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PERFORMANCE OF FOUR-STAGE CASCADED FIBER OPTICAL PARAMETRIC AMPLIFIER (FOPA) USING OPTISYSTEM FATIN NABILAH BINTI MOHAMAD SALLEH UNIVERSITI TUN HUSSEIN ONN MALAYSIA

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PERFORMANCE OF FOUR-STAGE CASCADED

FIBER OPTICAL PARAMETRIC AMPLIFIER

(FOPA) USING OPTISYSTEM

FATIN NABILAH BINTI MOHAMAD SALLEH

UNIVERSITI TUN HUSSEIN ONN MALAYSIA

PERFORMANCE OF FOUR-STAGE CASCADED FIBER OPTICAL

PARAMETRIC AMPLIFIER (FOPA) USING OPTISYSTEM

FATIN NABILAH BINTI MOHAMAD SALLEH

A thesis submitted in

fulfillment of the requirement for the award of the

Master of Electrical Engineering

Faculty of Electrical and Electronic Engineering

Universiti Tun Hussein Onn Malaysia

JULY, 2017

iii

To my beloved family

DEDICATION

iv

ACKNOWLEDGEMENT

Praise and thanks to Allah (SWT) who gave me the strength and courage to

complete this project.

I would like to express sincere thanks to my supervisor Dr. Nor Shahida Binti

Mohd Shah for her invaluable guidance throughout the course of this research. Her

guidance, ideas, encouragement, affable nature, kindness and support were greatly

helpful.

I would like to wish thanks to my mother Saidah Binti Hj Martan, for her daily

prayers and giving me motivation and strength. I also want to thank my late father,

Mohamad Salleh Bin Kassim for raising me up until his last breath. I will be ever

grateful for his assistance, and am sorry that he has not lived to witness my

achievements.

A special acknowledgment must be given to my brothers and sisters for their

support and help during my academic period at UTHM.

Finally, sincere gratitude to my friends who inspired me by their courage and

guidance throughout the period of my study.

v

ABSTRACT

An optical fiber plays a significant role to cater the increasing transmission capacity.

In optical fiber, there is a few nonlinear effects. One of the nonlinear effects is four-

wave mixing (FWM). In-depth analysis of FWM is conducted and it is found that one

of the applications in the FWM is a fiber optical parametric amplifier (FOPA). An

FOPA has an ability to achieve a high gain and bandwidth. One of the approaches is a

cascaded FOPA. A cascaded FOPA is a FOPA with two or more active media,

commonly known as a highly nonlinear fiber (HNLF). Previous experimental work

shows that the improvement in gain and bandwidth of the cascaded FOPA depends on

the passive or active devices inserted in between the HNLF. However, the results at

each stage of the cascaded FOPA are not discussed. The result at each stage is crucial

to ensure that the cascaded FOPA is amplifying power at the respective stage which is

the essence of this work. The cascaded FOPA is demonstrated by using an OptiSystem

software with four stages of HNLF with different parameters. Two research work

related to the cascaded FOPA are presented in this thesis. The first work focusses on

the effects of pump dithering to the cascaded FOPA, while the second work discusses

the effects of passive components to cascaded FOPA. The passive components

selected are isolator and optical bandpass filter (OBPF). The results show that the

FOPA with pump dithering can achieved the gain up to 27 dB, while without pump

dithering, only 9 dB gain is achieved. For the performance of the cascaded FOPA with

isolators, a high gain of 30 dB is obtained, while the cascaded FOPA with OBPFs, a

wider bandwidth of 36 nm is obtained. In conclusion, the pump dithering and isolator

can be used to achieved a high gain of FOPA and OBPF can be used to obtain a wider

bandwidth of FOPA.

vi

ABSTRAK

Gentian optik memainkan peranan yang penting bagi menampung peningkatan

kapasiti penghantaran. Terdapat beberapa jenis kesan tidak linear dalam gentian optik.

Salah satu kesan tidak linear tersebut ialah percampuran empat gelombang (FWM).

Kajian yang mendalam terhadap FWM telah dijalankan dan didapati bahawa FWM

mempunyai salah satu applikasi yang dikenali sebagai penguat parametrik gentian

optik (FOPA). FOPA mempunyai keupayaan untuk mencapai nisbah dan lebar jalur

yang tinggi. Salah satu pendekatan yang digunakan ialah lata FOPA. Lata FOPA

adalah FOPA dengan dua atau lebih aktif media, biasanya gentian silika amat tidak

linear (HNLF). Beberapa eksperimen lepas menunjukkan lata FOPA akan mempunyai

nisbah dan lebar jalur yang lebih baik jika peranti pasif atau aktif dimasukkan di antara

HNLF. Walau bagaimanapun, keputusan di setiap peringkat lata FOPA tidak

dibincangkan. Hasil disetiap peringkat adalah penting untuk memastikan bahawa lata

FOPA ditambah kuasa di setiap peringkat dan telah dikaji di dalam kajian ini. Dalam

kajian ini, simulasi lata FOPA dijalankan dengan menggunakan perisian OptiSystem

dengan empat peringkat HNLF yang mempunyai parameter berbeza. Dua kajian

penyelidikan berkaitan dengan lata FOPA secara simulasi telah ditunjukkan dalam

tesis ini. Kajian pertama memberi tumpuan kepada kesan penditeran pam terhadap lata

FOPA, manakala kajian kedua membincangkan kesan komponen pasif kepada lata

FOPA. Komponen pasif yang dipilih ialah pemencil dan tapis pita optik. Hasil kajian

menunjukan bahawa lata FOPA dengan penditeran pam mampu menjana gandaan

sehingga 27 dB, manakal tanpa pam penditeran hanya mampu mencapai gandaan

sebanyak 9 dB. Bagi prestasi lata FOPA bersama komponen pasif, pemencil berjaya

mendapat gandaan yang tinggi iaitu 30 dB manakala tapis pita optik berjaya

melebarkan lebar jalur lata FOPA sebanyak 36 nm. Konklusinya, penditeran pam dan

pemencil boleh digunakan bagi mendapatkan gandaan yang tinggi untuk FOPA dan

tapis pita optik mampu mendapatkan lebar jalur yang lebar.

vii

TABLE OF CONTENTS

DECLARATION ii

DEDICATION iii

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS AND ABBREVIATIONS xiii

LIST OF APPENDICES xvi

LIST OF PUBLICATIONS xvii

CHAPTER 1 INTRODUCTION 1

1.1 Preamble 1

1.2 Problem Background 2

1.3 Problem Statement 3

1.4 Research Objectives 3

1.5 Research Scopes 4

1.6 Report Outline 4

CHAPTER 2 LITERATURE REVIEW 5

2.1 Introduction 5

viii

2.2 Nonlinear Fiber Optics 5

2.2.1 Stimulated Raman Scattering 6

2.2.2 Stimulated Brillouin Scattering 7

2.2.3 Self-Phase Modulation 8

2.2.4 Cross-Phase Modulation 10

2.2.5 Four-Wave Mixing 10

2.3 Dispersion 12

2.3.1 Mode Dispersion 12

2.3.2 Chromatic Dispersion 12

2.3.3 Zero Dispersion Wavelength (ZDW) 13

2.4 Fiber Optical Parametric Amplifier (FOPA) 13

2.4.1 Theory of FOPA 14

2.4.2 Phase-Matching Condition 16

2.4.3 Gain Spectrum of FOPA 17

2.5 Cascaded FOPA 19

CHAPTER 3 METHODOLOGY 23

3.1 Introduction 23

3.2 Simulations in Optisystem software 23

3.3 The Simulation Components 24

3.3.1 Continuous-Wave Laser 24

3.3.2 Polarization Controller 25

3.3.3 Phase Modulator 25

3.3.4 Sine Generator 25

3.3.5 Erbium-Doped Fiber Amplifier 26

3.3.6 Optical Bandpass Filter 26

3.3.7 Pseudorandom Bit Sequences Generator 27

3.3.8 Non-Return-To-Zero Pulse Generator 28

3.3.9 Mach-Zehnder Modulator 28

3.3.10 Isolator 29

3.3.11 Highly Nonlinear Fiber 29

3.3.12 Optical Spectrum Analyser 30

3.4 The Four Stage Cascaded FOPA Simulation Setup 30

3.4.1 The Effects of Pump Dithering 31

ix

3.4.2 The Effects of Components Inserted In

Between The HNLF 32

3.5 Summary 34

CHAPTER 4 RESULT AND ANALYSIS 35

4.1 Introduction 35

4.2 Simulation of FWM phenomenon 35

4.3 The effects of pump dithering 38

4.4 The effects of passive components 42

4.4.1 Isolators 42

4.4.2 Optical bandpass filter 45

4.4.3 Gain Comparison for isolators and

OBPFs cases 47

CHAPTER 5 CONCLUSION 49

5.1 Introduction 49

5.2 Conclusion 49

5.3 Main Contribution 50

5.4 Future Work 50

REFERENCES 51

APPENDIX 57

x

LIST OF TABLES

Table 2.1: Summary of nonlinear effects in optical fiber 6

Table 2.2 Comparison of previous work for cascaded

FOPA 22

Table 3.1 : Parameters of the CW laser 24

Table 3.2 : The parameters of four HNLFs [40] 30

Table 4.1 : Comparison of experimental and simulation

results 39

Table 4.2 : The value of signal power for with and without

pump dithering at each stage 41

Table 4.3 : The pump and idler power at each stage of

with and without pump dithering cases 42

Table 4.4 : The comparison of signal power for cascaded

FOPA with and without isolator. 44

Table 4.5 : Pump, signal and idler power at each stage. 45

Table 4.6 : The pump, signal and idler power for cascaded

FOPA with OBPF 46

xi

LIST OF FIGURES

Figure 2.1: The optical power transfer (a) before and (b)

after the SRS effects [8]. 7

Figure 2.2: The SBS power depletion from the original

signals [8]. 7

Figure 2.3: Optical pulse as it propagates into the fiber [8]. 9

Figure 2.4 : The optical pulse experience spectral

broadening due to SPM [8]. 10

Figure 2.5: Two channel pump wave 11

Figure 2.6: One channel pump wave (degenerate FWM) 12

Figure 2.7: The gain spectrum of FOPA [24] 19

Figure 3.1 : The CW laser block diagram 24

Figure 3.2 : The polarization controller. 25

Figure 3.3 : The phase modulator 25

Figure 3.4 : The sine generator 26

Figure 3.5 : The EDFA 26

Figure 3.6 : The OBPF 26

Figure 3.7 : The PRBS Generator 27

Figure 3.8 : The NRZ pulse generator 28

Figure 3.9: The Mach-Zehnder modulator 28

Figure 3.10 : The isolator 29

Figure 3.11: The HNLF 29

Figure 3.12 : The OSA 30

Figure 3.13 : The simulation setup for cascaded FOPA 31

Figure 3.14 : Simulation setup of cascaded FOPA with

OBPF 33

Figure 4.1 : The pump wavelength spectrum 36

xii

Figure 4.2 : The pump and signal wavelength after

injected into fiber 36

Figure 4.3 : The FWM phenomenon inside the optical

fiber 37

Figure 4.4 : The gain spectrum for simulation done and

experimental from [40] 38

Figure 4.5 : The signal powers at each stage of cascaded

FOPA without pump dithering 40

Figure 4.6 : The signal power at each stage of cascaded

FOPA with a pump dithering 41

Figure 4.7 : The gain spectrum for cascaded with and

without isolator. 43

Figure 4.8 : The signal power at each stage of cascaded

FOPA without isolator 44

Figure 4.9 : Output spectrum for each HNLFs of cascaded

FOPA with OBPFs 46

Figure 4.10: Gain spectrum for cascaded FOPA with

isolators and OBPFs. 48

xiii

LIST OF SYMBOLS AND ABBREVIATIONS

if - First optical frequency

jf - Second optical frequency

kf - Third optical frequency

ijkf - Fourth intermodulation product

1111 - Third-order nonlinear susceptibility

- Channel spacing

n - Fiber refractive index

𝒟 - Degeneracy factor

effL - Effective length

effA - Effective area

- Attenuation

L - Length

iP - Input power at if

jP - Input power at jf

kP - Input power at kf

ijkP - Power generated at ijkf

1p - Angular frequency of pump one

2p - Angular frequency of pump two

i - Angular frequency of idler

xiv

s - Angular frequency of signal

c - Center angular frequency

pP - Pump power

sP - Signal power

iP - Idler power

- Nonlinear coefficient

- Low propagation mismatch

p - Propagation constant of pump

s - Propagation constant of signal

i - Propagation constant of idler

c - Speed of light

o - Zero dispersion wavelength

p - Pump wavelength

s - Signal wavelength

i - Idler wavelength

dD

d - Slope of dispersion at zero dispersion wavelength

4 - Fourth-order dispersion coefficient

p - Phase of the pump

s - Phase of the signal

i - Phase of the idler

- Relative phase difference

- Phase-matching condition

M - Material dispersion

W - Waveguide dispersion

xv

NL - Nonlinear dispersion

G - Gain

expG - Exponential gain

quadG - Quadratic gain

DCF - Dispersion Compensation Fiber

DSF - Dispersion-Shifted Fiber

EDFA - Erbium Doped Fiber Amplifier

FBG - Fiber-Bragg Grating

FOPA - Fiber Optical Parametric Amplifier

FWM - Four-Wave Mixing

HNLF - Highly Nonlinear Fiber

OBPF - Optical Bandpass Filter

OOK - On-Off Keying

OSA - Optical Spectrum Analyzer

PC - Polarization Controller

PCF - Photonic Crystal Fiber

PIA - Phase-Insensitive Amplifier

PM - Phase Modulator

PSA - Phase-Sensitive Amplifier

QPM - Quasi-Phase Matching

RF - Radio Frequency

SBS - Stimulated Brillouin Scattering

SPM - Self-Phase Modulation

SRS - Stimulated Raman Scattering

SSMF - Standard Single-Mode Fiber

WDM - Wavelength Division Multiplexing

XPM - Cross-Phase Modulation

ZDW - Zero-Dispersion Wavelength

xvi

LIST OF APPENDICES

A The cascaded FOPA with pump dithering

setup 57

B The cascaded FOPA without pump dithering

setup 58

C Optisystem software setup for cascaded FOPA

without isolators 59

D Optisystem software setup for cascaded FOPA

with OBPFs 60

xvii

LIST OF PUBLICATIONS

Journal:

(i) F. N. Salleh, N. S. M. Shah, N. N. Shamsuddin, S. N. S. Yaacob, N. Othman,

“Cascaded Fiber Optical Parametric Amplifier with Isolators and Optical

Bandpass Filter using Optisystem.” International Journal of Simulation

Systems, Science and Technology.

Proceeding:

(i) F. N. Salleh, N. S. M. Shah, N. N. Shamsuddin, S. N. S. Yaacob, “The

Investigation on Fiber Optical Parametric Amplifier (FOPA) Bandwidth

using Optisystem.” Proceeding of The National Conference for Postgraduate

Research 2016 (NCON-PGR), UMP, 24-25 September 2016.

(ii) S. N. S. Yaacob, N. S. M. Shah, F. N. Salleh, “High Non-Linear Fiber Length

Verification in Optical Regeneration using Non-Return Zero and Return Zero

Signal.” Proceeding of The National Conference for Postgraduate Research

2016 (NCON-PGR), UMP, 24-25 September 2016.

(iii) F. N. Salleh, N. S. M. Shah, N. Othman, “The Effect of Pump Dithering on

Cascaded FOPA at Each Stage by Using Optisystem.” Proceeding of

International Conference on Electrical and Electronic Engineering 2017

(IC3E), Johor Bahru, 14-15 August 2017.

CHAPTER 1

INTRODUCTION

1.1 Preamble

In the past, the way people communicate with each other is different from what that

have been practiced today. Back then, most of the communication were realized via

voice, writing and signals.

The technology keeps evolving from the increasing demands. One of them is

the transfer of the information within the considerable distance. From the historical

point of view, the rapid growth of the electrical communication is the result of the

invention of the telegraph by Samuel F. B. Morse. The Morse code is represented by

letters and numbers with a series of dots and dashes. The major invention in

communication history is the discovery of the telephone in 1876 by Alexander Graham

Bell [1].

As time goes by, the increasing portion of the electromagnetic spectrum has

enhanced the medium of communication to be more reliable and has the ability to cater

the high capacity to convey messages from one place to another. Optical fiber is one

of the approaches to send messages via long distance transmission. The long-haul

transmission of data is not a problem to optical fiber because of the lower transmission

loss. Besides that, the low operation cost can be achieved by reducing the number of

repeaters. At the same time, the reduction of elements will reduce the complexity of

the systems. The optical fiber is also immune from the electromagnetic interference

since

2

it is made from dielectric materials. The demanding factor of high data rate application

is the reason wider bandwidth is needed. The optical fiber is the medium that can

realize that purpose.

The optical fiber itself experiences nonlinear effects that start to appear at the

increasing level of optical power. The nonlinear effects in an optical fiber are four-

wave mixing (FWM), cross-phase modulation (XPM), self-phase modulation (SPM),

stimulated Brillouin scattering (SBS) and stimulated Raman Scattering (SRS). In this

work, the focus is on the FWM nonlinearities.

Basically, FWM occurs when a light of two or more with different wavelengths

is launched into the optical fiber. When the lights are fed into the fiber, a new

wavelength will appear which is known as an idler [2]. The idler has a different

wavelength as compared to the light that is launched into the fiber. When the two

pumps of FWM have the same frequency, it is known as the degenerated FWM.

In the transmission of the wavelength-division multiplexing (WDM), FWM is

commonly avoided because it can cause crosstalk in the signal that is transmitted

through the optical fiber [3][4]. However, FWM is a practical technological basis for

certain applications. There are many applications for the FWM such as phase

conjugation, parametric amplification, wavelength conversion, ultrafast optical

sampling, optical switching and all-optical regeneration. In this research, attention is

diverted to the fiber optical parametric amplifier (FOPA). FOPA is an amplifier that

can have an amplification bandwidth outside Erbium Doped Fiber Amplifier (EDFA).

FOPA has a potential for amplification and wavelength conversion in multi-terabit/s

dense wavelength division multiplexing (DWDM). There are two types of FOPA

which are one-pump FOPA and two-pumps FOPA [5][6]. In this study, the one-pump

FOPA is chosen because of its simplicity. Besides that, FOPA can offer high gain and

low noise. However, narrow bandwidth of FOPA is the problem. Thus, in this work, a

method to obtain high gain with a wider bandwidth of FOPA is investigated.

1.2 Problem Background

The currents trends of FOPA demand a high gain and bandwidth. One of the

technique to achieved a high gain and wider bandwidth is by using a cascaded FOPA.

Cascaded FOPA is a concatenation technique of a few fibers that had been cut into

3

short pieces and been splice together. The cascaded FOPA is chosen due to its ability

to achieve a high gain or wider bandwidth depending on the components inserted in

between the two fibers. The latest trend involved a four-stage of cascaded FOPA and

show a reliable gain and bandwidth despite it splice loss [7].

However, the result at each stage is not presented. The result at each stage is

an added contribution towards the analysis. The spectrum at each stage of four-stage

cascaded FOPA is observed where the spectrum of pump, signal and idler light is

shown. The observation is focussed on the signal power due to it is related to the gain

and bandwidth. The observation at each stage of cascaded FOPA is quite complicated

to apply in the experimental work. This is one of the reason to conduct a simulation

and observing a spectrum at each stage of cascaded FOPA.

1.3 Problem Statement

The cascaded FOPA can increased the gain and bandwidth with an in-line of highly

nonlinear fiber (HNLF) configurations. A previous work has been conducted which

discussed the effects of passive devices that are added in between the HNLF. However,

the results at each stage of cascaded FOPA is not presented. The results at each stage

is crucial to ensure the cascaded FOPA runs successfully.

This work investigates the effects of components inserted at each stage on the

gain and bandwidth of cascaded FOPA. The in-depth study is also conducted at each

stage to observe the output spectrum of the cascaded FOPA.

1.4 Research Objectives

The objectives of this work are:

(i) To perform four-stage cascaded FOPA configurations.

(ii) To investigate the effects of pump dithering and inserted components towards

cascaded FOPA

(iii) To analyse the signal power at each stage of the four-stage cascaded FOPA

and the gain and bandwidth of the whole system.

4

1.5 Research Scopes

This research is conducted by using an Optisystem software. This four-stage

cascaded FOPA is only focused on the Non-Return to Zero-On Off Keying (NRZ-

OOK) modulation. Besides that, the inserted passive components chosen in this

research are isolators and optical bandpass filter (OBPF). However, there is a

limitation in the characterization at each stage of the four-stage cascaded FOPA. The

analysis only involves the value of signal powers at each stage because it related to the

gain and bandwidth. The bandwidth range involve in this research are from 1535 nm

until 1570 nm.

This research is not considering the splice loss of the four-stage concatenation

fiber. It also neglected the polarization and the phase of the pump and signal light.

1.6 Report Outline

This thesis consists of five (5) chapters. The introduction of this research is

discussed in Chapter 1. The literature review is elaborated in detail in Chapter 2. Next,

the methodology is being examined in Chapter 3. It described the method conducted

to achieve the objective in this study. Subsequently, the results of this study are

presented in Chapter 4 and the analysis towards the cascaded performance is discussed.

Lastly, the study is concluded in Chapter 5.

2CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter describes the theoretical background of nonlinear effects and FWM

phenomenon. In addition, this chapter discusses the nonlinear fiber optics, dispersion,

phase matching, zero dispersion wavelength, fiber optic parametric amplifier (FOPA)

and cascaded FOPA.

2.2 Nonlinear Fiber Optics

Transmission of data in the optical fiber is a challenging process. One of the factors

that need to be considered is the nonlinear effects in the optical fiber. In the next

section, the nonlinear effects are discussed that include Stimulated Raman Scattering

(SRS), Stimulated Brillouin Scattering (SBS), Self-Phase Modulation (SPM),

Cross-Phase Modulation (XPM) and Four-Wave Mixing (FWM). The nonlinearities

can be divided into two categories, which are summarized in Table 2.1 [8].

6

Table 2.1: Summary of nonlinear effects in optical fiber

Nonlinearity category Single Channel Multiple Channel

Index related Self-phase modulation Cross-phase modulation

Four-wave mixing

Scattering related Stimulated Brillouin

Scattering

Stimulated Raman

Scattering

From the table, the first group arises from intensity-dependent variations in the

refractive index in silica fiber. It is known as Kerr effect. These are SPM, XPM and

FWM. The second group is scattering related which comprises of nonlinear inelastic

scattering processes. These are SRS and SBS. The SBS, SRS and FWM results in gain

or losses in a wavelength channel. The power variations, on the other hand, depend on

the optical signal intensity.

2.2.1 Stimulated Raman Scattering

Stimulated Raman Scattering is an interaction between light waves and vibrational

modes of silica molecules [9]. The SRS process generates scattered light at a

wavelength longer than the incident light. If there is a light present in this longer

wavelength, the SRS light will amplify it. This will reduce the power of the pump

wavelength. Consequently, SRS can severely limit the performance of a multichannel

optical communication system by transferring energy from short -wavelength channels

to neighboring higher-wavelength channels.

Figure 2.1 demonstrates the effect. Figure 2.1 (a) illustrates the lights launched

into the fiber before its experience SRS effects. Figure 2.1 (b) shows the light

experience the SRS effects and it scattered the wavelength longer than incident light

up to 125 nm. SRS amplify the signal at the longer wavelength. The pump-wavelength

limiting the power of the signal.

7

Figure 2.1: The optical power transfer (a) before and (b) after the SRS effects [8].

2.2.2 Stimulated Brillouin Scattering

Stimulated Brillouin Scattering (SBS) occurs when the high optical signal generated

an acoustic wave that produces differences in the refractive index. It will cause the

depletion of signal power because the backscattered light receives the gain from the

forward propagating signals. The backscattered light exists when there are variations

in the refractive index. The lightwave will scatter in the backward direction of the

transmitter. Figure 2.2 illustrates the power depletion of SBS.

Figure 2.2: The SBS power depletion from the original signals [8].

SBS is limiting the maximum amount of optical power that can be coupled into

a waveguide [10]. SBS implies a strict limit to the power that will be delivered into the

8

fiber due to the generated backward propagating wave due to the material properties.

This input is known as SBS threshold and can be define as equation 2.1.

21 eff B P

th

o eff B

kA v vP

g L v

(2.1)

where:

k is the polarization state,

effA is the effective modal area,

effL is an effective interaction length,

og is the Brillouin gain parameter,

Bv is the Brillouin gain bandwidth,

Pv is the incident pump linewidths

Most of the fiber that useful for FOPA systems is expected having an extremely

small value of the SBS threshold. Because of this limitation, the SBS suppression

methods must be employed to create a FOPA with net gain.

2.2.2.1 Pump Dithering Method

One of the method to suppress the SBS is by using a pump dithering. In the

pump dithering, the phase or frequency of the pump dithering manipulates the incident

pump linewidth, Pv to minimize the spectral overlap between the incident laser and

the Brillouin bandwidth [11]. Usually, the pump is modulated by using several RF

signals to broaden the linewidth of the pump. It results a limited gain experienced by

the back-reflection.

2.2.3 Self-Phase Modulation

Self-phase modulation (SPM) refers to the phenomenon in which the laser beam

propagating in a medium interacts with the medium and imposes a phase modulation

itself. The nonlinearity in the refractive index is known as Kerr nonlinearity. The

nonlinearity produces a carrier-induced phase modulation of the propagating signal

9

which is known as Kerr effect. It will convert optical power fluctuations to spurious

phase fluctuations in the same waves.

Figure 2.3 indicates the optical pulse propagates in a fiber. Here the time axis

is normalized to the parameter 0t , which is the pulse half-width at the 1 e -intensity

point. The edges of the pulse represent a time-varying intensity, which rises rapidly

from zero to a maximum value, and then returns to zero. In a medium having an

intensity-dependent refractive index, a time-varying signal intensity produces a time-

varying refractive index. Thus, the index at the peak of the pulse is slightly different

than the value in the wings of the pulse. The leading edges is at positive dn dt ,

whereas the trailing edge is at negative dn dt .

This temporally varying index change results in a temporally varying phase

change, shown by d dt in Figure 2.4. The consequence is that the instantaneous

optical frequency differs from its initial value across the phase. That is, since the phase

fluctuations are intensity-dependent, different parts of the pulse undergo different

phase shifts. This leads to what is known as frequency chirping. Frequency chirping is

the rising edge of the pulse (red shift in frequency) which means that the shifting

towards the lower frequencies or longer wavelengths. The trailing edge will experience

a blue shift which is the shifting of the pulse towards the higher frequencies.

Figure 2.3: Optical pulse as it propagates into the fiber [8].

10

Figure 2.4 : The optical pulse experience spectral broadening due to SPM [8].

2.2.4 Cross-Phase Modulation

Cross-Phase Modulation (XPM) exists in WDM systems and has a similar origin as

SPM. Since the refractive index seen by a particular wavelength is influenced by both

optical intensity, SPM is always present when XPM occurs. However, XPM only

arises when two interacting light beams overlap in space and time. But if the light

travels in different group velocities because of the dispersion, the slide past each other

and the XPM effect reduces. The XPM effect is reduced as the polarization of light is

not identically polarized.

2.2.5 Four-Wave Mixing

Four-Wave Mixing (FWM) is a phenomenon when two or more light is pumped into

the optical fiber. In this case, a new light will arise which is called an idler. As

mentioned before, FWM is a third-order nonlinearity in optical fibers that is analogous

to intermodulation distortion in electrical system. When the pumped wavelength is

near zero dispersion wavelength, three optical frequencies mix together to produce the

fourth-order intermodulation product. Figure 2.5 and Figure 2.6 illustrate the two

channel pump wave and one channel pump wave (degenerate FWM), respectively.

The light i j,f f and k i, j kf will interact with each other inside the optical fiber

and generate a new frequency,ijkf .

11

     iij j kkf f f f (2.2)

For the 1-channel pump wave cases, the equation is changes to Equation 2.3,

where i j

2 iijk kf f f (2.3)

These idlers will travel with the first wave and will grow at the expense of the

signal-strength depletion. The efficiency of four-wave mixing depends on the fiber

dispersion and channel spacing. The pump light must be near zero-dispersion

wavelength to achieve the phase-matching condition. The idler power will decrease as

the channel spacing become wider. The idler power can be calculated by Equation 2.4.

2

ijk   0 0 0i j kP L P P P exp L (2.4)

where the nonlinear interaction constant, 𝜅 is:

3

eff1111

2 eff

32 

L

n c A

(2.5)

From Equation 2.5, 1111 is the third-order nonlinear susceptibility, is the

efficiency of the four-wave mixing, n is the refractive index of the fiber, and 𝒟 is the

degeneracy factor which has the value 3 or 6 for two waves mixing or three waves

mixing, respectively. eff

L and eff

A are the effective length and effective area in optical

fiber. α is the attenuation in the fiber and L is the length of the fiber.

Figure 2.5: Two channel pump wave

12

Figure 2.6: One channel pump wave (degenerate FWM)

2.3 Dispersion

Dispersion plays a significant role in optical fiber. Dispersion is the phase velocity that

depends on the optical frequency. In telecommunication, the dispersion is used to

explain the phenomenon where the signals carried by the electromagnetic wave will

have some degradation. The degradation occurs because radiations have various

frequencies and velocities. The dispersion can be divided into two types which are

mode dispersion and chromatic dispersion.

2.3.1 Mode Dispersion

Mode dispersion appears only in multimode. Mode dispersion is a result of each mode

having different values of group velocity at a single frequency. It exists only in

multimode because of the core is larger as compared to the single mode and the rays

can travel to different paths.

2.3.2 Chromatic Dispersion

Chromatic dispersion is a pulse spreading within a single mode. Since the dispersion

depends on the wavelength, it also affects the signal distortion as the signal distortion

increases with the increasing spectral width. The two leading causes of the chromatic

dispersion are:

13

2.3.2.1 Material dispersion

Material dispersion is the variations of the refractive index of the core material as a

function of wavelength. Material dispersion is also known as chromatic dispersion in

which a prism spreads out the spectrum.

2.3.2.2 Waveguide dispersion

Waveguide dispersion effects pulse spreading because of the optical power

propagation is confined to the core. The wavelength will vary the distribution of the

light because of the cross-sectional of the core. It is the reason why the shorter

wavelengths are more confined to the center. The longer wavelengths will propagate

in the cladding. Waveguide dispersion can usually be ignored in multi-mode fibers,

but it is crucial in a single-mode fiber.

2.3.3 Zero Dispersion Wavelength (ZDW)

Zero dispersion wavelengths are the wavelength at which material dispersion and

chromatic dispersion will cancel each other and is equal to zero. The wavelength is

1300 nm for all silica-based optical fiber. For the dispersion shifted fibers, the zero

dispersion wavelengths are 1550 nm.

The phase matching is satisfied when the zero-dispersion wavelength is

positioned at the middle between the two lights. The phased match frequency

bandwidth is narrower for larger wavelength difference [2].

2.4 Fiber Optical Parametric Amplifier (FOPA)

Fiber optical parametric amplifier (FOPA) is one of the applications that is based on

the FWM. FOPA builds on the third-order Kerr nonlinearity of the optical fiber itself.

The higher value of nonlinearity coefficient, γ (about 5-10 times than conventional

fiber [12]) and high power of the input source are necessary to achieve the

amplification outside the Erbium Doped Fiber Amplifier (EDFA). Historically, the

14

first FOPA was demonstrated in 1976 by using low-loss fiber [13].The discovery of

EDFA in late 1980s has sparked the interest on FOPA. It has also contributed to the

development of dispersion-shifted fiber (DSF) with the zero-dispersion wavelength

(ZDW) at 1550 nm in the C-band area. The DSF with the highest value of γ has been

discovered in 1995 by increasing the germanium concentration and decreasing the core

diameter [14].

FOPA has been choosen as an amplifier because of its various advantages. One

of the benefits is it can avoid the degradation due to the chromatic dispersion since it

operates in the ZDW region. It also has low noise figure that can enhance the signal

amplification for long-haul communication. The most important factor is FOPA offers

wider bandwidth and high gain in phase-matching condition. The phase-matching

condition will be described later in this chapter. The research of FOPA has gained

more interest because of the adjustable center wavelength. This is due to the fact that

the Kerr nonlinearity varies slowly with wavelength. Thus, the parametric gain can

achieve the arbitrary wavelength. It also has the advantages of operating on the

(S-C-L) band wavelength [15]. Many features can be applied by using FOPA such as

wavelength conversion, phase conjugation and supercontinuum generation [16].

However, it has limited bandwidth and the methods to widen it have become a

significant interest.

2.4.1 Theory of FOPA

There are two types of FOPA which are One-Pump FOPA and Two-Pump FOPA. One

pump FOPA has a simple configuration as compared to the two-pump. However,

two-pump FOPA offers a wider bandwidth than one-pump FOPA[17].

As mentioned before, FOPA consists of one or two high power waves at

angular frequencies of 1p and

2p that will serve as the pump light sources. The new

wave at angular frequency, i will give rise to an idler. i will be generated at the

mirror image of the signal angular frequency, s where the signal input is the weak

signal that has been interacting with the pump light. Idler will be located at the center

wavelength, c which can be calculated by using Equation 2.6:

15

1 2c p p( ) / 2 , (2.6)

where 𝜔c is located at the halfway of pump 1 and pump 2 and can be simplified using

Equation 2.7:

s i c2 (2.7)

For one-pump FOPA, c is equal to the angular frequency of

pump source, 𝜔P . One pump FOPA is also known as degenerate FWM while the two-

pump is known as non-degenerate FWM [18].

The basic equations in describing the process of FOPA by neglecting the fiber

losses with respect to optical power and phases are as follows [19][20]:

1/2p 2

p s i  4 sin ;dP

P PPdz

(2.8)

1 2

2sp s i2 sin ;

dPP PP

dz (2.9)

1 2

2ip s i2 sin ;

dPP PP

dz (2.10)

1 2 1 2 1 22 2

p s i p s i p s i s i2 4 cos ;d

P P P P PP P P P PPdz

(2.11)

where , sPP P and iP are the powers of the pump, signal, and idler waves, respectively.

is the nonlinearity of the fiber. The linear phase mismatch, can be calculated by

using the formula in Equation 2.12:

s i p2 (2.12)

where the longitudinal propagation constant of p , s and i are expanded by using

Taylor series around ZDW. Therefore, ∆𝛽 is given by:

2

2 4p 4p o s p s p

2 12

dD

c d

(2.13)

16

where:

c is the speed of light in vacuum,

o is the ZDW of the fiber used,

dD

d is the dispersion slope,

p is the pump wavelength,

4 is the fourth-order dispersion coefficient.

The relative phase difference between the waves is described as:

s i p s i2z z z z z z z (2.14)

where p z , s z and i z are the phases of the pump, signal and idler wave.

By referring to the Equation 2.8 to 2.11, the FOPA can be distinguished from

the phase-sensitive by controlling the phase relation, . By controlling the phase

relation, the direction of the power from the pump to the signal to the idler and vice

versa can be controlled. In addition, the signal can be attenuated or amplified by

controlling the phase relation. If 2 , this means that the parametric amplification

is occuring. The signal will be attenuated when 2 . It proves that FOPA can

be either a Phase-Insensitive Amplifier (PIA) or a Phase-Sensitive Amplifier (PSA).

2.4.2 Phase-Matching Condition

Phase-matching is defined as the balance between material dispersion, waveguide

dispersion and nonlinear dispersion [21]. By following the work in [22], it states that

the equation of phase-matching applies to the sum of the wavevectors of the different

waves participating in the process and can be written as:

M W NL (2.15)

17

where M , W and NL is material dispersion, waveguide dispersion and

nonlinear dispersion, respectively.

This condition can only be satisfied if one of the three dispersions is having a

negative value. M is in an anomalous dispersion regime. For single-mode fibers;

M is far less than W except for the region near the ZDW as the waveguide

dispersion and nonlinear dispersion can be adjusted to cancel the small dispersion.

In addition, FOPA must operate in a phase-matched condition. By following

the equations in 2.8 to 2.11; when 𝜃(𝑧) is in phase-matched condition, the value is

close to 2 . Thus, the third term in Equation 2.11 can be neglected and the

approximation in Equation 2.16 can be made [23]:

p s i p s i p2 2 2d

P P P P P P Pdz

(2.16)

where κ is the phase mismatch parameter.

The second approximation is only valid when the amplifier is operating in an

undepleted mode. The linear phase mismatch is crucial to achieve the broad bandwidth

of FOPA. The equation of the linear phase mismatch, shows that it is proportional

to the fiber dispersion slope. The small value of dispersion slope will enhance the

signal bandwidth further.

2.4.3 Gain Spectrum of FOPA

The gain of a parametric amplifier is dependent on the phase-matching condition. The

parametric gain is approximately exponentially proportional to the applied pump

power in the perfectly phase-matched condition.

In addition to the phase-matching, the gain value that can be attained is

dependent on the nonlinear phase shift in the fiber. It can be identified that in the ideal

case of perfect phase matching, where the relative phase is π/2, and does not change

during propagation; the growth of the gain is exponentially dependent on 2 PP L In

the absence of perfect phase matching, the change of the relative phase during

18

propagation need to be considered. Thus, by assuming no pump depletion and

neglecting the signal and idler SPM and XPM due to its small values; the expression

of the gain that relates to the phase mismatch parameter, κ can be derived as

Peff1 sinh

PG gL

g

, (2.17)

Where:

2 22

p 2g P

. (2.18)

In the first case where 0 , which implies perfect phase matching; Equation

2.17 with the large nonlinear phase-shift can be further simplified by using the Taylor

expansion and can be calculated as follows [19]:

exp p eff

1exp 2

4G P L . (2.19)

This case is known as the exponential gain because it depends exponentially

on the nonlinear phase shift. The second case is when 𝜅 = −2𝛾𝑃p which means that

there is no relative phase shift. It is because the signal and the pump wavelength is

similar. Equation 2.17 can be used in case of large nonlinear phase-shift and it is

simplified as Equation 2.20 [19]:

2

quad p eff2G P L (2.20)

This case is known as quadratic gain because of the gain quadratically

depending on the nonlinear phase-shift. Figure 2.7 shows the gain spectrum of FOPA

with the specified exponential and quadratic gain regimes.

19

Figure 2.7: The gain spectrum of FOPA [24]

The previous work in [24] has shown enormous achievement involving gain

spectrum of FOPA. For one-pump FOPA, the gain and bandwidth have been

investigated. In that work, broad bandwidth has been introduced at first by combining

the FOPA with a Raman gain and provided the 200 nm bandwidth with a low pump

power of 13 dBm [25]. Next, the high pump power of 10 W and 16 W are used for one

pump FOPA have managed to achieve bandwidths of 230 nm and 360 nm, respectively

[26][27]. Practically, FOPA is assumed free from depletion, but there are cases where

the reduction is included. In that case, the gain is 62 dB with a bandwidth of 420 nm

and is performed by using the photonic crystal fiber (PCF) as a medium [28]. PCF has

the advantage of broad bandwidth because of the high nonlinearity coefficient. For

example, the PCF also has been used in other cases and achieved 520 nm bandwidth

with small negative anomalous dispersion, 𝛽2 ≤ 0 and positive value of fourth-order

dispersion parameter, +𝛽4 [29].

2.5 Cascaded FOPA

Cascaded FOPA is a technique that uses a concatenation of a few highly nonlinear

fiber (HNLF). The fiber is cut into a few short lengths and spliced together. The shorter

fiber can enhance the bandwidth of the gain spectrum. The first approach of cascaded

FOPA is by rearranging the short pieces of fiber, considering the zero-dispersion of

the fiber [30]. This method has relieved the phase mismatch and an extensive

20

conversion has been achieved. The cascaded FOPA is investigated from the Quasi-

phase matching (QPM) theory. The QPM is one of the techniques to mitigate the

phase-matching effect [31]. QPM technique has been applied to the slot waveguide to

alter the phase-mismatch to achieve the broadband wavelength conversion [32]. In

addition, the QPM has been implemented for transparent optical demultiplexer for

160 Gb/s – 10 Gb/s demultiplexer [33]. There is also an investigation conducted to

observe the modulation instability of the multisection fiber with a numerical

simulation of the nonlinear Schrodinger equation [34]. The design shows that the gain

spectrum bandwidth is exceeded by 100nm with a ripple and 200nm when a pump

power of 5 W is used.

Besides that, a dispersion compensation fiber (DCF) is placed in between the

two HNLF to compensate the HNLF dispersion [35][36].It is known as a periodic

compensation. The widest bandwidth is achieved by using three stages of HNLF with

a DCF. In the same way, the standard single-mode fiber (SSMF) is used to compensate

the dispersion [37]. The difference of dispersion parameter can relieve the phase

matching condition. The value of dispersion is set to get a high absolute value of 𝛽2

that would lead to a high linear phase mismatch and eventually can compensate the

HNLF dispersion and improve the gain. The performance is examined by observing

each stage.

The cascaded FOPA can be analysed by using genetic algorithm [38][39]. The

cascaded FOPA can also be done by rearranging the fiber and putting the isolators in

between the HNLF [40]. The isolators have the ability to suppress the SBS effect [41].

Meanwhile, the highest gain achieved by the two-segment FOPA with an isolator is

60 dB [7]. The gain smoothened with a two-segment has been discussed before by

using the idler removal filter to achieve the dispersion mismatch [42].

An optical bandpass filter (OBPF) has also been used in cascaded FOPA [43].

The gain of FOPA is enhanced as compared to the gain without an OBPF. The pump

shifters have also been used in the cascaded FOPA where a gain of 21dB has been

achieved with a gain flatness bandwidth of 25 nm [44]. Other than that, the cascaded

FOPA with a phase shifter has widened the bandwidth from 9 nm to 30 nm [45]. Fiber-

Bragg grating (FBG) can enhance the bandwidth when it is used in the cascaded

configuration [46]. The cascaded FOPA with a FBG has achieved a 22-dB gain with a

50 nm bandwidth of gain flatness [47].

21

Cascaded FOPA without any elements is an advantage in wavelength

conversion application. The previous work has achieved a 49 dB gain with 56 nm

bandwidth [48]. Additionally, the cascaded FOPA can be used for

polarization-insensitive configuration [49]. The advantages of cascaded FOPA over

the polarization-insensitive configuration is the arbitrary input or output operation

wavelength and the signal transparency. Moreover, the cascaded structure has an

ability to obtain the PSA and PIA [50]. PSA has achieved the bandwidth of 170 nm

while the PIA has reached 160 nm. It is considered significant as compared to the

conventional PSA and PIA. Besides that, the SMF and DCF have been placed in

between PIA and PSA segments to achieve power equalization and the gain bandwidth

is broadened to 15 nm [51]. Table 2.2 shows the previous work of cascaded FOPA.

From the table below, the previous work has been focusing on the gain and

bandwidth because they are the most important parameters to measure the performance

of cascaded FOPA. However, because of the structure of the cascaded FOPA it which

has a few stages of HNLF, the spectrum at each stage needs to be observed to monitor

the changes at the respective stage. In this work, the characteristics at each stage are

observed. It is crucial as it is a lot easier to detect the problems from the stage by stage

basis.

22

Table 2.2 Comparison of previous work for cascaded FOPA

Ref. Element in between

Cascaded FOPA

Number

of Stages

Methodology Performance

Bandwidth Gain

[31] No element (DSF

cascaded with SMF-28)

3 Simulation and

Experimental

16.1 nm 16 dB

[33] No element 2 Experimental 50 nm 23 dB

[34] No element 4 Simulation 100 nm 12 dB

[35] DCF 4 Numerical 40 nm 20 dB

4 Experimental 40 nm 19 dB

[36] 4 Numerical 220 nm 22.84 dB

4 Simulation 80 nm 12.4 dB

[37] SSMF 2 Experimental Not

mention

Not

mention

[38] No element (Genetic

algorithm)

2 Simulation 110 nm 10.5 dB

[39] 3 405 nm 21.54 dB

[40] Isolator 4 Experimental 27 nm 26 dB

[7] 2 50 nm 60 dB

[43] OBPF 2 Simulation 12 nm 40 dB

[44] FBG 3 Experimental 25 nm 21 dB

[45] 4 Experimental 30 nm 10 dB

[46] 2 Experimental Not

mention

33 dB

[47] 2 Experimental 50 nm 22dB

3CHAPTER 3

METHODOLOGY

3.1 Introduction

This chapter highlights the techniques and methods employed to study the

performance of a cascaded FOPA. The effects of pump dithering towards the cascaded

FOPA is investigated. Then, the effects of passive components towards the gain and

bandwidth are observed. The details of simulation work are also explained in this

chapter.

3.2 Simulations in Optisystem software

OptiSystem is a comprehensive software design suite that enables users to plan, test,

and simulate the optical links in the transmission layer of modern optical networks.

The simulations feature the result of each parameter that needs to be observed in this

work.

In this work, each layout can have certain component parameters assigned to

be in a sweep mode. The number of sweep iterations to be performed on the selected

parameters is defined beforehand. It is observed that at the value of the parameters

changes at each sweep of iterations which produces a series of different calculation

results.

24

3.3 The Simulation Components

The simulation is performed to observe the phenomenon of FWM inside the optical

fibers and the gain and bandwidth of the four stages of cascaded FOPA. Besides that,

the output at each stage of cascaded FOPA is observed to monitor the signal power.

The cascaded FOPA setup includes the optical sources, optical amplifier,

optical filter, modulation and visual analyzer. Each of the components is discussed in

the following section.

3.3.1 Continuous-Wave Laser

A continuous-wave (CW) laser is an optical source that will continuously emit

the light. The CW laser is chosen as the input source to the optical fiber due to the

ability of the laser to reach a gain saturation by using a small signal input power [52].

The block diagram of the CW laser is shown in Figure 3.1. In this simulation setup,

the CW laser is used as a pump and signal input source. Table 3.1 tabulates the

parameters of the pump and signal light.

Figure 3.1 : The CW laser block diagram

Table 3.1 : Parameters of the CW laser

Input sources Wavelength (nm) Power (dBm)

Pump light 1554.1 30

Signal light 1540 – 1570 -20

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