Design and Fabrication of All-Fiber Flat-Top Interleaver for DWDM Applications

A dissertation submitted in partial fulfillment of the requirements for the

degree of

Master of Technology

(Optoelectronics and Optical communication)

by

S Ravi Kumar

(2005JOP2128)

Under the guidance of

Prof. B. P. Pal & Dr. R. K. Varshney

Departments of Physics and Electrical Engineering

Indian Institute of Technology Delhi May 2007

i

CERTIFICATE

This is to certify that the dissertation entitled “Design and fabrication of all-fiber flat-top

interleaver for DWDM applications” being submitted by Mr. S Ravi Kumar

(2005JOP2128) to the Department of Physics and Department of Electrical Engineering,

Indian Institute of Technology, Delhi, in partial fulfillment of the requirement for the

degree of Master of Technology in Optoelectronics and Optical Communication, is a

record of bona fide work carried out by him under our supervision.

The results contained in this report have not been submitted elsewhere for any degree or

diploma.

Prof. B. P. Pal Professor Department of Physics IIT Delhi

Dr. R. K. Varshney Principal Scientific Officer Department of Physics IIT Delhi

ii

ACKNOWLEDGEMENTS

I am greatly indebted to my supervisors Professor B. P. Pal and Dr. R. K. Varshney for

their invaluable support, guidance and utmost interest during the course of this project. In

ways many more than I can express, they have motivated me to work hard and taught me

to think independently. I have truly learnt much from their optimistic way of thinking.

But for their helpful inputs, this project would have been far from completion. Thanks

also to Prof. M. R. Shenoy for his kind help and suggestions.

I must thank Dr. Naveen Kumar for the time and effort he has spared for me and the

valued inputs that were given by him. I express my gratitude to Mr. Nagaraju for being

with me in the lab and creating a work environment, all during my lab work. He has

taught me the coupler fabrication technique among other useful things. Thanks to Mr.

Raja Vinayagam for providing me with the lab equipment whenever I needed.

Special thanks to Prof. Vinod Chandra and Electrical Engineering Department for

allowing me to use lab equipment which was greatly useful in carrying out this project.

I would also like to thank my classmates Krishnan, Pavan, Kapil, Praveen, Saha, Anil,

Renuka, Abhinav, Sumitha, Deepak, Anoop, Sudhir and Vidya for their support

throughout my stay in IIT.

Last, but not the least, I thank my parents and other family members for their constant

support and influencing me in every way of life.

iii

ABSTRACT

The deployment of optical networks for communication has lead to rapid development in

the area of communication. This has given rise to newer applications with greater demand

for data bandwidth. Dense wavelength division multiplexed (DWDM) optical networks

with high spectral efficiency are indispensable means to cater to present day need of

bandwidth. In this work, the focus has been on design and fabrication of all-fiber flat-top

interleaver for DWDM applications.

The concept of DWDM is introduced in the first chapter of this thesis. A fair idea of

DWDM networks is essential to understand the role of an interleaver in DWDM

networks. To enhance research and development in this field, technical specifications

have been recommended. These have been briefly discussed herein.

We have studied and analyzed various design approaches used for filters in general, and

interleavers in specific. Simulation was carried out to calculate structure parameters using

these approaches. The results have been verified by comparing with data from literature.

Design to compensate dispersion has also been studied.

A two-stage flat-top interleaver was fabricated in the lab and was characterized. The

technique to implement the interleaver has been discussed.

Polymer based optical components have several advantages and therefore have been

receiving much attention in recent years. An interleaver based on Y-junctions instead of

directional couplers, using polymer technology has been reported. But it does not have

appreciable characteristics of an ideal interleaver, like flat passband and high extinction

ratio. We have proposed and worked out a design to achieve these characteristics in a

polymer Y-junction based interleaver. This structure has been analyzed and the structure

parameters that would give the optimum characteristics have been derived.

iv

CONTENTS

CERTIFICATE...............................................................................................i

ACKNOWLEDGEMENTS...........................................................................ii

ABSTRACT .................................................................................................iii

LIST OF FIGURES ......................................................................................vi

LIST OF TABLES......................................................................................viii

Introduction....................................................................................................1

1.1 DWDM ............................................................................................................... 1 1.2 DWDM Operation .............................................................................................. 2 1.3 Technical Requirements and Specifications ....................................................... 3 1.4 Role of Interleavers/De-interleavers in Present day DWDM Links ................... 3

Interleaver Types and Design Methods..........................................................5

2.1 Interleaver ........................................................................................................... 5 2.2 Interleaver Types ................................................................................................ 5 2.3 Single-stage MZI Interleaver .............................................................................. 6 2.4 Desired Characteristics of an Interleaver............................................................ 9 2.5 Two-stage MZI Interleaver ............................................................................... 10

2.5.1 Delay line in the upper arm of the second stage ....................................... 12 2.5.2 Delay line in the lower arm of the second stage ....................................... 14

2.6 Design Approaches ........................................................................................... 16 2.7 Synthesis of Two-port Lattice Form Optical Delay Line Circuits.................... 17 2.8 Optical Half-Band Filters.................................................................................. 18 2.9 Dispersion Compensation ................................................................................. 18 2.10 Optical All-Pass Filter Structures ..................................................................... 19

Results and Discussion ................................................................................21

3.1 Simulation ......................................................................................................... 21 3.1.1 Single-stage MZI Interleaver Spectral Response...................................... 21 3.1.2 Two-stage MZI Interleaver Spectral Response......................................... 22 3.1.3 Design of Interleaver Based on the Passband Ripple ............................... 23 3.1.4 Synthesis of Two-port Lattice Form Optical Delay Line Circuits............ 26 3.1.5 Simulation for Optical Half-band Filters .................................................. 29 3.1.6 Optical All-Pass Filter Structures ............................................................. 29 3.1.7 Tolerance of Structure Parameters............................................................ 31

v

3.2 Experimental Work........................................................................................... 33 3.2.1 Fabrication and Characterization of Fused Fiber Couplers ...................... 33 3.2.2 Techniques to Achieve Optical Path Difference between MZI Arms ...... 35 3.2.3 Tuning Channel Spacing and Channel Wavelengths................................ 35 3.2.4 Estimation of the Differential Delays in a Two-stage MZI ...................... 37 3.2.5 Implementation of 2-stage MZI Interleaver.............................................. 38 3.2.6 Tuning of 2-stage MZI Based Wavelength Interleaver ............................ 42 3.2.7 Discussion ................................................................................................. 43

Y-Junction Flat-Top Interleaver...................................................................44

4.1 Introduction....................................................................................................... 44 4.2 Principle of Operation....................................................................................... 44 4.3 Parameter Optimization .................................................................................... 47 4.4 Discussion ......................................................................................................... 49

FUTURE SCOPE ........................................................................................50

BIBLIOGRAPHY........................................................................................51

Appendix A..................................................................................................53

Appendix B..................................................................................................54

vi

LIST OF FIGURES

Figure 1: Schematic of a typical DWDM optical fiber long-haul link ............................... 2

Figure 2: Schematic of different interleavers...................................................................... 6

Figure 3: Schematic of an all-fiber MZI based interleaver................................................. 7

Figure 4: A 2-stage MZI configuration 2LΔ is in the upper arm of the second stages ..... 10

Figure 5: A 2-stage MZI configuration wherein the second delay line 2L′Δ is in the lower

arm ............................................................................................................................ 14

Figure 6: Configuration of coherent two-port lattice-form optical delay-line circuit....... 17

Figure 7: A 2 x 2 FIR optical half-band filter circuit configuration ................................ 18

Figure 8: Ring cascade architecture for all-pass optical filter ......................................... 20

Figure 9: Simulated spectral response in linear scale at Port 3 of the MZI-based

interleaver ................................................................................................................. 21

Figure 10: Simulated spectral response in log scale at Port 3 of the MZI-based interleaver

................................................................................................................................... 21

Figure 11: Simulated spectral response of a 2-stage MZI interleaver .............................. 22

Figure 12: Variation of 0.1dB-passband width with increasing passband ripple ............. 23

Figure 13: Variation of 0.5dB-passband width with increasing passband ripple ............. 23

Figure 14: Variation of 25dB-stopband width with passband ripple................................ 24

Figure 15: Variation of crosstalk with passband ripple .................................................... 24

Figure 16: Matlab GUI to calculate the structure parameters and the interleaver

characteristics based on channel spacing and the specified passband ripple............ 25

Figure 17: Linear Chebyshev filter designed using optical delay line circuits................. 26

Figure 18: Multi-channel selector filter designed using optical delay line circuits .......... 27

Figure 19: Transmittance and relative group delay in a group-delay dispersion equalizer

................................................................................................................................... 28

Figure 20: Group delay equalization for 2-stage MZI interferometer .............................. 30

Figure 21: Spectral response when deviation of coupling ratios is 5% from the optimum

values ....................................................................................................................... 31

vii

Figure 22: Spectral response when deviation of delay lengths is 1µm from the optimum

value.......................................................................................................................... 32

Figure 23: Photograph of the fusion fiber coupler fabrication rig .................................... 33

Figure 24: Experimental set-up used to measure the wavelength response of an all-fiber

MZI ........................................................................................................................... 38

Figure 25: Photograph of the two-stage MZI interleaver that was fabricated in the lab .. 39

Figure 26: Power spectrum of EDF broadband source used for the experiment .............. 39

Figure 27: Power spectrum of EDF broadband source over a range of 2nm.................... 40

Figure 28: Spectral response 1-stage interleaver before tuning........................................ 41

Figure 29: Spectral response 1-stage interleaver after tuning........................................... 41

Figure 30: Spectral response of 2-stage interleaver during the process of tuning ............ 42

Figure 31: Spectral response of partially tuned 2-stage interleaver.................................. 43

Figure 32: Schematic diagram of Y-junction based 2-stage MZI interleaver .................. 45

Figure 33: Spectral response of a Y-junction based 2-stage interleaver........................... 48

Figure 34: Optimum values of ΔβS1 and ΔβS2 when both the delays are on the same side

................................................................................................................................... 48

Figure 35: Optimum values of ΔβS1 and ΔβS2 when both the delays are on opposite sides

................................................................................................................................... 49

viii

LIST OF TABLES

Table 1: Simulated structure parameters for the designed Linear Chebyshev filter ......... 26

Table 2: Simulated structure parameters for the Multichannel selective filter ................. 27

Table 3: Simulated structure parameters for the designed group-delay dispersion

equalizer.................................................................................................................... 28

Table 4: Circuit parameters for Maximally-flat Half-band filter...................................... 29

Table 5: Circuit parameters for Chebyshev Half-band filter. ........................................... 31

Table 6: Zeros, poles and circuit parameters for dispersion equalizer for an optimized 2-

stage MZI interleaver................................................................................................ 29

Table 7: Effect of additional stages in all-pass filter for equalizing dispersion................ 30

Table 8: Typical measured characteristics of the couplers fabricated .............................. 34

Table 9: Optimized splitting ratios of the 3 couplers K1, K2 and K3 in a 2-stage MZI-

based interleaver when the delay line effnLL 2/2 12 λ±Δ=Δ in the upper arm ....... 53

Table 10: Optimized splitting ratios of the 3 couplers K1, K2 and K3 in a 2-stage MZI-

based interleaver when the delay line 12 2 LL Δ=Δ is in the lower arm.................... 53

Table 11: Optimized parameters for a 2-stage MZI configuration using Y -junctions when

the delay is in the upper arm..................................................................................... 54

Table 12: Optimized parameters for a 2-stage MZI configuration using Y -junctions when the delay line is in the lower arm line is in the lower arm……………………………….54

i

1

Chapter 1

Introduction

To meet bandwidth demand and make optimum use of existing amplifier

bandwidth, dense wavelength division multiplexing (DWDM) systems must offer higher

channel counts at narrower channel spacing and the requirements are on an incessant

increase [1]. Use of 160 channels with 40 Gbps bit rate per channel is quite common

today. A number of different DWDM technologies exist to meet the needs of system

designers, but each forces design tradeoffs in terms of narrowness of channel spacing,

cost, reliability, and manufacturability. Nowadays, interleaver technology is being

deployed as it allows designers to achieve narrow channel spacing with mature

technology.

1.1 DWDM The predominant aspect of a DWDM communication link is that several

wavelengths (at least four), each carrying digital signals @ ≥2.5 Gbit/s, could be sent

through a single-mode fiber simultaneously within the 1530-to-1610-nm gain bandwidth

of a fiber amplifier with inter-channel spacing ≤ 200 GHz. The key features of DWDM

are

Transmission capacity upgradation: As demand for bandwidth grows, each wavelength

channel can carry data at independent data rates and can be upgraded independently.

Transparency: Each optical channel can carry data in any transmission format and at any

data rate. This makes the network design and engineering simpler and more flexible as

there is no need for common signal structure.

Wavelength routing and switching: Wavelength can be exploited as a new dimension for

routing besides space and time. Further, wavelength-switched architectures allow

2

reconfiguration of optical layer. Optical add/drop multiplexers, optical cross connects and

wavelength converters are used for implementation of these networks.

1.2 DWDM Operation DWDM networks are sought after to utilize the enormous transmission bandwidth

of an optical fiber beyond what could be achieved by simply increasing the bit rate of a

transmitter-receiver pair. In DWDM, multiple transmitters, each at a different

wavelength, are combined onto a single fiber by a multiplexer (Mux). At the other end, a

demultiplexer (DeMux) separates out the wavelengths into separate receivers. In this

way, multiple transmitter-receiver pairs share the same fiber. The schematic of a typical

modern DWDM optical link is shown in Fig1.

Figure 1: Schematic of a typical DWDM optical fiber long-haul link[11]

A genre of high-quality semiconductor lasers, called distributed-feedback (DFB)

lasers, is typically used in a DWDM system. Electronic digital inputs modulate individual

lasers, each emitting at a different peak wavelength. The spectral linewidth of modulated

output of a DFB laser is typically of the order of 10-3 nm. An array of DFB lasers, each

tuned to a different but well-defined and standardized wavelength are used. Interference

among the wavelength channels is avoided and the integrities of the independent signals

Laser Diode at ITU Wavelengths

OE

Multiplexer

EDFA EDF

Long Bragg Circulator

EDF

Demultiplexer OE

OE

OE

OE

OE

λ

λ

λ

λ

λλ

λ3

Add-Drop multiplexer

Optoelectronic Converter

Isolator

λ3

3

from each source are maintained for subsequent filtering and conversion to electrical

signals at the receiving end by sufficiently spacing them from their neighbours.

1.3 Technical Requirements and Specifications To coordinate and facilitate the growth of DWDM fiber links, International

Telecommunication Union (ITU) has set certain wavelength standards, referred to as ITU

wavelength grids, for DWDM optical transmission systems. As per ITU standards (ITU-

T recommendation G.692), the reference frequency ( 0ν ) is chosen to be that

corresponding to the Krypton line i.e. 193.1 THz. (≡ 1552.52 nm in wavelength), and the

chosen channel spacing are expected to follow the relation

νΔν ±0 (THz) = 193.1 ± 0.1I, where I is an integer.

The recommended standard channel spacings are 200 GHz (≡ 1.6 nm), 100 GHz (≡ 0.8

nm), 50 GHz (≡ 0.4 nm), and 25 GHz (≡ 0.2 nm). It is to be noted that ITU standards

specify fixed frequency spacing, rather than constant wavelength spacing. Variations in a

laser’s peak wavelength lead to crosstalk between adjacent channels. Therefore it is

necessary to keep the variations in wavelength small compared to the spacing between

adjacent channels i.e. a laser signal should be prevented from “wandering” into an

adjacent channel in a DWDM stream. One would have to use the manufacturer’s design

specifications for a particular DWDM system. Those specifications may be tighter than

the 10% allowed by ITU.

1.4 Role of Interleavers/De-interleavers in Present day

DWDM Links Due to the difficulties encountered in attaining high-speed electronic components at

speeds beyond 40 Gbit/s, increase in the number of channels has evolved as the best near-

term option to achieve high spectral efficiency.. This can be done in two ways

1. Increasing the operational communication bandwidth per channel.

2. By decreasing the inter-channel spacing.

4

These two aspects are combined to define spectral efficiency, which refers to the

amount of information that can be transmitted over a given bandwidth.

A DWDM optical network requires a variety of passive and active components like

wavelength multiplexers/de-multiplexers, EDFAs, gain flattening filters for EDFAs, add-

drop multiplexers, dispersion compensators, bandpass filters, lasers, and so on. Since,

most of the current DWDM networks operate in the C-band, which corresponds

approximately to the gain band from 1530 nm to 1565 nm of an erbium doped fiber

amplifier (EDFA), increasing the operational communication bandwidth involves

replacing the present components. The newer components would be costlier as they

would require technologies different from the ones used presently. Also, additional

amplifiers have to be used for the other bands namely, L-band (1570 nm - 1620 nm) and

S-band (1480 nm ∼ 1525 nm).

The alternative option, i.e. to decrease the inter-channel spacing, is generally preferred.

But, this would still mean replacing some components for e.g., filters with narrower

passbands would be required at the receivers, which is also expensive. Interleavers/de-

interleavers provide an easy solution in this regard and therefore have received much

attention.

5

Chapter 2

Interleaver Types and Design Methods 2.1 Interleaver Interleaver/de-interleaver is an optical filter with a periodic response that is capable of

separating a comb of densely spaced signal channels into several sets of channels with

wide channel spacings or doing the converse [3]. Because of the periodic nature of

interleave filter, its transfer function consists of fewer number of Fourier components

compared to, say, add/drop filters. For this reason, the interleaver is simpler to realize

than other filters.

2.2 Interleaver Types As a functional block, interleavers can be considered to be of different types [4]

1:2 interleaver: It combines two or more input streams of wavelength-channels

having a constant spacing νΔ in the frequency domain into a single dense stream of

channels with separation 2/νΔ at the output (see Fig. 2a ). When operated in the reverse

direction, it separates the even and odd signal channel streams.

1:4 interleaver: The natural extension of the 1:2 interleave filter is the periodic

separation of one in every 2n channels, such as 1: 4 demultiplexer depicted in Fig. 2b.

This device has four different output ports. This kind of interleaving (i.e. 1:2n) can also be

achieved by cascading 2n-1 stages of 1:2 interleave filters.

Banded interleaver: This type of interleaver separates/combines, one stream of

wavelength channels into two bands of channels, coming from the two different output

ports, periodically. It is difficult to fabricate such device in practice because the

6

requirements to achieve sharp skirt for the filter to meet the ITU specifications are very

tight.

Asymmetric interleaver: The other variation in contrast to the three types of

interleaving mentioned above is the asymmetric interleaver which separates one

wavelength from the stream of wavelength channels such that one channel appear at one

output port whereas the remaining (n-1) channels exit from the other output port

periodically i.e. it separates one channel out of n.

Figure 2: Schematic of different interleavers. a) 1:2 interleaver b) 1:4 interleaver c) Banded interleaver d) Asymmetric type interleaver

2.3 Single-stage MZI Interleaver An all-fiber single-stage unbalanced MZI can be formed by splicing two 2×2 fiber

couplers in such a way that the lengths of the two arms are slightly unequal [5] by an

amount 1LΔ . The differential path length ( 1LΔ ) is equivalent to a differential delay line in

one of the arms. The corresponding differential phase delay 1ϕ suffered by the channel

wavelength λ is given by

λΔπϕ /2 11 Lneff=

1:2

Banded 4:8

a)

c)

d)

λe

λb2

Asym 1:8

λa1

λa7

λo

1:4 b)

λa

λb

λc

λd

λb1

λ……..

λ……..

λ……..

λ……..

(2.1)

7

where )(λeffn is the effective index of the guided mode at λ .

Figure 3: Schematic of an all-fiber MZI based interleaver, realized through concatenation of two 3-dB couplers; ΔL1 represents a delay line in the upper arm of the interferometer.

The transmission characteristics of an interleaver based on MZI can easily be described

in terms of transfer matrices of the individual couplers and the differential delay lines [6].

From the coupled mode equations for the electric field amplitudes, the transfer matrix for

the coupler is given by

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

cjsjsc

M coupler

where )cos( zc κ= , and )sin( zs κ= ;κ is the coupling coefficient and z is the interaction

length of the couplers. The transfer matrix corresponding to the differential phase delay

1ϕ between the two arms is given by

⎟⎟⎠

⎞⎜⎜⎝

⎛=

1001

1

ϕ

Δ

j

Le

M

Thus, product of the transfer matrices for the couplers with those of the differential delay

line would yield the transfer function of an unbalanced MZI (shown in Fig. 7), and is

given as

12 1 couplerLcouplerMZI MMMM Δ=

If 1E and 2E are input fields to the MZI at Ports 1 and 2, respectively, then the output

fields TE and CE at Ports 3 and 4 can be expressed as

Port 1

Port 2

3 dB 3 dB

Port 4

Port 3Coupler 1 Coupler 2

)( 22 λP

LΔ

)( 11 λP

4P

),( 213 λλP

(2.4)

(2.2)

(2.3)

8

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

2

1

EE

MEE

MZIC

T

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

2

1

11

11

22

22

1001

EE

cjsjsce

cjsjsc

EE j

C

Tϕ

where ii zc )cos(κ= , iz)sin(si κ= , i = 1, 2.

Thus, if *1 1 1 1 1 1( ) ( ) ( )P E Eλ λ λ= =1 and )()()( 2

*22222 λλλ EEP = =1 represent the normalized

powers at the two input ports, corresponding to the channel wavelengths 1λ and 2λ ,

respectively, then the fractional output powers at the throughput and coupled ports are

respectively given by

* 2 21 1 1 21 1 2 2

( ) ( )( )sin ( )cos2 2T T TP E E P Pϕ λ ϕ λλ λ= = +

* 2 21 1 1 21 1 2 2

( ) ( )( ) cos ( )sin2 2C C CP E E P Pϕ λ ϕ λλ λ= = +

The splitting ratios of the couplers 1 and 2 in the MZI configuration have been assumed

to be 50:50. In order to achieve wavelength interleaving by an unbalanced MZI

configuration, the differential phase 1ϕ has to satisfy either of the following conditions:

πλϕ )12()( 11 += n and πλϕ n2)( 21 = ; (PC = 0, PT = Pmax)

or

πλϕ n2)( 11 = and πλϕ )12()( 21 += n ; (PT = 0, PC = Pmax)

where n is an integer. From Eq. (2.9) and Eq. (2.10), we can observe that

πλϕλϕ =− )( ( 21 11 ) .

Thus, by substituting the values of )( 11 λϕ and )( 21 λϕ in Eq. (2.1), we get

λΔλλ

Δeffn

L2

211 =

Physically, if the DWDM signal channels are input at Port 1, the signal wavelengths that

suffer a differential phase delay of π)12( +n will exit through Port 3, and the

wavelengths that suffer a differential phase delay of πn2 will exit from Port 4. These

wavelengths correspond to the peaks in the spectral response. The single-stage MZI

exhibits a sinusoidal spectral response at the output ports 3 and 4 that are complementary.

(2.5)

(2.7)

(2.6)

(2.8)

(2.10)

(2.9)

(2.11)

(2.12)

9

The wavelength separation between the consecutive peaks at any output port represents

the free spectral range (FSR) of the MZI; the FSR is determined solely by 1ϕ between the

propagating signals in the two arms of the MZI. If we change 1LΔ by an amount

effn2/λ (which introduces an additional phase change ofπ ), the spectral response at the

output ports gets reversed.

The spectral response of the single-stage MZI is shown in Fig.7 of next chapter.

2.4 Desired Characteristics of an Interleaver

Low insertion loss: Any component used in a DWDM network has to be of low insertion

loss since a lossy device would lead to attenuation of signal and thus degradation of

signal-to-noise ratio, even after amplifying. Any initial imbalance in channel-power will

have a cascading effect, as the signal is normally required to pass through multiple stages,

and may affect the signal-to-noise performance of the system

Wide Pass band: The wavelength emitted by the laser source in the transmitter can vary

slightly due to changes in ambient conditions like temperature. The components used

should allow for this small variation.

Wide Rejection band: The power in the rejection band should be considered as noise to

the channel from other channels (crosstalk). Also this would reduce the power in the

passband leading to higher insertion loss.

High extinction in the Rejection band: The response at the rejection band is the power

that would be coupled as crosstalk from this channel to other channels. Hence, the

attenuation in the rejection band should be as high as possible.

Good wavelength accuracy: The interleaver’s spectral response should not change over

time and should be fixed to the DWDM wavelength grid specified by the ITU. The

variation in spectral response can lead to severe performance degradation through

attenuation of signal as well as crosstalk from adjacent channels.

10

Low dispersion: The filters and other components used in DWDM networks have strict

requirement of low dispersion since very high bit rates (40 Gbps, typically) are used.

Low Polarization dependency: The various kinds of polarization dependencies like

polarization mode dispersion (PMD), polarization dependent loss (PDL), and polarization

dependent wavelength shift (PDλ) cause loss of signal and have to be avoided.

Uniformity across channels: The interleaver should have uniform spectral response over

the optical bandwidth used for DWDM, since the transmission characteristics should be

independent of the wavelength used for transmission.

2.5 Two-stage MZI Interleaver

A 2-stage MZI configuration has been proposed to meet the just discussed requirements

[7]-[9]. It can be realized by concatenating three couplers through two differential delay

lines in the two stages, as shown in Fig. 4. In order to achieve a uniform flattop response

with minimum insertion loss, one has to choose optimum splitting ratios for the couplers

K1, K2, and K3, as well as magnitudes of the differential delay lines 1LΔ and 2LΔ .

Figure 4: A 2-stage MZI configuration realized by concatenating three couplers K1, K2, and K3; the two delay lines 1LΔ and 2LΔ are introduced in the upper arms of the first and second stages, respectively

The phase difference between the fields E13 and E14 at ports 3 and 4 of the single-stage

MZI configuration (see Fig. 3) plays an important role in deciding the magnitude of the

delay line to be introduced in the second stage for achieving a flattop spectral response of

)( 11 λP

4P3 dB

K1 K2

)( 22 λP

1LΔ

K3

2LΔ),( 213 λλP

11

the 2-stage MZI; Considering unit input at only port1, the resultant output fields at Ports

3 and 4 are given as [5, 6]

212113 1 sseccEE jT −== ϕ

)( 212114 1 csescjEE jC +== ϕ

If the splitting ratio of the first coupler is 50:50, and that of second coupler is more than

50: 50 (i.e. s2 > c2), the phase difference (θ) between the output fields E13 and E14 is given

by [11]

1413

14131 .cos

EEEE

−=θ (s2 > c2)

Likewise, if the splitting ratio of the first coupler is 50:50 and that of second coupler is

less than 50:50 (i.e. c2 > s2), the phase difference (θ) between the output fields E13 and E14

is given by [11]

1413

14131 .cos2

EEEE

−−= πθ (c2 > s2)

It is imperative from the Eq. (2.15) and (2.16) equations that the magnitude of the

optimum delay-line in the second stage would depend on whether the splitting ratio of the

second coupler is more, or less than 50:50. Often a compromise is made between

achieving a flattop passband and a low insertion loss, since additional filtering elements

are usually added to an original sinusoidal passband shape to achieve a uniform flattop

response.

Position of the Second Delay Line

To realize a 2-stage MZI configuration with a flattop response, a second 2×2 coupler is

concatenated to a single-stage MZI with an optimum differential delay line in the second

stage. There are two possible choices for a designer- the second delay line could be

introduced either in the upper arm or in the lower arm of the second stage of the 2-stage

MZI [12, 10]. Though these two optional configurations appear to be apparently

identical, the performance of these two configurations are dictated by the splitting ratios

of the constituent couplers as well as the phase differences between the fields at ports 3

and 4, and also by the magnitude of the delay lines in the second stage.

(2.13)

(2.14)

(2.15)

(2.16)

12

2.5.1 Delay line in the upper arm of the second stage The transfer matrix corresponding to this 2-stage MZI configuration is given by [9, 12]

1232 12 couplerLcouplerLcouplerstageMZI MMMMMM ΔΔ=−

If the DWDM signal channels are input at Port 1, then the output fields at Ports 5 and 6

can be expressed as

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛− 0

12

16

15stageMZIM

EE

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛01

100

100

11

11

22

22

33

33

16

15 12

cjsjsce

cjsjsce

cjsjsc

EE jj ϕϕ

or

( ) )exp()(exp)exp( 223121132321132115 LjcssLLjcsscssLjcccE ΔβΔβΔβΔβ −+−−=

( )[ ])exp()(exp)exp( 223121132321132116 LjccsLLjccssssLjsccjE ΔβΔβΔβΔβ +++−−=

where β is the propagation constant at the channel-wavelength (λ ) such that 22 LΔβϕ =

and 11 LΔβϕ = . The fractional output powers exiting through ports 5 and 6, are given by

the relations *151515 EEP = and *

161616 EEP =

The right hand side of the Eq. (2.22) and Eq. (2.23) are similar to a finite Fourier series,

and in order to obtain a box-like (flattop) response, we must have [7, 10]

πΔβΔβ nLL ±= 12 2

( ) ( )23

22

21

23

22

21

23

22

21

23

22

21

21

212323

23

232121

1223131

2231

scsssccssccccsLsscccsLsscc

LLssscLLcscscP

++++

−+−+

−++−=

)Δcos(2)Δcos(2)ΔΔcos(c2)ΔΔcos(2

21

2132115

ββββββ

( ) ( )23

22

21

23

22

21

23

22

21

23

22

21

21

212323

23

232121

31223131

2231

ccscscsssscc

scLssccscLsscc

LLcssscLLcscscP

++++

−+−+

−−+=

)Δcos(2)Δcos(2

)ΔΔcos(2)ΔΔcos(2

21

212116

ββ

ββββ

(2.17)

(2.18)

(2.19)

(2.20)

(2.21)

(2.22)

(2.23)

(2.24)

13

where n is an integer. The earlier reports [10, 12] considered only the case of n = 0 but

Eq. (2.24) is for a more general case. The value of n should be chosen to satisfy the

condition of constructive interference. The other fundamental requirement is that the

insertion loss should be minimum, which demands constructive interference between the

channel-wavelengths coming from the ports 3 and 4 at the output of the coupler K3. Thus,

conditions for the odd- and even channel wavelengths to emerge from ports 5 and 6,

respectively, with minimum loss would be met when

πΔβΔβ )12(2 12 −±= nLnL , 22 sc < and 33 cs < .

Since the conditions for flattop and minimum loss are to be met simultaneously, Eq.

(2.24) and Eq. (2.25) imply n = 1.

Alternatively, if the odd and even channels were required to emerge from ports 6 and 5,

respectively, the condition for interference would be met when

12 2 LmL ΔβΔβ = , 22 sc ′<′ and 33 cs ′>′ .

where m is an integer; we have used the prime notation to distinguish the parameters

from those corresponding to the former case. This leads to n = 0 and m = n + 1. The

fractional output powers emanating from ports 5 and 6 are given by

( ) ( )2

32

22

12

32

22

12

32

22

12

32

22

1

21

21323

23

232121

312

231312

231

scsssccssccc

csLsscccsLsscc

LLcssscLLcscscP

′′′+′′′+′′′+′′′+

′−′′′′′+′−′′′′′+

−′′′′′++′′′′′−=′

)Δcos(2)Δcos(2

)ΔΔcos(2)ΔΔcos(2

221

212115

ββ

ββββ

( ) ( )2

32

22

12

32

22

12

32

22

12

32

22

1

21

212323

23

232121

312

231312

231

ccscscssssccscLssccscLssccLLcssscLLcscscP

′′′+′′′+′′′+′′′+

′−′′′′′+′−′′′′′+

−′′′′′−+′′′′′=′

)Δcos(2)Δcos(2)ΔΔcos(2)ΔΔcos(2

21

212116

ββββββ

Since the expression for 15P and '16P represent the two cases corresponding to the

channel streams ..,, 531 λλλ emanating from ports 5 and 6, respectively, '1615 PP = .

Similarly, 16P and '15P represent the powers corresponding to the channel streams

..,, 642 λλλ emanating from ports 6 and 5, respectively, '1516 PP = . This gives us

11 cc ′= , 11 ss ′= , 22 cc ′= , 22 ss ′= , 33 sc ′= and 33 cs ′= .

(2.26)

(2.25)

(2.27)

(2.28)

(2.29)

14

2.5.2 Delay line in the lower arm of the second stage The schematic of a 2-stage MZI configuration with the second delay-line inserted in the

lower arm (of the second stage) is shown in Fig.5.

Figure 5: A 2-stage MZI configuration wherein the second delay line 2L′Δ is introduced in the lower arm

As before, if the DWDM signal channels are input at Port 1, then the fields at the output

Ports 5 and 6 can be expresses as

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛01

100

001

11

11

22

22

33

33

16

15 1

2 cjsjsce

cjsjsc

ecjsjsc

EE j

j

ϕ

ϕ

The fractional output powers exiting through ports 5 and 6 (shown in Fig. 4), are given by

( ) ( )15 1 2 1 2

1 2

2 cos( Δ ) 2 cos( Δ Δ )

2 cos( Δ ) 2 cos( Δ )

2 21 3 2 1 3 1 3 2 1 3

2 2 2 21 2 1 2 3 3 3 2 3 2 1 1

2 2 2 2 2 2 2 2 2 2 2 21 2 3 1 2 3 1 2 3 1 2 3

T p q q q p L L p q p q p L L

p p s p L q p q p q q L q p

p p p p q p p q q q p q

β β β β

β β

′ ′= Δ + − −

′ ′+ − + −

+ + + +

( ) ( )23

22

21

23

22

21

23

22

21

23

22

21

21

212323

23

232121

31223131

2231

ppqpqpqqqqpppqLqqpppqLqqppLLpqpqpLLpqqqpT

++++

−′−−−

′−+′+−=

)Δcos(2)Δcos(2)ΔΔcos(2)ΔΔcos(2

21

212116

ββββββ

where ii zp )cos(κ= , i sin( )iq zκ= , i = 1, 2, 3. The conditions for achieving flattop

response and constructive interference for channel wavelengths 531 ,, λλλ .. and

642 ,, λλλ .. to emanate from ports 5 and 6, respectively, would be met when

12 2 LmL ΔβΔβ =′ , 22 qp > and 33 qp > .

The prime notation has been used to distinguish the parameters from those corresponding

to the former case. On the other hand, if one requires that the channel

K3 K2 K1

Port 1 Port 5

Port 6

1LΔ 15E

16E

1E

2L′Δ

Port 3 Port 4

(2.30)

(2.31)

(2.32)

(2.33)

15

wavelengths 531 ,, λλλ .. and 642 ,, λλλ .. exit from ports 6 and 5, respectively, then the

condition would be

πΔβΔβ )12(2 12 −±=′ nLnL , 22 qp ′>′ and 33 qp ′<′ .

The output powers exiting through ports 5 and 6 are given by

( ) ( )15 1 2 1 2

2 21 3 3 2 2

2 cos( Δ ) 2 cos( Δ Δ )

2 cos( Δ ) 2 cos( Δ )

2 21 3 2 1 3 1 3 2 1 3

2 21 2 1 2 3 2 3 1 1

2 2 2 2 2 2 2 2 2 2 2 21 2 3 1 2 3 1 2 3 1 2 3

T p q q q p L L p q p q p L L

p p q p L q p q p q q L q p

p p p p q p p q q q p q

β β β β

β β

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= Δ + − −

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′+ − + −

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′+ + + +

( ) ( )16 1 2 1 2

1 2

2 cos( Δ Δ ) 2 cos( Δ Δ )

2 cos( Δ ) 2 cos( Δ )

2 21 3 2 1 3 1 3 2 1 3

2 2 2 21 2 1 2 3 3 3 2 3 2 1 1

2 2 2 2 2 2 2 2 2 2 2 21 2 3 1 2 3 1 2 3 1 2 3

T p q q q p L L p q p q p L L

p p q q L q p p p q q L q p

p p q q q q p q p q p p

β β β β

β β

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= − + + −

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′− − − −

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′+ + + +

As in the previous case, 15T and '16T represent the two cases corresponding to the

channel wavelengths ..,, 531 λλλ to exit from ports 5 and 6, respectively, and

therefore '1615 TT = . Similarly, 16T and '

15T represent the fractional powers corresponding

to the channel wavelengths ..,, 642 λλλ to emanate from ports 6 and 5, respectively,

making '1516 TT = . Such a comparison yields

11 pp ′= , 11 qq ′= , 22 pp ′= , 22 qq ′= , 33 qp ′= and 33 pq ′= .

This particular aspect of the location of the delay line in the second stage and its effect on

the splitting ratios of the couplers and channel wavelengths would play an important role

in the fabrication of flattop wavelength interleaver in the 2-stage MZI configuration. It is

apparent that for obtaining identical spectral response from each of these configurations

with the channel wavelengths ..,, 531 λλλ and ..,, 642 λλλ emanating from ports 5 and 6,

respectively, we should have 1515 TP = , and 1616 TP = , which yields

πΔβΔβ )12(22 −±′= nLL

33331111 ,,, qspcqspc ====

22 ps = , 22 qc = .

(2.34)

(2.35)

(2.36)

(2.37)

(2.38)

(2.39)

(2.40)

16

Hence, it could be observed that when a delay line of the optimum value is inserted in the

lower arm of the second stage, the optimum splitting ratios of the first and third couplers

remain the same but that of the second coupler gets interchanged, i.e., if it was 60:40 in

the former case, it would be 40:60 in the latter case.

2.6 Design Approaches There are various approaches to design interleavers for DWDM using all-fiber MZIs [9,

10]. The design, typically involves specifying some of the characteristics of the

interleaver, like the spectral response, passband ripple, number of stages, insertion loss,

passband width, stopband width, crosstalk, dispersion, etc and calculating the structure

parameters like the coupler ratios and differential delay path lengths.

An iterative approach followed by [11] is by minimizing loss matrix, to within specified

limits, calculated from transfer matrices. This also discusses the difference between the

cases when the second delay line is in same or opposite side with respect to the first delay

line.

A different approach is followed by Qian Wang, et al in [12]. A genetic algorithm has

been used to model the structure. The structure parameters i.e., the coupling ratios and the

phase shifts correspond to genes. The chromosomes are encoded and the selection

process is carried out. Mutation avoids trapping of chromosomes in the local maxima.

The first delay line is fixed according to the channel spacing and the second delay line is

double the length of the first.

S.W.Kok, et al, [10] have given a design recipe considering the structure analyzed by

Qian Wang, et al. [12]. In this design, the structure is analyzed based on Fourier

components due to the delay lines. For a specified passband ripple the recipe is to

calculate the coupling ratios of the second and the third couplers. To this end, the flatness

is described in terms of derivatives of the transfer function with respect to wavelength.

The second derivative is shown to be related to the passband ripple. Taking this as the

constraint and using Lagrange approach of using multiplier for optimization, the

parameters are calculated.

17

φN φ3

ΔL

φ2 φ1

θ2

ΔL

θ1 θ0

ΔL

θN θN-1

ΔL

2.7 Synthesis of Two-port Lattice Form Optical Delay Line

Circuits

K. Jinguji, et al [13] have given a method for synthesizing two-port lattice form optical

delay line circuits that are composed of optical delay lines, directional couplers, and

phase shifters and is applicable to the design of optical filters in general, including

wavelength interleavers. Methods and algorithms used in digital signal processing have

been adapted to calculate the structure parameters. It can be shown that two-port optical

delay-line circuits can have the same transmission characteristics as finite impulse

response (FIR) digital filters with complex expansion coefficients.

The method is based on the use of a unimodulus para-unitary matrix as a transfer matrix

and on the division of the transfer matrix into basic component transfer matrices. a

transfer function with complex expansion coefficients and design of filter characteristics

with arbitrary symmetries is made possible by the use of phase shifters. It has been shown

that arbitrary filter characteristics corresponding to Nth-order complex FIR digital filters

can be realized by N-cascaded, two-port lattice-form, optical delay-line circuits (see Fig.

6).

The desired transfer function is approximated and the Fourier coefficients are calculated

using Fourier expansion method. The coupling ratios and the phase shifts are obtained by

solving recurrent equations derived from the transfer function.

Figure 6: Configuration of coherent two-port lattice-form optical delay-line circuit

18

φ1 φ2

θ3 θ1 θ2

2ΔL2ΔL

2.8 Optical Half-Band Filters Optical half-band filters are important components of wavelength division multiplexing

(WDM) systems. A 2 x 2 Infinite Impulse Response (IIR) circuit configuration with one

or two feedback loops optimized for IIR half-band filters is known, and this configuration

has been used to realize a millimeter-wave waveguide circuit and a millimeter-wave bulk

filter with resonators [15]. An optical multi/demultiplexer with this configuration has also

been fabricated using silica-based planar lightwave circuits (PLC’s). K. Jinguji, et al [14]

have proposed optimized 2 x 2 circuit configurations for Finite Impulse Response (FIR)

optical half-band filters (see Fig. 7).

These FIR circuit configurations have a power half-band property

1)2

()(2

02 =++w

wGwG

Where )(wG is transfer function; 0w is angular frequency period.

Figure 7: A 2 x 2 FIR optical half-band filter circuit configuration

2.9 Dispersion Compensation In high-speed systems, dispersion plays an important role in the overall system

performances. Up to now, the most common way to deal with fiber dispersion has been

the usage of prechirp technique [16]. The prechirp is normally obtained by the laser in

both direct and external modulated experiments. The possibility to let the external

modulator perform the prechirp of the transmitted signal has also been examined [17].

On the receiver side, there is a well known technique based on heterodyne mixing and

dispersion compensation at an internal microwave frequency [18]. However, a full scale

heterodyne receiver is today considered less attractive in a system point of view.

(2.41)

19

A third known method is to compensate the fiber dispersion using dispersion shifted

fibers and dispersion compensating fibers. The disadvantages with this method are the

extra fiber loss and the cost for the dispersion compensating fiber.

Recently a fourth known method has been demonstrated [19]. The method is based on a

spectral inversion at the midpoint of the transmission length. A problem with this method

is that the conversion efficiencies still are low, about -25dB, besides being expensive and

complicated.

Using optical filters to counter chromatic dispersion seems to be cost effective and viable

solution.

2.10 Optical All-Pass Filter Structures All-pass filters (APF’s) are devices that allow phase correction or equalization without

introducing any amplitude distortion. An optical implementation of such devices is very

attractive since they can be used for dispersion compensation. In contrast to other

dispersion control devices, optical APF’s can correct any order of dispersion. This can be

achieved by careful design of multistage APF’s to approximate a target phase profile.

However, large dispersion is usually narrow band or requires many filter stages.

Mathematically, if the frequency response of a filter is written as

[ ])(exp)()( wjwHwH φ= then for an APF constwH =)( and )(wφ can be made

arbitrarily close to any desired phase response.

A continuous linear system characterized by an impulse response function )(th has a

corresponding system function )(sH which is the Laplace transform of )(th . Any input

results in an output that is the convolution of the input with the impulse response. The

system function is in general a complex function of the complex argument s also known

as the complex frequency. The frequency response may be derived by evaluating )(sH at

s = jw (i.e., on the imaginary axis in the complex -plane).

20

For a discrete system characterized by a discrete impulse response function )(nh and a

corresponding system function )(zH (the z-transform of the frequency response is given

by evaluating )(zH at z = exp(jw) (i.e., on the unit circle in the complex z- plane). The

APF system response and frequency response are

∏−

= −−

=1

0* 1

)(N

i i

i

zzzz

zH

∏−

=− −−

=1

0)( 1

)(N

iwj

i

ji

jw

i

i

erere

wH θ

θ

where iz are poles inside the unit circle with corresponding zeros outside the unit circle

in a symmetrically conjugate manner. Again it is easily verified that these functions have

magnitude 1. Also the above frequency response is periodic in the normalized frequency.

This period is known as the free spectral range (FSR).

Figure 8: Ring cascade architecture for all-pass optical filter [20]

In Out

κ2 κ1 κ3

φ1 φ2 φ3

(2.43)

(2.42)

21

1.5485 1.549 1.5495 1.55 1.5505 1.551 1.5515

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Wavelength (µm)

Nor

mal

ized

Tra

nsm

ittan

ce

1.5485 1.549 1.5495 1.55 1.5505 1.551 1.5515

-50

-40

-30

-20

-10

Wavelength (µm)

Nor

mal

ized

Tra

nsm

ittan

ce (d

B)

Chapter 3

Results and Discussion 3.1 Simulation 3.1.1 Single-stage MZI Interleaver Spectral Response

Figure 9: Simulated spectral response in linear scale at Port 3 of the MZI-based interleaver at 1550 nm.

ΔL = 2.1 mm corresponding to channel spacing of 100 GHz

Figure 10: Simulated spectral response in log scale at Port 3 of the MZI-based interleaver at 1550 nm.

ΔL = 2.1 mm corresponding to channel spacing of 100 GHz

22

The spectral response of the single stage MZI interleaver discussed herein has been

simulated in Matlab using the transfer matrix approach for variable differential length

corresponding to variable channel spacing.

3.1.2 Two-stage MZI Interleaver Spectral Response The spectral response of the 2-stage MZI interleaver has been simulated in Matlab using

the transfer matrix approach. The simulation was carried out by varying the differential

lengths as well as the coupling ratios of the couplers.

The following observations were made:

1. The transfer function corresponding to an interleaver was obtained only for

certain values of differential lengths.

2. The periodicity of the interleaver (channel spacing) depends on the differential

length.

3. The response when the second differential length is placed on the same side as the

first was different from the response obtained when it is placed on the opposite

side with respect to the first delay line.

4. Maximum throughput power at the centre of the passband was obtained only

when the first coupler has 50:50 coupling ratio.

1.549 1.55 1.551

0.2

0.4

0.6

0.8

Wavelength (µm)

Nor

mal

ized

Tra

nsm

ittan

ce

1.549 1.55 1.551-35

-30

-25

-20

-15

-10

-5

Wavelength (µm)

Nor

mal

ized

Tra

nsm

ittan

ce (d

B)

Figure 11: Simulated spectral response of a 2-stage MZI interleaver for the following parameters:

Coupler1- 50:50, Coupler2- 68:32, Coupler3- 4:96 at 1550 nm. ΔL2 = 2ΔL1; ΔL1 = 2.1mm for a channel spacing of 100GHz

23

3.1.3 Design of Interleaver Based on the Passband Ripple Following S.W.Kok, et al, [10] simulation has been done for the design of flat-top interleaver based on the passband ripple. The results are summarized in the following graphs.

0 0.02 0.04 0.06 0.08 0.1 0.12-5

0

5

10

15

20

25

30

Passband Ripple (dB)

Pas

sban

d w

idth

at 0

.1 d

B (

GH

z)

Figure 12: Variation of 0.1dB-passband width with increasing passband ripple for interleaver at 1.55μm

and 50 GHz channel spacing

0 0.1 0.2 0.3 0.4 0.529

30

31

32

33

34

35

36

Passband Ripple (dB)

Pas

sban

d w

idth

at 0

.5 d

B (G

Hz)

Figure 13: Variation of 0.5dB-passband width with increasing passband ripple for interleaver at 1.55μm

and 50 GHz channel spacing

24

0 0.005 0.01 0.015 0.020

2

4

6

8

10

12

14

16

Passband Ripple (dB)

Sto

pban

d w

idth

at 2

5 dB

(GH

z)

Figure 14: Variation of 25 dB-stopband width with passband ripple for interleaver at 1.55 μm and 100 GHz channel spacing

0 0.1 0.2 0.3 0.4 0.5-150

-100

-50

0

Passband Ripple (dB)

Cro

ss T

alk

leve

l (dB

)

Figure 15: Variation of crosstalk with passband ripple for interleaver at 1.55 μm and 100 GHz channel spacing

From the above plots (Figs. 12-15) the following conclusions can be drawn:

1. Passband width increases with passband ripple. This indicates that there is a trade-

off between the insertion loss and the passband width.

25

2. Stopband width also increases with passband ripple. This indicates that there is a

trade-off between the insertion loss and the stopband width as well.

3. However, the crosstalk also increases with passband ripple.

Also, for easy visualization of the effect as well as for better insight, a graphic user-interface has been developed using Matlab.

Figure 16: Matlab Graphics User Interface to calculate the structure parameters and the interleaver characteristics based on channel spacing and the specified passband ripple

26

3.1.4 Synthesis of Two-port Lattice Form Optical Delay Line

Circuits

Using the synthesis method proposed by K. Jinguji, et al [13], filters of various kinds can

be designed for varied purposes. Simulation has been done to calculate the structure

parameters for these designs. To validate the results, the simulation has been done for the

filters proposed therein and the structure parameters have been found to match very

closely with the results in literature.

-40 -20 0 20 40-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Tran

smitt

ance

(dB

)

Relative optical frequency (GHz)

Figure 17: Linear Chebyshev filter designed using optical delay line circuits for channel spacing of 100 GHz at 1.55 μm

Table 1: Simulated structure parameters for the designed Linear Chebyshev filter

Coupling Coeffiecient Angle x

Phase shift value

0.26699 00.31679 00.80763 0

0.244 00.88003 00.98036 0

0.002907 00.91915 00.10944 00.86837 00.22856 00.64306 00.64264 00.22869 00.8685 0

0.10941 00.91893 0

0.002667 00.98052 00.8791 0

0.24403 00.80797 00.31628 00.26716 0

27

The multi-channel selector is an optical frequency filter designed to select signals at

certain frequencies from eight frequency-division multiplexing (FDM) signals. This filter

is expected to be applied as a multiplexer/demultiplexer for FDM communications. An

optical filter designed to select three signals out of eight is shown below.

Because of the asymmetry in the filter characteristics, the coupling coefficients are

complex numbers.

-50 0 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Nor

mal

ized

Tra

nsm

ittan

ce

Relative optical frequency (GHz) Figure 18: Multi-channel selector filter designed using optical delay line

circuits for a channel spacing of 12.5 GHz at 1.55 μm

Table 2: Simulated structure parameters for the Multichannel selective filter

The values obtained by simulating the filter using this method in Matlab, match the

values given in the literature.

The group-delay dispersion equalizer is an optical frequency filter designed to equalize

group-delay dispersion of long-distance optical fibers at a wavelength of 1.55 μm.

Coupling Coeffiecient Angle x

Phase shift value x

0.57261 00.031002 0.907790.033352 -0.169230.025959 -0.169890.10165 0.931270.033703 0.94060.043298 -0.191760.034377 -0.191070.10618 0.943620.0289 0.945860.035181 -0.188040.033039 -0.177720.082071 0.919820.014458 0.892010.021713 -0.127470.4754 0.85938

28

-25 -20 -15 -10 -5 0 5 10 15 20 25-6

-4

-2

0

2Tr

ansm

ittan

ce (d

B)

Relative optical frequency (GHz)

-25 -20 -15 -10 -5 0 5 10 15 20 250

200

400

600

Rel

ativ

e G

roup

del

ay (p

s)

Relative optical frequency (GHz)

Figure 19: Transmittance and relative group delay in a group-delay dispersion equalizer designed using optical delay line circuits for a channel spacing of 12.5 GHz at 1.55 μm

Coupling Coeffiecient Angle x

Phase shift value x

Coupling Coeffiecient Angle x

Phase shift value x

0.53148 0 0.067461 0 0.063407 0 0.10254 0 0.098902 0 0.87911 0

0.1018 0 0.9632 0 0.036766 0 0.13243 0 0.93172 0 0.93126 0 0.86705 0 0.96441 0 0.96275 0 0.10195 0 0.12122 0 0.89845 0 0.10286 0 0.064595 0 0.93241 0 0.46847 0 0.88215 0

Table 3: Simulated structure parameters for the designed group-delay dispersion equalizer

29

3.1.5 Simulation for Optical Half-band Filters Structure parameters for two different kinds of filters designed based on half-band

property have been calculated through simulation.

Coupling Coeffiecient Angle x

Phase shift value x

0.62799 00.28602 00.45467 00.38132 0

Table 5: Circuit parameters for Maximally-flat Half-band filter (N=4)

The values obtained from simulation have been verified by comparing with the literature

values.

3.1.6 Optical All-Pass Filter Structures

Since all-pass filters allow manipulation of phase without affecting the amplitude, these

can be used to compensate for various kinds of dispersion. We use a structure that has

been designed to equalize group delay dispersion in a 2-stage MZI interleaver proposed

as optimum design in [10].

For a 2nd order all-pass dispersion equalizer

Zeros Poles Coupling Ratios Relative Phase values

-8.4537 + 0.011955i -0.11829 + 0.00016729i 0.98601 -3.1402-8.4537 - 0.011955i -0.11829 - 0.00016729i 0.98601 3.1402

Table 6: Zeros, poles and circuit parameters for dispersion equalizer for an optimized 2-stage MZI

interleaver

Coupling Coeffiecient Angle x

Phase shift value x

0.65019 00.24486 00.41859 00.42032 0

Table 4: Circuit parameters for Chebyshev Half-band filter (N=4)

30

-20 -15 -10 -5 0 5 10 15 20-1

-0.5

0

Relative optical frequency (GHz)

-20 -15 -10 -5 0 5 10 15 206

7

8

9

Relative optical frequency (GHz)

-20 -15 -10 -5 0 5 10 15 2030

31

32

33

Relative optical frequency (GHz)

Equalized Group delay

Unequalized Group delay

Insertion loss (dB)

Figure 20: Group delay equalization for 2-stage MZI interleaver proposed in [10]. The group delay variation has been reduced by a factor of 15.5

Order of filter 2 4 6 8 10 Group delay variation reduced by factor: 15.255 1572.1 2000.5 2811.4 2821

Table 7: Effect of addition of stages to the All-pass filter designed to equalize dispersion

From Table 7, we can see that the effect of addition of stages beyond four is not very

significant. Also, since, addition of more stages introduces more loss and makes the

device cumbersome, it should not, generally, be preferred.

31

3.1.7 Tolerance of Structure Parameters

Practically, it is not possible to fabricate components with the exact required

characteristics. Hence, to construct the interleaver with flat-top response it is important to

know the tolerance of the spectral response of the interleaver towards each of the

structure parameters i.e. the coupling ratios and delay lengths. Therefore, simulation was

carried out to investigate the effect of deviation of the coupling ratios of the couplers and

the delay lengths on the spectral response of the interleaver from the optimum values

predicted by the theory.

Figure 21: Spectral response when deviation of coupling ratios is 5% from the optimum values of 50:50, 32:68 and 5:95

1550 1550.1 1550.2 1550.3 1550.4 1550.5 1550.6 1550.7 1550.8 1550.9 1551-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Wavelength (nm)

Tran

smitt

ance

(dB

)

For optimum coupling ratiosFor a change of 5% in 1st coupling ratioFor a change of 5% in 2nd coupling ratioFor a change of 5% in 3rd coupling ratio

32

1550 1550.2 1550.4 1550.6 1550.8 1551-40

-35

-30

-25

-20

-15

-10

-5

0

Wavelength (nm)

Tran

smitt

ance

(dB

)

For optimum delay lengthsFor a change of 1µm in 1st delay lengthFor a change of 1µm in 2nd delay length

Figure 22: Spectral response when deviation of delay lengths is 1µm from the optimum value of 2.1mm

The simulation results showed that the tolerance towards delay lengths was minimal and

very accurate control over the lengths is required. However, there was not appreciable

deviation from optimum response due to variation in coupling ratios within the

achievable precision.

33

3.2 Experimental Work 3.2.1 Fabrication and Characterization of Fused Fiber Couplers To construct a 2-stage MZI interleaver, we need to fabricate couplers. Fused fiber

couplers were fabricated using the in-house made rig [21] (see Fig. 23). First, the

couplers were fabricated at 632.8 nm so as to learn the process of fabrication, since it is

easier to setup the experiment and also control the process at visible wavelengths.

Figure 23: Photograph of the fusion fiber coupler fabrication rig

Then, couplers at 1.55 μm were fabricated since these are required for the construction of

the MZI interleaver for DWDM applications.

The fabrication process involves stretching a pair of single-mode fibers together, which

are held in intimate contact with each other across a short unjacketed length, in a high

temperature (>1100 0C) oxy-butane flame. The fusion followed by stretching leads to

narrowing of the two fibers into a single biconical tapered junction. The tapered region is

essentially a multimode near-rectangular region with the core formed from the cladding

of the original fibers and the surrounding air acting as the cladding. Light from the input

fiber excites the two lowest order modes of this waveguide. Coupling of light from one

34

fiber to another is due to beating between the supermodes. This fabrication technique

consists of fusion, pulling and simultaneous tapering. Hence, it is also called as fuse-pull-

taper method in the literature. Due to symmetry in the structure formed, either end can be

used as input end. Hence these are known as bi-directional couplers. First appropriate,

stable and uniform flame is created. The various valves at different levels of the gas

ensure safety while providing fine pressure control. The temperature profile of the flame

affects the characteristics of the coupler significantly. A short length of fibers is

unjacketed using dichloromethane to soften the jacket. The unjacketed region is then

cleaned with acetone or iso-propyl alcohol. The fibers are twisted over each other in this

region and placed on the holder. Light is input at one end and the light from the two

output ports are monitored. The flame is positioned under the unjacketed region. The

fibers are then pulled slowly. When the required distribution of light between the output

ports is observed, the flame is withdrawn and the pulling is stopped a few seconds later.

Then the coupler is appropriately packaged. Table 8 depicts the typical measured

characteristics of the couplers fabricated in our lab.

Wavelength (nm) Coupling Ratio Excess Loss (dB) Directivity (dB)

1 632.8 48:52 1.32 33.4

2 632.8 46:54 1.02 44.2

3 632.8 48:52 1.17 40.5

4 1550 40:60 0.74 38.1

5 1550 95:5 1.10 32.2

6 1550 45:55 1.46 35.3

Table 8: Typical measured characteristics of the couplers fabricated using the in-house rig

35

But, as can be seen from the Table 8, the fabricated couplers at 1.55 μm have a loss much

greater than the expected loss (0.1 dB). The reasons for the loss could be attributed to the

following:

1. Only one detector was used to monitor power at two output ports, requiring the

fused fiber to be taken in and out of the flame a number of times leading to lossy

couplers.

2. It is difficult to manually control the pulling process. Due to malfunctioning of the

system used for controlling the pulling process through software, the fabrication is

now being done manually.

3.2.2 Techniques to Achieve Optical Path Difference between MZI

Arms As was seen from the simulation, to implement flat-top interleaver, precise control over

the phase difference between the arms of the MZI (which is caused due to delay lengths,

in this case) is required. There are two ways to control the phase difference i.e., by

modifying the mode effective index and changing the delay length. It requires a rather

complicated technique to induce a change in refractive index by ion bombardment, and

also, the induced changes in the refractive index slowly drift with time leading to drift in

the channel wavelength. Yonglin et al. [6] have reported technique to achieve phase

change by mechanical stretching of the fiber in one of the arms of the MZI, in real-time

while monitoring the wavelength response of the interleaver. But since these techniques

do not allow precise control on the length over which the fiber is stretched, they are at

best suited for coarse-WDM systems. Kumar et al. [11] have reported a technique of

selective heating and controlled stretching of fiber for tuning while real-time monitoring

the spectral response of the interleaver. We have adopted this method as it is convenient

and the response has been reported to be stable.

3.2.3 Tuning Channel Spacing and Channel Wavelengths In this section we derive relations necessary to estimate the change in the differential

path-length for tuning the channel wavelengths and inter-channel spacing. In order to

36

interleave two wavelengths 1λ and 2λ in an unbalanced MZI, the differential path length

1LΔ should satisfy

where 21 λλλΔ −= is the channel spacing. Suppose the differential path length is

changed 1LΔ to '1LΔ , and the corresponding new wavelengths, say, are 3λ and 4λ , then

' 3 41

eff2L

nλ λ

λΔ =

′Δ

where 43 λλλΔ −=′ .

From Eq. (3.1) and Eq. (3.2), we get the change in the differential path-length

' 1 2 3 41 1

eff2L L L

nλ λ λ λ λ λδ

λ λ′Δ − Δ

= Δ −Δ =′Δ Δ

ITU has fixed certain fixed channel wavelengths and inter channel spacing for DWDM

networks, to set standards for telecommunication networks spread across the world, To

conform to ITU recommendations, the channel wavelengths have to be tuned to match

the ITU defined grid, and, the channel spacing has to be tuned to the prescribed values

(viz. νΔ = 100 GHz, 50 GHz, or 25 GHz).

To tune the center wavelengths of the channels from 1λ and 2λ to 3λ and 4λ ,

respectively, without changing the channel spacing, we write

3 1 4 2, , with λ λ δλ λ λ δλ δλ λ= + = + < Δ and λΔλΔ ′=

Substituting the Eq. (3.4) in Eq. (3.3), we get

λΔδλΔΔδ LLLL 2'

11 ≈−=

whereδλ is the shift in the wavelength channels, and 2/12121 )(2/)( λλλλλ ≈+= . Note

that for shifting the spectrum towards higher wavelengths

(i.e. δλλλδλλλ +=+= 2413 , ), 1'1 LL ΔΔ > , which implies that the longer arm of the

interferometer has to be further elongated by an amount Lδ . Similarly, to shift the

spectrum towards lower wavelengths (i.e. δλλλδλλλ −=−= 2413 , ), 1'1 LL ΔΔ < , and

hence the shorter arm of the interferometer is to be elongated by an amount Lδ . Eq. (3.5)

1 21

eff2L

nλ λ

λΔ =

Δ

(3.5)

(3.4)

(3.3)

(3.2)

(3.1)

37

shows that in order to tune an interleaver in accordance with the ITU wavelength grid for

DWDM systems (say, 100GHz spacing), a precise control over Lδ ∼ 1 µm is necessary.

To illustrate tuning of the channel spacing, consider a situation in which the channel

spacing λΔ has to be tuned to a new value λΔ ′ . Using Eqs. (3.1) and (3.2),

λΔλΔ

λΔΔδ′

−≈−=′11

2

2'11

effnLLL

where we have assumed 2/143

2/121 )()( λλλλλ ≈≈ . Thus, in order to increase the channel

spacing, one has to elongate the shorter arm of the MZI by an amount L′δ . Similarly, to

decrease the channel spacing, one has to further elongate the longer arm of the MZI by an

amount L′δ . In this analysis, the higher order terms in λΔδλ, and λΔδλ , can be neglected

as the effects of these terms are insignificant.

3.2.4 Estimation of the Differential Delays in a Two-stage MZI If the splitting ratio of the second coupler is less than 50:50, then the differential delay

has to be introduced in the lower arm of the second stage so as to achieve the flattop

response. If the splitting ratio of the second coupler is greater than 50:50, then the

differential delay line has to be introduced in the upper arm of the second stage for

achieving flattop spectral response. In practice, when we fabricate an all-fiber interleaver,

there will be an initial differential delay between the upper and lower arms of the first-

and second stages. Before tuning, we must have a priori knowledge of the existing

differential delay between the arms of the interferometer and its location. Therefore, it is

important to identify which arm is longer, and by how much. In an all-fiber MZI (as

shown in Fig.4), the first delay line is used to achieve channel spacing, and it solely

determines the FSR of the configuration. The second delay line is used for obtaining the

flattop response. When we concatenate two fiber directional couplers to realize an MZI,

the FSR of this interleaver can be measured from the spectral response on an OSA, which

gives us the information about the magnitude of the first delay line 1LΔ . In order to

identify whether the upper arm or the lower arm of the first stage is longer, one may

elongate the upper arm by a small amount. This would result in either decrease or

(3.6)

38

increase in the channel, implying that the lower arm is either longer or shorter,

respectively. For example, if the upper arm was longer, then elongation of the upper arm

would result in a decrease in the FSR. But if the upper arm was shorter, then elongation

of the upper arm would result in an increase in the FSR. We then concatenate another

coupler to the single-stage configuration to realize the targeted two-stage MZI-based

interleaver.

To estimate the initial differential path length in the second stage (see Fig 4) and its

location, light is launched from port 5, and the output is measured at ports 1 and 2. This

configuration for couplers with optimum splitting ratios is then simulated for the two

cases when the second differential path length is located in the upper arm and in the

lower arm. By matching these simulated curves with the observed ones on the OSA, we

can know whether the upper or the lower arm of the second stage is longer. In this way,

one can get the information required to realize a flattop interleaver before tuning.

3.2.5 Implementation of 2-stage MZI Interleaver The first part of the experiment consists of constructing the first MZI stage. For this, two

fused fiber couplers were used which were fabricated using our in-house developed

coupler-fabrication rig. This forms a single-stage all-fiber MZI (Fig 3).

Figure 24: Experimental set-up used to measure the wavelength response of an all-fiber MZI

Port3Optical fiber

Port1 Coupler 1 Coupler 2

ΔL1

Port4

OSA Broadband EDF Source

39

1520 1530 1540 1550 1560 1570-40

-35

-30

-25

-20

-15

Pow

er (d

Bm

)

Wavelength (nm)

EDF source full spectrum

Figure 25: Photograph of the two-stage MZI interleaver that was fabricated in the lab

A broadband super-fluorescent EDF source was used as the source at the input (Port 1) of

the MZI. The source was found to have a nearly flat spectral response in the range 1548-

1558 nm.

Figure 26: Power spectrum of EDF broadband source used for the experiment

40

1549.0 1549.5 1550.0 1550.5 1551.0

-39.75

-39.70

-39.65

-39.60

-39.55

-39.50

-39.45

-39.40

Pow

er (d

Bm

)

Wavelength (nm)

EDF source over 2nm range

The fibers at the output ports of the MZI were connected to an OSA using fiber

connectors. Figure 27 shows the spectral response of the unbalanced MZI. In order to

achieve tuning of the FSR, the required differential phase delay is introduced by selective

heating and controlled stretching of the longer arm of the MZI; a small unjacketed

segment of the fiber was exposed to an oxy-butane micro-flame, while simultaneously

monitoring the spectral response on the OSA. When the FSR was close to but still larger

than the required channel spacing, the flame burner was withdrawn and the elongation

process was stopped after a few seconds. This was done to avoid any sagging of the

fiber. However since the spectral response was not stable when the fiber was above the

flame, the fiber was withdrawn several times and the FSR was measured when the arms

of the MZI were away from the flame to ensure that the spectral response was stable. By

slowing down the pulling rate, the interleaver was also tuned to standard ITU wavelength

grid. The wavelength response of the fabricated MZI was then recorded in the OSA (see

Fig. 29).

Figure 27: Power spectrum of EDF broadband source over a range of 2 nm

To achieve tuning of wavelength response, the heating and elongation was essentially

done over a fiber length of about 2cm, along which the variation in the overall diameter

of the fiber (125 μm) was ∼ 15 μm. For this extent of tapering, the physical parameters of

41

1549.32 1550.12 1550.92-54

-52

-50

-48

-46

-44

-42

Pow

er (d

Bm

)

Wavelength (nm)

1541.34 1542.14 1542.94 1543.74-49

-48

-47

-46

-45

-44

-43

-42

Pow

er (d

Bm)

Wavelength (nm)

the fiber do not alter appreciably, and the fiber still retains its robustness. The device was

eventually lifted off the tuning rig and the arms of the MZI were appropriately protected

and heat-shielded to circumvent temperature-induced fluctuations in the wavelength

spectrum.

Figure 28: Spectral response of 1-stage interleaver before tuning

Figure 29: Spectral response of 1-stage interleaver after tuning

42

1543 1544 1545 1546 1547 1548 1549 1550 1551-50

-48

-46

-44

-42

-40

Pow

er (d

Bm)

Wavelength (nm)

3.2.6 Tuning of 2-stage MZI Based Wavelength Interleaver Fused fiber couplers of splitting ratios 45:55, 35:65 and 5:95 which were fabricated in the

lab were used. But later, the second coupler was replaced with 30:70 coupler that was

available in the lab (procured from Renka corp.). The first two couplers were initially

concatenated to realize a single-stage MZI. The initial FSR was measured, and the

differential delay was determined to be present in the upper arm.

Then we concatenated the third coupler (5:95) to the single-stage MZI to realize a two-

stage MZI. The initial output spectrum of the 2-stage MZI was recorded on the OSA. By

following the procedure, described previously for estimating the initial differential path

length in the second stage, we found that the upper arm of the second stage was longer

than the lower arm.

Figure 30: Spectral response of 2-stage interleaver during the process of tuning

As described earlier, since the splitting ratio of the second coupler is 30:70, the required

differential delay to achieve flattop response is 12 2 LL ΔΔ =′ , and it should be inserted in the

lower arm. Following the technique described in section (3.2.3) for tuning a single-stage

MZI, the lower arm of the second stage of the 2-stage MZI was elongated. The spectrum

obtained after partially tuning the second delay is shown in Fig. 31. The interleaver was

found to have 3.4 dB to 3.6 dB loss and peak-to-peak extinction ratio of 10dB.

43

1549.32 1550.12 1550.92 1551.72-54

-52

-50

-48

-46

-44

-42

Pow

er (d

Bm)

Wavelength (nm)

Figure 31: Spectral response of partially tuned 2-stage interleaver

3.2.7 Discussion The spectral response was found to be quite unstable when the fiber was exposed to the

flame. Hence online monitoring was not possible while adjusting differential paths of

both MZI stages. Hence, length was first increased, then, after the flame was withdrawn,

once the spectrum was stable, measurements were made. Therefore it was not possible to

tune exactly with the precision the technique allows. The peak-to-peak extinction ratio of

the interleaver was seen to increase with the FSR; this extinction ratio could be increased

further by a proper choice of splitting ratios of the couplers. The wavelength resolution

limit of the OSA also limits a precise measurement of the actual extinction ratio. The

minimum possible change in the FSR during tuning of the MZI by this technique was

difficult to estimate because of the following reasons: the smallest real-time change in the

FSR during tuning was much less than the resolution of the OSA. Further, the effect of

this small change in FSR was difficult to record in real-time during the tuning process

because of short-duration small-scale real-time fluctuations that occur in the online

response of the MZI.

44

Chapter 4

Y-Junction Flat-Top Interleaver 4.1 Introduction Interleavers play an important role in increasing the data carrying capacity of the

networks as the demand for the same has been on the rise. Interleavers exist in various

forms which use different principles or technology, using the optical fiber. But all of

these suffer from lack of compactness and ruggedness. Planar Lightwave Circuits (PLC)

offer a workable solution to these shortcomings. Polymer based waveguides have

attracted much attention of late due to their tunability over a wide range of wavelength

and wide choice of materials with varied properties. Recently, Qiang Wu, et al.,[2] have

reported polymer optical waveguide interleaver using Y junctions. They have replaced

directional couplers by Y junction components as they have following advantages:

1. Ease of fabrication

2. Wavelength insensitivity leading to much larger overall bandwidth of the

interleaver

3. Compact length due to smaller interaction length

4.2 Principle of Operation The structure consists of five Y junctions forming a cascade of two MZI’s similar to the

flat-top interleaver in the all-fiber form. The direction couplers are replaced by Y

junctions as shown in Fig. 23. The arms in between the Y-junctions are of unequal

lengths and form unbalanced MZI’s.

The first Y-junction (Y1) is a single-mode Y-junction, i.e., all of its branches support only

a fundamental mode. Here, its function is as a 3dB power splitter. The remaining Y-

45

junctions are of similar structure with their branches and stems being of different

dimensions. Their function is to convert, split and combine modes.

Figure 32: Schematic diagram of Y-junction based 2-stage MZI interleaver

Consider field E1 of amplitude A input at Y1. The two signals arriving at Y-junction differ

by a phase β' ΔL1 corresponding to path difference of ΔL1, where β' is the

propagation constant of each Mach-Zehnder arm.

At Y2 the fields entering the junction would be [2]

E1 = A cos α exp (iβ' ΔL1/2)

E2 = A sin α exp (-iβ' ΔL1/2)

These fields together create two lowest order propagating modes in Y2 because this

junction has a larger V number and is such that it supports these modes. The fields of the

two lowest-order local normal modes in S are the same E1/√2 with propagation constants

β0 and β1 respectively. Y3, Y4, Y5 are structurally identical to Y2. Let Δβ be the

difference in the propagation constants of these two modes. It is also noted that the

branches of the junctions support the fundamental mode only. Y3 splits the two modes in

the main arm into two single modes in the branches at its output end. Field at the upper

output branch of Y3 due to field E1 and E2 is given by

E3 = E1 cos(1/2 ΔβS1) − i E2 sin(1/2 ΔβS1)

Similarly, field at the lower output branch of Y3 due to field E1 and E2 is given by

E4 = − i E1 sin(1/2 ΔβS1) + E2 cos(1/2 ΔβS1)

This shows that the combination of Y-junctions in the above manner acts as a directional

coupler [2].

Using the same logic as in the case of all-fiber flat-top interleaver it can be shown that

Y5 Y4Y3Y2 Y1

ΔL1 ΔL2

S1S2

(4.4)

(4.3)

(4.2)

(4.1)

46

λλΔ

=Δeffn

L2

2

1

The two signals arriving at Y4 differ by a phase β' ΔL2 corresponding to path difference

of ΔL2. these fields can be expressed as

E5 = E3 exp (iβ' ΔL2/2)

E6 = E4 exp (-iβ' ΔL2/2)

Y4 and Y5 together act as another directional coupler. Thus the fields at the ouput

branches of the last junction are given by

E7 = E5 cos(1/2 ΔβS2) − i E6 sin(1/2 ΔβS2)

E8 = − i E5 sin(1/2 ΔβS2) + E6 cos(1/2 ΔβS2)

This resulting power at the upper output branch of the last junction is

P = -2 cos(1/2 ΔβS2) sin(α) sin(1/2 ΔβS2) cos(α) cos(1/2 ΔβS1) 2 sin(β' (ΔL2+ΔL1))

-2 sin(β' (-ΔL2+ΔL1)) sin(1/2 ΔβS2) cos(α) cos(1/2 ΔβS2) sin(α) cos(1/2 ΔβS1) 2

+ 2 sin(β' (-ΔL2+ΔL1)) cos(1/2 ΔβS2) sin(α) sin(1/2 ΔβS2) cos(α)

-4 sin(β' ΔL1) cos(1/2 ΔβS2) 2 sin(α) sin(1/2 ΔβS1) cos(α) cos(1/2 ΔβS1)

+2 sin(β' ΔL1) sin(α) cos(1/2 ΔβS1) cos(α) sin(1/2 ΔβS1)

+2 cos(β' ΔL2) sin(1/2 ΔβS2) sin(1/2 ΔβS1) cos(1/2 ΔβS2) cos(1/2 ΔβS1)

-4 cos(β' ΔL2) sin(1/2 ΔβS2) cos(α) 2 sin(1/2 ΔβS1) cos(1/2 ΔβS2) cos(1/2 ΔβS1)

-2 cos(α) 2 cos(1/2 ΔβS1) 2

+4 cos(1/2 ΔβS2) 2 cos(α) 2 cos(1/2 ΔβS1) 2

+ cos(1/2 ΔβS2) 2

-2 cos(1/2 ΔβS2) 2 cos(α) 2

-2 cos(1/2 ΔβS2) 2 cos(1/2 ΔβS1) 2

+ cos(1/2 ΔβS1) 2

+ cos(α) 2

To achieve a flat response with the high extinction ratio, the parameters ΔL1, α, ΔβS1,

ΔβS2 have to be appropriately chosen. The channel spacing is solely determined by ΔL1.

Therefore the criterion for choosing ΔL1 is given by Eq. (4.5).

(4.6) (4.7)

(4.5)

(4.8) (4.9)

(4.10)

47

In the case of all-fiber interleaver the two cases considered with respect to the arm of the

second MZI in which the path delay has to be placed lead to choice of different path

lengths for those two cases. However, in this case, since the first junction does not change

the phase of the fields, both these cases lead to the same choice of second delay length:

ΔL2 = 2 ΔL1

4.3 Parameter Optimization There are several design recipes to find the parameters ΔβS1 and ΔβS2. These have been

discussed in the previous section for the all-fiber case. We have used iterative method to

obtain these parameters. In this approach, for each choice of ΔβS1, the loss and flatness is

calculated for the different choices of ΔβS2. Only those values of ΔβS1 and ΔβS2 that

satisfy the requirements of loss below the specified value and flatness better than the

specified value are retained as the optimum parameters.

The optimum parameters (phase difference between the two modes in each of the straight

arms of the Y-junctions) correspond to following criteria in the passband of the response

over 15% of the FSR:

1. Intrinsic loss: < 0.05 dB

2. Flatness: < 0.05dB

Intrinsic loss is defined as the loss at the center of the passband i.e, -10 log P,

where P is normalized with respect to the input power.

Flatness is defined as: 1

)log10(ϕ∂

∂ P and is a measure of ripple amplitude.

11 LΔ= βϕ is the phase difference due to first delay line.

We have found empirical relations between ΔβS1 and ΔβS2 for the combinations which

give flat-top response by curve-fitting the obtained optimum values for the two cases

with respect to the presence of second delay line in upper or lower arm of the MZI (see

Fig. 34 and Fig. 35).

(4.12)

48

1550 1550.2 1550.4 1550.6 1550.8 1551 1551.2 1551.4 1551.6 1551.8-40

-35

-30

-25

-20

-15

-10

-5

0

Wavelength (nm)

Tran

smitt

ance

(dB

)

Figure 33: Spectral response of a Y-junction based 2-stage interleaver

The spectral response of the 2-stage Y Junction interleaver is similar to the

spectral response of the directional coupler interleaver as shown in Fig.33 for the

following parameters: n = 1.5, ΔβS1 = 1.94, ΔβS2 = 0.40, ΔL1 = 2 mm.

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Δβ S1 (radians)

Δβ

S2 (

radi

ans)

y = 2.3*x4 - 15.8*x3 + 41.3*x2 - 47.9*x + 21

Calculated Optimum Values 4th degree polyomial fit

Norm of residuals = 0.012612

Figure 34: Optimum values of ΔβS1 and ΔβS2 when both the delays are on the same side

49

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.62

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Δβ S1 (radians)

Δβ S

2 (rad

ians

)

y = - 2.7*x4 + 15*x3 - 31*x2 + 29*x - 8.1

Calculated Optimum Values 4th degree Polynoial fit

Norm of residuals = 0.01312

Figure 35: Optimum values of ΔβS1 and ΔβS2 when both the delays are on opposite sides

4.4 Discussion Y-junctions have several advantages over directional couplers as discusses in the first

section of this chapter. However, it is impractically difficult to fabricate them in all-fiber

form. Nevertheless, the structure proposed in this chapter is not only viable for

fabrication in planar waveguides, but also easier to fabricate compared to the similar

structure using directional couplers.

We have not considered the propagation loss in the waveguide in our simulation. But

considering the fact that the loss in planar waveguides is not insignificant, we expect that

the actual device would have loss much more than directional coupler based all-fiber

interleaver discussed in this thesis. However with newer materials and development of

the technology of fabrication of planar waveguides, this loss is expected to reduce.

50

FUTURE SCOPE

In this work we have analyzed various design recipes for interleavers and

filters in general. These can be applied to various interesting applications. Also since

we have the facility to fabricate fused fiber couplers, which form the main

components in most of these structures, it would be interesting and useful to try out

newer applications. Structures for tunable dispersion and dispersion slope

compensation, variable optical attenuation (VOA), and multichannel selection may be

investigated and implemented.

Polarization characteristics like polarization mode dispersion (PMD),

polarization dependent loss (PDL), and polarization dependent wavelength shift

(PDλ) of the all-fiber flat-top interleaver can be investigated.

The fabrication rig can be automatically controlled through instructions from a

PC. However, the system developed a few problems. The problem now lies in the

hardware interface between the motors and the microprocessor. Excess loss of the

fabricated couplers can be minimized, and couplers of required splitting ratios can be

made easily, if this problem is sorted out.

We have proposed design and optimum parameters for polymer based Y-

junction flat-top interleaver. This device is expected to have high degree of tunability

and uniform characteristics over a wide range of wavelength, while being rugged and

compact. From our preliminary discussions with the scientists of City University of

Hong Kong, it is likely that our designed Y-junction based flat-top interleaver would

be fabricated in the near future. It would be remarkable if the fabrication could be

completed.

51

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52

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53

Appendix A Optimum combinations of the splitting ratio of the couplers K1, K2 and K3

10021 ×s 1002

2 ×s 10023 ×s

50 56 2 50 64 3 50 68 4 50 71 5 50 74 6 50 75 7 50 75 8 50 76 8 50 76 9 50 77 8 50 77 9 50 78 10 50 78 11 50 79 10 50 79 11 50 79 12 50 80 11 50 80 12 50 80 13 50 81 13 50 81 14 50 82 14 50 82 15 50 82 16 50 82 17 50 83 17 50 83 18 50 83 19 50 84 19 50 84 20 50 84 21 50 85 21 50 85 22

10021 ×q 1002

2 ×q 10023 ×q

50 15 21 50 16 18 50 17 16 50 17 17 50 17 18 50 17 20 50 18 15 50 19 12 50 20 13 50 21 10 50 21 11 50 21 12 50 22 10 50 22 11 50 23 8 50 23 9 50 23 10 50 24 7 50 24 9 50 25 7 50 26 6 50 27 7 50 29 5 50 29 6 50 32 4 50 33 4 50 35 4 50 36 3 50 39 3 50 40 3 50 44 2 50 46 2 50 47 2

Table 9: Optimized splitting ratios of the 3 couplers K1, K2 and K3 in a 2-stage MZI-based interleaver when the delay line

effnLL 2/2 12 λ±Δ=Δ is introduced in the upper arm of the second stage.

Table 10: Optimized splitting ratios of the 3 couplers K1, K2 and K3 in a 2-stage MZI-based interleaver when delay line

12 2 LL Δ=Δ is introduced in the lower arm of the second stage.

54

Appendix B Optimum combinations of parameters of the Y-junctions

ΔβS1 (radians)

ΔβS2 (radians)

1.69 0.33 1.72 0.34 1.74 0.35 1.76 0.36 1.78 0.37 1.8 0.38

1.82 0.39 1.84 0.4 1.85 0.41 1.87 0.42 1.9 0.44

1.93 0.46 1.94 0.47 1.97 0.49 1.98 0.5 1.99 0.51

2 0.52 2.06 0.58 2.07 0.59 2.08 0.6 2.09 0.61 2.1 0.62

2.12 0.65 2.13 0.66 2.14 0.68 2.15 0.69 2.16 0.71 2.17 0.72 2.18 0.74 2.19 0.75 2.2 0.77

2.21 0.79 2.22 0.81 2.23 0.83 2.24 0.85 2.25 0.87 2.26 0.89 2.26 0.9

ΔβS1 (radians)

ΔβS2 (radians)

0.79 2.07 0.8 2.1

0.81 2.13 0.82 2.16 0.83 2.18 0.84 2.21 0.85 2.24 0.86 2.26 0.87 2.28 0.89 2.33 0.9 2.35

0.93 2.4 0.94 2.42 0.96 2.45 0.98 2.48

1 2.51 1.01 2.52 1.04 2.56 1.05 2.57 1.06 2.58 1.07 2.59 1.08 2.6 1.09 2.61 1.1 2.62

1.11 2.63 1.12 2.64 1.17 2.68 1.2 2.7

1.21 2.71 1.26 2.74 1.33 2.78 1.35 2.79 1.42 2.82 1.47 2.84 1.52 2.86 1.55 2.87 1.58 2.88

Table 11: Optimized parameters for a 2-stage MZI configuration using Y-junctions when the delay line is in the lower arm

Table 12: Optimized parameters for a 2-stage MZI configuration using Y-junctions when the delay line is in the upper arm