the modes changes faster with the increasing refractive index difference leading
to alternating constructive and destructive coupling to the second mode in region of
strong coupling. The power transmission decreases sharply with increase in opening
angle α because then the power starts being radiated into the substrate.
Low power in the second mode is very important for the performance of a DOS which
is usually judged by the Cross talk (CT). Cross talk gives the relationship between the
switching behavior and mode conversion factor in a quantitative way:
Crosstalk = −C.MCF .
10
[dB]
ln (10)
Where C is an empirical constant with a value of approximately 3.
(3.2)
31
3.3.1 Geometry of Y-junction cross section:
The considered dimensions of the channel waveguides are 5 by 5 µm. The
effective index-contrast between the channel of higher refractive index and channel with
decreasing refractive index is 0.012.
Fig 3.3 shows the vertical cross section through a DOS.
The thermal conductivity of the polymer layers used- Polyurethane and
Polymethylmethacrylate is taken to be 0.17 W/m/K and for silicon (SiO2) buffer layer(
thickness 2µm) a thermal conductivity of 0.015 W/m/k is assumed. The silicon substrate
is treated as perfect heat sink with zero temperature. The thermo- optic coefficient is
zero, except for PMMA layer where it is taken to be -1.2 x 10-4 K-1. The gap, d between
the parallel branches is assumed to be 20µm whereas the gap between the Y-shape
branches is assumed to be 15µm, as shown in the Fig.3.3. The width,w of arm 1 and
arm2 are considered same as 5µm with the thickness,t of 2.5µm. However the branching
32
angle α is assumed to be least of the order (0.50 to 1.60) to have low crosstalk in the
heated arm. The electrode width,W is taken to be identical to the width of the
waveguides for the sake of simplicity i.e. 5µm. The wavelength for all measurements is
assumed to be 1.3µm.
33
CHAPTER 4
MODELING AND DESIGN OF WAVEGUIDE
In this chapter, the model and design of Optical Y-junction power splitter is
obtained using FEMLAB2.0 and Beam Propagation Method (BPM).The first task of this
chapter is to make the user friendly with the basic equations involved using various
numerical methods, followed by modeling of the waveguide design using software.
4.1 Numerical Methods
Numerical methods solve Maxwell’s equations exactly and the results they
provide are often regarded as benchmarks. Numerical methods, such as the Finite
Difference (FD), Finite Elements (FE) and Finite Difference Beam Propagation
(FDBPM) methods are robust, versatile and applicable to a wide variety of structures.
Unfortunately, this is often achieved at the expense of long computational times and
large memory requirements, both of which can become critical issues especially when
34
structures with large dimensions are considered or when used within an iterative design
environment. In this section, a short overview of these numerical methods is given.
4.1.1 Finite Difference Method
The Finite Difference (FD) method is one of the most frequently used numerical
techniques [M.N.O. Sadiku,1992]. Its application to the modelling of optical waveguides
dates from the early eighties, originally evolving from previous FD models for metal
waveguides [J.B.Davis,1996]. The FD method discretisizes the cross-section of the
device being analysed and is therefore suitable for modelling arbitrarily shaped dielectric
guides which could be made out of isotropic homogeneous, inhomogeneous, anisotropic
or lossy material. The essence of the FD method is to map the structure onto a
rectangular mesh [M.S,Stern,1988], as shown in Fig4.1, allowing for the material
discontinuities only along mesh lines. There are two possible ways of placing nodes on
the mesh: at the centre of each mesh cell so that node is associated with a constant
refractive index, (Fig.4.2(a)), [M.S.Stern,1988], and on mesh points so that each node
can be associated to maximum of four different refractive indices, (Fig4.2(b)),
[K.Bierwirth,1986].
Fig4.1. Finite Difference mesh for modeling of a rib waveguide
35
(a)
(b)
Fig.4.2 Locating nodes (a) on centre of a mesh cell, or (b) on mesh points
The differential vector, semi-polarized or scalar wave equation is then
approximated, usually with a five point finite difference form, in terms of the fields at
the nodes of the mesh. For improved convergence more accurate difference forms can be
used [M.N.O. Sadiko,1992]. Taking into account the continuity and discontinuity
conditions of the electric and magnetic field components at the grid interfaces, the eigen
value problem becomes of the form
[A]φ = β 2φ
(4.1)
where [A] is a band matrix which is symmetric for scalar modes [E. Schweig, W. B.
Bridges,1984] or nonsymmetrical for semi-vectorial [K. Bierwirth, N. Schulz, F. Arndt,
1986] and vector modes [S. S. Patrick, K. J. Webb,1982]. β is the modal propagation
eigenvalue and Φ is the eigenvector representing the modal field profile.Eq.4.1) can be
solved using direct method such as Gaussian elimination (suitable when the matrix is
small) or more efficiently, using iterative methods such as the shifted inverse power
iteration method [L. W. Johnson, R. D. Riess,1977].
In this project we used BPM_CAD(Beam Propagation Method) which is a stepby-step method of stimulating the passage of light through any wave guiding medium
36
using finite difference method. In integrated and fiber optics, an optical field can be
tracked at any point as it propagates along the guiding structure. BPM allows computer
simulated observation of the light field distribution. The radiation and the guided field
are examined simultaneously. This project involves 2D model of Optical Y-junction
power splitter. Thus 2D simulator is based on the unconditionally stable finite difference
method algorithm of Crank-Nicholson described below.
4.1.1.1 Crank Nicolson method
In the mathematical subfield numerical analysis, the Crank-Nicolson method is a
finite difference method used for numerically solving the heat equation and similar
partial differential equations. It is a second-order method in time, implicit in time, and is
numerically stable. The method was developed by John Crank and Phyllis Nicolson in
the mid 20th century. The Crank-Nicolson is based on central difference in space, and
the trapezoidal rule in time, giving second order convergence in time(Crank J. and
Nicolson P. (1947). Equivalently, it is the average of forward Eular and backward Eular
in time. Crack-Nicolson for the heat equation is one spatial dimension, ut = auxx,reads
or, for a uniform grid in two spatial dimensions, ut = a(uxx+uxx)
37
Usually the Crank-Nicolson scheme is the most accurate scheme for small time steps.
Besides heat equation calculations, the algorithm of Crank-Nicolson includes calculation
of starting field launched at an angle and refractive index change.
4.1.2 Finite Element Method
The Finite Element (FE) method is another well established numerical technique
for solving boundary value problems. The method is based upon dividing the problem
region into non-overlapping polygons, usually triangles, as shown in Fig.4.4.
Fig4.4 Modeling of a buried waveguide using a Finite Element mesh
The field over each element is then expressed in terms of low-degree
interpolating polynomials weighted by the field values at the nodes of each element. The
total field is found as a linear summation of the fields over each element[C. L. Xu,
W.P.Huang,1995]. The FE method uses a variational expression which is formulated
from Maxwell’s equations [F. Fernandez, Y. Lu,1996]. By differentiating the variational
38
functional with respect to each nodal value, the eigenvalue problem is obtained of the
form
[A][x]-λ[B][x]=0
(4.4)
where [A] and [B] are sparse matrices, usually symmetric, [x] is the nodal matrix and
λ is the natural eigenvalue of the problem. Eq.(4.2) is solved for all eigen values using
iterative techniques. Solution of the problem can be in terms of its natural frequency or
in terms of the propagation constant β, depending on the variational formulation [F.
Fernandez, Y. Lu,1996]. The former case is less preferred since an initial guess for β is
required which can be especially difficult in situations whereβ has a complex value. The
accuracy of the FE method can be increased by using a finer mesh or by employing
higher order polynomials. A finer mesh increases the size of the matrices [A] and [B],
and higher order polynomials reduce their sparsity involving increased programming
effort.
Fig.4.5 The buried type waveguide is divided into sub domain region, which are triangles
In this project, design work is done using FEMLAB2.0 version. The finite
element method is a numerical analysis technique used by engineers, scientist, and
mathematicians to obtain solutions to the differential equations that describe or
approximately describe a wide variety of physical (non-physical) problems range in the
39
diversity
from
solid,fluid
and
soil
mechanics,to
electromagnetism
or
dynamics(R.D.Cook, Malkus D.S, and Plesha M.E,1989)
The finite element method always follow an orderly step-by-step process to
generate the result. The followed steps are enlisted below:
1. Discretize the region. This includes locating and numbering the node points, as
well as specifying their co-ordinate values.
2. Specify the approximation equation. The order of the approximation,linear or
quadratic,must be specified and the equations must be written in terms of the
unknown nodal values. An equation is written for each element.
3. Develop the system of equations. This generates one equation for each unknown
nodal value. This gives one equation for each of the unknown displacements.
4. Solve the system of equations.
5. Calculate quantities of interest. These quantities are usually related to the
derivation of the parameter such as heat flow.
The fundamental concept of finite element method is that any continuous
quantity. In this case is temperature can be approximated by discrete model composed of
a set piecewise continuous functions defined over a finite number of elements. The more
common situation is where the continuous quantity is unknown and some of the points
inside the regions are needed to be determined. The construction of the discrete model
is done as under:
40
1. A finite number of points in the domain are identified. These points are called
nodal point or nodes.
2. The value of the continuous quantity at each nodal point is denoted as a variable
which is to be determined.
3. The domain is divided into finite number of sub domains called elements. These
elements are connected at common nodes and collectively approximate the shape
of the domain.
4. The continuous quantity is approximated over each element by a polynomial that
defined using the nodal values of the continuous quantity.
4.3 Heat Transfer Equation
In this project, the main objective is to change the refractive index leading to the
thermal coupling obtained by the transfer of heat from heater to the core across the
cladding.Achieving this goal requires a thorough understanding of heat transfer
fundamentals as well as knowledge of available interface materials and how their key
physical properties affect the heat transfer process. The heat transfer equation gives the
measure of heat transfer over an area within a certain amount of time.
(4.5)
On substituting the parameters, the heat transfer equation becomes:
41
(4.6)
where ρ is the density, Cp is the mass heat capacity in erg g-1 K-1, d is the diffusion
distance, and
is the thermal diffusivity in cm2 s-1.
(4.7)
The rate at which heat is conducted through a material is proportional to the area normal
to the heat flow and to the temperature gradient along the heat flow path. For a steady
state heat flow the rate is expressed by Fourier’s equation:
(4.8)
Where:
k = thermal conductivity, W/m-K
Q = rate of heat flow, W
A = contact area
d = distance of heat flow
∆T = temperature difference
Thermal conductivity, k, is an intrinsic property of a homogeneous material
which describes the material’s ability to conduct heat. This property is independent of
material size, shape or orientation. For non-homogeneous materials, those having glass
mesh or polymer film reinforcement, the term “relative thermal conductivity” is
appropriate because the thermal conductivity of these materials depends on the relative
thickness of the layers and their orientation with respect to heat flow.
42
4.5 Simulation Guide.
The goal of this section is to familiarize the FEMLAB environment, focusing
primarily on how to use its graphical user interface.
4.5.1 Setting up the model in FEMLAB
To begin the modeling process, an obvious first step is to install MATLAB and then
execute FEMLAB.
1. To do so on any platform, type the following entry into MATLAB command window:
Femlab.
This command invokes FEMLAB Model Navigator. The Model Navigator is a multipurpose dialog box in which we control the general settings of a FEMLAB session as
shown in Fig 4.6. The FEMLAB session can also be started from start menu.
Fig4.6 Model Navigator showing five tabbed pages
43
2. Go to multiphysics page, and check that 2-D button. The space dimension must
always be selected first, as the physics modes available differ.
3. Select the heat transfer application mode from the list of available modes. Press the
right arrow(>>) in the center of the page. This will accept the settings in the Application
mode name, Dependent variables and Element fields, and transfer the heat transfer
mode to the list of active modes on the right.
4. Repeat step 3 but select wave equation application mode now from the available
modes.
5. Press OK to confirm the selected choices and close the Model Navigator, as shown in
Fig 4.7 below
Fig 4.7 Model Navigator showing application modes
44
At this point, the graphical interface opens up in the heat transfer application
mode. We can always find out in which application mode the package is presently
working because its name appears on the bar at the top of the FEMLAB window
4.5.2Options and Settings
We need the physical properties of polymers used, temperature of heater, the
refractive indices of cladding and core. This date is entered as constants in the Add/Edit
Constants dialog box. The values used in this model are all given in SI units.
1. Select the Options menu at the top of the FEMLAB window and choose Add/Edit
Constants.
2. Add all the constant value like temperature, refractive index for core, cladding and
substrate, velocity of light etc. used in the design, as shown in Fig 4.8.
3. Finally , press OK.
Fig 4.8 Add/Edit Constant dialog box.
45
The model size is in the order of a few centimeters, while the area visible in the
graphical interface is in the order of meters. Before we start drawing the geometry, we
therefore have to change the size of the drawing area and grid spacing.
1. On the menu bar at the top of the screen select the Option menu, and from the dropdown choices choose Axes/Grid settings.
Fig 4.9 Axes/Grid settings
2. A dialog box opens up, and on the Axis page set the x and y for minimum and
maximum value, and then select the grid page and set the spacing, as shown in Fig 4.9.
4.5.3 Draw Mode
Next task is to draw the model’s geometry. The model involves on rectangles.
1. Draw the buried type waveguide structure as shown below in Fig 4.10 with heater
width is 2µm and the distance from heater also being 2µm
46
2. To change the properties of the rectangle we can double click on the name of the
rectangle.
Fig 4.10 Draw Mode for buried type waveguide structure
4.5.4 Boundary Mode
Above mentioned steps made the geometry ready, the next step is to start
defining the physics of design. The boundary conditions and equation coefficients are set
independently for the two application modes namely Heat transfer mode and Wave
equation mode. First, set the boundary conditions for the Heat transfer.
1. Choose boundary settings from the boundary menu. This opens the boundary setting
dialog box, and transfers FEMLAB to boundary mode. The dialog box had different
options in different application modes.
47
2. Start by insulating all boundaries except the heat inflow boundary between the heater
n the wafer as shown in Fig 4.11. In this case the domain selection should be 14 which
will leave desired boundary uninsulated which is shown by red boundary in Fig 4.12.
Fig 4.11 Showing the Boundary settings
Fig 4.12 Showing Insulated boundaries and uninsulated boundary (red)
48
4.5.5 Sub domain mode
The coefficients in the governing equations can be interpreted, depending on the
application mode.
1. Choose Sub domain settings from the sub domain menu to open the sub domain
settings dialog box, and the user interfaces need to put in sub domain mode.
2. Select the single sub domain which is 5 in this case, and put the entire coefficient
respectively, as shown in Fig 4.13 below.
3. The temperature also needs an initial value.The red block in Fig 4.14 shows the heater
generating heat inflow.
Fig 4.13 Sub domain settings
49
Fig 4.14 Sub domain settings showing the selected domain (heater in red)
4.5.6 Mesh Mode
Because FEMLAB is based on the finite element method (FEM),it needs a
subdivision of the geometry known as a mesh. A standard mesh is created automatically,
as we press the mesh mode.
1.Initialize the default mesh by processing either the Initialize Mesh button or the Mesh
Mode button, both on the main toolbar,as shown in the Fig 4.15. Both in this case have
the same effect.
2. If a need for different mesh resolution is required, or require mesh to be denser in
some parts of the geometry, than in others we can work with Mesh Parameters dialog
box, accessible from the Mesh menu.
50
Fig 4.15 Mesh mode settings
51
CHAPTER5
RESULTS AND DISCUSSION
This Section of thesis presents the obtained simulation results for the
investigation of thermal distribution, electric field generation, S-bend attenuation and
other Optimum configurations.
5.1 Project Methodology
This project methodology gives the procedural work followed in this project. The first
task is made to select the polymer material for core, cladding and substrate. The
properties like thermal conductivity, resistivity and specific heat capacity are considered.
Those polymers need to be selected which have very high thermo-optic(TO) coefficients
10 to 40 times more than that of glass . The next step is the design of structure which
makes it better than other conventional Y-junction Optical power splitters available.
Since light being an electromagnetic wave, thus undergoes electric and magnetic
52
phenomena at the macroscopic level described by Maxwell’s Equations, Vector wave
equations and Heat transfer equations using Femlab software. The last step involved is
the study of light coupling from heated arm to unheated arm using Gold (Au) electrode.
The flowchart below shows the methodology for this research work.
Selection of
polymer material
for core, cladding
and substrate
Design and Geometry using Software Tools
Introducing mathematical equations with boundary conditions
Maxwell
Equations
Vector Wave
Equation
Heat Transfer
Equation
Thermal Coupling using Thermo Optic Effect
Fig5.1 Flowchart defining the procedural work done in this project
53
Table 5.1: Opto-thermal parameters for utilized materials (Data Sheet, Technology Evaluation
Report for Optical Interconnections and Enabling Technologies)
Polymers
n
dn/dT[K-1]
k[W/mK]
Cv[J/gK]
Ρ[g/cm3]
PMMA
1.56
-1.2E-4
0.167
1.466
1.17
PUR
1.573
-3.3E-4
0.19
1.70
1.1
Table 5.2: Numerical values for the design parameters of designed DOS.
Parameter
Description
Numerical value
H1
Distance of heater from corearm1
2µm
H2
Distance of core from cladding and
substrate interface
2µm
W
Width of heater
5µm
w
Width of each arm of core
5µm
d
Gap between the two arms
15µm
h
Thickness of each arm
2µm
t
Thickness of substrate
1µm
X
Width of wafer
30µm
L
Length of wafer
7mm
Ld
Length at which the linear waveguide
Tw
splits into two arms
3mm
Thickness of wafer
7µm
54
5.2 Propagation Of light through the device
The light launched within the Optical Y-junction power splitter is using the Laser
emitting light at the wavelength of 1.55µm.The simulations are obtained for the device
using passive and active components (use of micro heater driven externally).
5.2.1 Propagation of light through the parallel arms of Y-junction
FEMLAB software is not used to present the top view of the Optical Y-junction
power splitter. The Beam Propagation method is used to view the top view in 2D when
the device is acting as passive device (without any active component, like micro heater).
The device length is 7mm whereas the gap maintained between the two arms is 15µm
with the constant width of core being 5µm,as shown in Fig 5.2 below.
Fig 5.2 The top view of the buried type Y-junction power splitter (using BPM)
55
Fig5.3 Showing the simulation within passive waveguide using BPM
The top left quadrant in Fig 5.3 gives the topographical map of Optical field.
However the Optical field is basically the electric field designated as ‘E’
in the
electromagnetic waves derived by Maxwell’s Equations. This field is generated when
the device is passive without any active component. The top left quadrant of Fig 5.3
presents the 3D graphical representation of the generated field amplitude which varies
with the thickness of the two arms of the junction. The bottom left quadrant gives 2D
representation of the relation between generated Optical field with respect to the index
distribution within the waveguide . The bottom left quadrant gives the graph showing
⎛ η − η2 ⎞
⎟⎟ with respect to width and Electric
3D representation of effective index varying ⎜⎜ 1
⎝ η1 ⎠
field
56
5.2.2 Propagation of light through S-bends of Y-junction
It is observed practically the considered buried type waveguide doesn’t hold
tapered edges but S-arcs are present at the edges. Fig 5.4 a) shows one of the S-arcs/Sbend present in Optical Y-junction power splitter.
The S-bend however leads to attenuation and fiber curve/bend loss which are
discussed further. This is due to the enrgy in the evanescent field at the bend exceeding
the velocity of light in the cladding and hence the guidance mechanism is inhibited,
which causes light energy not to be radiated from the fiber.
Fig 5.4a) The top view of the S-bend of buried type Y-junction power splitter (using BPM)
57
Fig5.4b) Showing the simulation within S-bend of waveguide using BPM
The obtained Fig 5.4b) using Beam Propagation Method provides the simulation
in a window form with four sections. Each quadrant presents a specific relation among
various parameters. The top left quadrant gives the topographical field in S-bend when
Y-junction behaves as the passive waveguide. The top right quadrant gives the 3D
representation of the field amplitude within S-bend. The bottom left quadrant shows the
graphical relation between field and effective index distribution with S-bend in two
dimensional form. This simulation result is obtained when no active component like
micro heater is used for the thermal coupling. However, the further results show the
simulations using active component like micro heater placed on one of the S-curves of
the Optical Y-junction power splitter.
58
5.3. Electric field generated within the two branches of Y-Junction
In this project we consider buried type waveguide which means the cladding of
refractive index,η1 is sandwiched between cladding of refractive index,η3.As the
refractive index within the guide is η1, the optical wavelength in this region is reduced to
λ/ η1. When θ is the angle between the wave propagation vector or the equivalent ray
and the guide axis,the plane wave can be resolved into two component plane waves
propagating in the z and x directions. The component of the phase propagation constant
in the z direction βz is given by
β z = η1k cosθ
(5.1)
The component of the phase propagation constant in the x direction βx is
β x = η1k sin θ
(5.2)
The optical waveguide supports both TE and TM modes in transverse direction
which exhibit their own propagation constants. Hence the light propagating within the
guide is formed into discrete modes,each typified by a distinct value of θ. These modes
have a periodic z dependence of the form exp(-jβzz) where βz becomes the propagation
constant for the mode as the modal field pattern is invariant except for a periodic z
dependence.
When light is described as an electromagnetic wave it consists of a periodically
varying electric field E and magnetic field H which are oriented at right angles to each
other. The propagating modes are said to be transverse electric (TE) when the electric
field is perpendicular to the direction of propagation and hence Ez=0, but a
corresponding component of the magnetic field H is in the direction of propagation.
59
Alternatively, when a component of E field is in the direction of propagation, but
Hz=0,the modes formed are called transverse magnetic(TM).The mode numbers are
incorporated as TEm. However in this project we considered only the TE modes. The
incoming power excites the fundamental mode till device symmetry exists.
Fig 5.5a) The transverse normalized mode field distribution of mode0 at Ld =2.5mm where Ld is length of
the device.
As soon as the waveguide arm1 is slightly wider (asymmetric -junction) or its
index of refraction is lowered by means of a heater the fundamental mode starts shifting
into arms with higher index while the second mode shifts in the arm with lower index. A
ray of light travels more slowly in an optically dense medium than in one that has less
dense, and the refractive index gives a measure of this effect. The light beam deviates
from it’s path as son as the refractive index of heated arm starts decreasing. The Fig
5.5a) shows the fundamental mode excited within the linear waveguide before it splits
into Y-junction arms that is at a distance of 2.5mm from origin.. In this figure it is
assumed that the interference forms the lowest order (where m=0) standing waves,
where the electric field is a maximum at the centre of the guide decaying towards zero at
the boundary between the guide and cladding.
60
To visualize the dominant mode propagating in the z direction we consider plane
waves corresponding to rays at different specific angles in planar guide. These plane
waves give constructive interference to form standing wave patterns across the guide
following a sine or cosine formula. Figure 5.5.b) shows such rays for m=1 together with
the electric field distribution x-direction. The letter m denotes the order of the mode and
is know as the mode number. This mode corresponds to the lowest cut off frequency,fc10
f c10 =
1
2a µε
(5.3)
and is denoted as TE10 (m=1,m=0) mode. Thus the TE10 mode is the dominant mode
and is the overall dominant mode of the Optical waveguide.
Fig55b). Mode1 at Ld=4.5mm,X=10µm
61
The effects become more stronger with increasing the refractive index difference
by means of heating process. Finally the modes are exclusively localized in arm with
higher refractive index ,leading to the phenomenon of thermal coupling. This mode is
known as the dominant mode, as shown in Fig 5.5c).
Fig5.5c). showing the fundamental exclusively excited in the non heated arm.
Power in terms of electric field modes is also calculated, taking only the real part
of the cross product integral of electric field’E’ and magnetic field’H’. The power flow
down the waveguide for the TE10 mode is calculated as :
a
P10 =
=
b
1
Re ∫ ∫ E × H ∗ zˆdydx
2 x =0 y =0
ωµa 3 A10
4π 2
(5.4)
2
Re(β )
(5.5)
62
5.4 Thermal distribution within waveguide
In this project, the performance of a thermo-optic waveguide structure is
investigated using Femlab software mode solvers. In the TO waveguide structure a Gold
metal,Au heater, is located on top of polymer waveguide, generating thermal energy. It
is assumed that the waveguide structure is infinite in extent in the direction of the
propagation wave (Sewell,P. et al,2002)
Using two dimensional heat transfer we simulated for buried type waveguide
structure. In this design the core of the structure is used Polyurethane(PUR) and the
cladding is made by Polymethymethacrylate(PMMA). Fig 5.6 shows the thermal model
with width of heater 5 µm and thickness being 2.5µm. and the distance between heater
to the core is 2.5µm. Size of the core is 2.5µm x 5µm. Temperature at the heater is
100K. The distribution of the heat can be seen clearly surface and contour plot, referring
Fig 5.6. The maximum temperature 200K.
.6 2D thermal distribution with core dimension 2.5µm× 5µm and H= 2.5µm, at heater
temperature 300K using FEMLAB 2.0
63
Consequently, longitudinal heat flow can be neglected and only the crosssectional temperature distribution is studied. Heat transfer from the heater to the air
cladding is also neglected. By controlling the electrical power supplied to the heater the
temperature profile inside the structure and hence the associated change in refractive
index is calculated.
In order to obtain separate temperature profile plots of the obtained simulation on
various geometry cross sections in FEMLAB the Draw line for Cross Section line plot
button is used for drawing a line across the area we need to know the temperature
profile. In Fig 5.7a) the line is drawn between heater and core to obtain the temperature
profile. However this temperature profile is obtained in the S-curve of the waveguide at
z= 4mm.
Fig5.7a) Temperature profile plot at z=4mm with fixed heater distance, H=2.5m.
64
Fig5.7b) Graph plotted shows waveguide temperature versus boundaries of the core (S-bend at
z=4mm) with fixed heater distance, H=2.5m.
The red line shows the temperature profile in S-bend of waveguide where the
temperature varies with the arc length. The arc length defines the radius of curvature of
S-bend. with respect to the central axis In this case the radius of curvature is taken as
3.5mm. The graph shows that the flow of heat is maximum where the S-bend connects
the input linear waveguide with the end linear waveguide or where the arc ends.
The heater electrode in the S-bend region is located along the inboard side of the
S-bend. The electrode in the Y-junction and the S-bend is connected in series to simplify
the control of the switch.
The next stage is made to see the effect of heat generated by the electrode on the
unheated arm. The Fig 5.8a) shows the temperature profile calculated in between the two
arms of the Y-junction. The line is drawn between the two arms across the whole wafer
65
as can be seen from the figure below. The width of the heater is 5µm and thickness
being 2.5µm. The heater is placed at 2.5µm from core.
Fig5.8a) Temperature profile plot at the gap between two parallel arms of the waveguide) with
fixed heater distance, H=2.5m.
Fig5.8b) Graph plotted shows waveguide temperature versus boundaries of the core (gap
between two parallel arms of the waveguide) with fixed heater distance, H=2.5m.
66
It can be well seen from Fig. 5.8b) the temperature profile within the gap ranges
from 0 to 16K only. The graph indicates that very less amount of heat generated by
electrode on arm1 reaches to arm2. Therefore the refractive index of arm1 changes
tremendously; whereas the refractive index of arm2 remains same thereby deviating the
light path (power) from arm1 into arm2.The change of refractive index with temperature
depends on two counteracting effects : change in density cause by positive or negative
coefficient of thermal expansion(CTE) and the increase in polarizability with
temperature (Blum,R. 2003).
5.5 Optimum Configurations of Y-junction
Besides design and simulation of Optical Y-junction power splitter, the intention
of this investigation is a qualitative description of the Crosstalk performance of Digital
Optical switch and Mode conversion factor with respect to refractive index change
,branching angle, driving power and attenuation in S-bend.
5.5.1 Mode conversion factor And Refractive index Change
Qualitatively mode coupling is described by mode conversion or coupling
coefficients and the phase relation between the two modes. The fundamental mode is
launched in the input channel waveguide, which gradually transforms itself to the
fundamental system mode of the combined branches. The division of the modal power
over the two arms is related to the opening angle α and effective indices of the output
67
branches. It is known if |MCF| <<0.43 the Y-junction acts as symmetric power splitter
and if |MCF|>> 0.43 then nearly all output power is concentrated in the branch with
highest effective index. However this project involves an active component (micro
heater) to change the refractive index, thus analysis is made using asymmetric
waveguide for which the value of MCF must come to be greater than 0.43
The mode conversion coefficients reach a maximum for a certain waveguide
separation along the structure. The results show by increasing refractive index difference
the maximum is reached for smaller opening angle,α and thus smaller waveguide
separation. We carried the analysis by keeping constant values for α but varying the
refractive index difference using MATLAB and obtained the figure 5.9a).The best
suitable value at which mode conversion factor is appreciable with respect to other
parameters like crosstalk is α=0.3o
Fig5.9a) Mode conversion factor And Refractive index Change
68
5.5.2 Crosstalk and Mode conversion factor
As the temperature is raised using Gold, Au electrode, the effective index
contrast between the branches will increase, causing gradual shift of power from one
arm to another. It is possible to relate the switching behavior and mode conversion factor
in a quantitative way by means of Crosstalk. However, crosstalk provides the measure of
directional isolation of power in heated arm achieved by the device. Low power in the
second mode is very important for the performance of a Digital Optical switch which is
judged by Crosstalk and Insertion loss.
The analysis is made using various formulations showing the direct
proportionality between crosstalk and mode conversion factor. The Fig 5.9b) shows that
with the increase in refractive index change the crosstalk gets decreased in the heating
arm.. It is seen from the results that if the branching angle is as small as 0.10 the
crosstalk is also small but the length of the device becomes larger for a digital switching
characteristics, it can even exceed 2cm. Hence, larger angle 0.30 is considered in this
analysis which leads to mode conversion factor higher than 2.32 and crosstalk smaller
than -30dB.
Fig5.9b) Plot showing relationship between Crosstalk and Mode conversion factor
69
5.5.3 Attenuation in S-bend And Heating
By introducing the active component like micro heater (Au electrode) driven by
external supply in the device, attenuation is recorded in the S-bend more than any other
region within the Y-junction. The reason is that the guidance mechanism gets inhibited
when the energy in the evanescent field at the bend exceeds the velocity of light in the
cladding which may cause the light energy to be radiated into the cladding causing light
energy to radiate into cladding. Thereby causing attenuation in S-bend. With increase in
heat power, the light in the S-bend gets attenuated which is analyzed using BPM (Beam
Propagation Method) as shown in the Fig. 5.9c)
The figure shows the attenuation as a function of heat power. It is seen with the
increase in heat power the attenuation in S-bend is found decreasing. At heating power
of 140mW,the corresponding attenuation in S-bend is found to be -30dB.
Fig5.9c) Plot showing relation between Attenuation in S-bend And Heating Power
70
5.5.4 Crosstalk and Heating Power (Coupling Efficiency)
As the temperature is increased, the optical power will gradually shift from one
output channel to the other. This switching behavior is simulated in BPM. The obtained
Beam Propagation Method result shows that the obtained crosstalk is -50dB for heat
power of 140mW. This graph provides the efficiency of the device. It is seen that the
crosstalk for heated arm starts decreasing however for unheated arm it remains the same.
Fig5.9c) Plot showing the relationship between Crosstalk and Heating Power(Coupling
Efficiency)
71
CHAPTER 6
FUTURE WORK AND CONCLUSION
This project dealt with the investigation of parameters such as waveguide
configuration and structure, the branching angle and index change needed in order to
give stable switching characteristics, lower power consumptions, high switch speed and
low crosstalk, using the heating phenomenon. The thermal analysis became an important
issue when considering TO waveguides. A low power consumption splitter, dissipating
140mW, and having length of approximately 7mm and a branching angle of 0.3 degrees,
resulted as the optimum device in this research work.
6.1 Thermal Analysis Model
The thermal analysis is made on a buried type S-bend waveguide structure. The
research and investigation has been done on how thermal coupling is obtained by
heating phenomenon. By using the thermo optic effect (TO), the interaction occur
72
between heat and light causing the change in refractive index. The change in refractive
index with temperature depends on two counteracting effects: (1) The change in density
caused by positive or negative thermal expansion coefficients (CTE) and (2) The
increase in polarizability with temperature (Robert Blum,2003).Effective index change
depends on the distance from heater to the waveguide core(H). It was observed that as
the temperature of one electrode is raised, the optical power will gradually shift from
one output channel to other, leading lower crosstalk in the heated arm and thus low
excess loss. Next, a start field is calculated for the structure, in this case the field of the
fundamental channel mode.
The field is propagated through the structure using 2D BPM. In order to avoid
excessive heating of the waveguide material we made use of maximum electrode heating
temperature(300K) is 30K above the heat sink temperature. The reason behind setting
the temperature was the branching angle considered in the design is 0.150. And this
requirement is met only by the designs with DOS angles smaller than 0.2 degrees
because they have a switching temperature lower than 30K. The temperature profile
within the wafer was obtained using FEMLAB. the effect of heating by using the gold
electrode was measured at various geometrical points within wafer like between the two
channels, between the heater and the core. Also the crosstalk and the mode conversion
factor, two contributing factors for all investigation were measured for various
branching angle values.
6.2 Thermal Coupling Model
In this part, we are considering the effect of heat on buried type waveguide. Heat
generate by micro heater spread out causing the temperature of nearby waveguide arm to
73
increase. Thermal coupling is related to waveguide spacing and branching angle. The
coupling estimation is increased with the increase in the waveguide depth but increase in
waveguide spacing.
6.3Future work
After design of low crosstalk, low power consumption and compact size Optical
Y-junction power splitter, the future work involves the design of such a switch which
will overcome the S-bend attenuation and will decrease the crosstalk more in cascaded
stages.
6.3.1 Variable Optical Attenuator (VOA)
The Digital Optical switch (DOS) has attracted extensive attention due to its
promising applications in dense wavelength –division-multiplexing systems. The
polymer material has been widely used in the fabrication of various integrated optical
devices. Furthermore, the temperature stability and transmission loss of the polymer
material have also been greatly improved. To achieve low crosstalk in the output of the
switch, the branching angle needs to be very small(0.050-0.150), which makes
fabrication of the device quite difficult.
74
For large-scale integration of photonic switches, it is, therefore , preferable to
increase the branching angle substantially and employ to reduce the crosstalk to
acceptable levels. The S-bend waveguides in 1x2 DOS can be designed as VOA. The
integration of the S-bend VOA will decrease the crosstalk dramatically, without
increasing the length or complexity of the device.
Fig 6.1 Top view of DOS with S-bend VOA
75
6.3.2 Double Digital Optical Switch (DDOS)
If the crosstalk of a single 1x2 switching unit (fig 6.2a) is not sufficient, it can be
improved by cascading several of these devices and thereby multiplying the crosstalk
(dB) by the number of cascaded stages. The second stage in figure 6.2b can be simply
operated like an attenuator (discussed above in 6.2.1) reducing the cross talk in the cross
port. The attenuator functionality is also implemented by a DOS operated in reverse and
consequently the second stage can be turned around by maintain in the properties of the
switch (figure 6.2c).
Fig 6.2 Evolution from DOS to DDOS
76
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