SIGNAL LOSS AT OPTICAL FIBER SPLICED JOINTS

A PROJECT REPORT SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF

MASTER OF ENGINEERING (M.ENG) IN ELECTRONIC ENGINEERING (COMMUNICATION OPTION)

BY

MOJEKWU, OKWUCHUKWU EMMANUEL PG/M.ENG/07/43630

UNIVERSITY OF NIGERIA NSUKKA FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRONIC ENGINEERING

DECEMBER 2011

2

i

TITLE PAGE

SIGNAL LOSS AT OPTICAL FIBER SPLICED JOINTS

A RESEARCH PROJECT PRESENTED TO THE DEPARTMENT OF ELECTRONIC ENGINEERING UNIVERSITY OF NIGERIA,

NSUKKA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE AWARD OF MASTER OF ENGINEERING (M.ENGR) IN

ELECTRONIC ENGINEERING

BY

MOJEKWU OKWUCHUKWU EMMANUEL PG/M.ENG/07/43630

ii

APPROVAL/ CERTIFICATION PAGE

This project was submitted to the Department of Electronic Engineering, University

of Nigeria, Nsukka for the award of the degree of Master of Engineering

(Communication Option)

------------------------------------------------------- ---------------------------------- Mojekwu Okwuchukwu Emmanuel Date PG/M.ENG/07/43630 (Student) ------------------------------------------------------- ---------------------------------- Engr. Prof. A. N. Nzeako Date (Supervisor) ------------------------------------------------------ ---------------------------------- Engr. Prof. O. U. Oparaku, Date (Head of Department) ------------------------------------------------------- ---------------------------------- Engr. Prof J.C. Agunwamba Date (Dean Faculty of Engineering) ------------------------------------------------------- ---------------------------------- (External Examiner) Date

iii

DEDICATION

This work is dedicated to my parents late Mr. Mojekwu Ngoka Emmanuel and late

Mrs. Mojekwu Afubene Patricia, for sowing the seed of excellence in my life.

iv

ACKNOWLEDGEMENTS

I sincerely thank God Almighty, my ultimate source of hope and strength for guiding

me throughout the duration of the study.

I express my earnest and sincere thanks to my supervisor, Engr. Prof. A. N. Nzeako

for painstakingly supervising this work and making constructive criticisms.

Engr. Prof. O. U. Oparaku, the Head of the Department, Dr C. I. Ani, Engr. M. A.

Ahaneku, Engr. Fred Eze, Engr. Okonor Obinna, Mr. Uwakwe and other staff of the

department also share in the glory of my academic training.

My appreciation also to Dr L. N. Binh of Monash University; Clayton Australia for

his help in the use of MATLAB© Simulink to model optical network.

My profound appreciation to Engr. C.C. Nzekwe and Engr. Shola Joseph Omoyode of

Astera Engineering Nigeria Ltd; for allowing me to use their facilities.

I thank Mr. Obiora Okoye, MD of Vast Ltd, Engr. Silas Obinwa and John Mathew ;

NAOC AGIP/Eni-Saipem Spa, Nigeria –Sao Tome Joint Development Authority

(JDA –BLOCK 4) and the Petroleum Technology Development Fund (PTDF) for

their financial assistance and help.

I wish to express my appreciation to my classmates especially Val, Dozie, James,

Rhema, Dubem, Ify and Joy for the great moments we shared together.

Outside the classroom, I thank Chief and Mrs. Uche Mojekwu (Ijeneme I), Engr. D.

C. Mojekwu of the Federal College of Education (Technical) Umunze, Bldr (Sir) and

Lady (Dr) J. A. Ezeuchu of Nnamdi Azikiwe University Awka, Dr (Mrs.) Chinyere

Nwabunwanne, Chukwuma Aguata of McCemag Nigeria Ltd; and Ikechukwu D.

Mojekwu (Opokonja), Mrs. Bridget I. Ezimadu, Dame Mercy Onebunne , Dr A. O. C

Mojekwu, Barr C. C. Mojekwu, Air Commodore C. K. S. Mojekwu, Prof Oby

Okonkwo –Mojekwu, Pharm. Ezeuchu Onyiye and Ngozi Ilebo for help rendered.

v

Members of the Catholic Association of Postgraduate Students, St. Peters’

Chaplaincy, University of Nigeria, Nsukka especially 2007/08 executives where I

served as the image maker including Mbachu Vitalis-the President, Okeke Ogo, Izu

Ndukaihe, Uzoma Osualla, Eboh Frank, Ekwem Oge Hannah, Desmond Nnamani,

Nseh Obong Utoh and Chukwuma Azuka for their constant prayers.

I remember the help I got from Bede Ugwu, Oje Obinna, Ufondu Nwankwo, Nwaka,

Joe Ikenyiri, Tony Nkwocha and Anthony Chibuko.

May God reward your efforts.

vi

TABLE OF CONTENTS

Page Cover page i

Approval/Certification ii

Dedication iii

Acknowledgement iv

Table of Contents vi

List of Figures xi

List of Tables xiv

List of Abbreviations xv

Abstract xvii

Chapter One Introduction 1

1.1 Background of the Study 1

1.2 Statement of Problem 2

1.3 Objectives of the Study 3

1.4 Scope and Limitations of the Study 4

1.5 Thesis Outline 4

Chapter Two Literature Review 5

2.1 Splicing Loss Equations for Single Mode Fibers 5

2.1 Splicing Loss Equations for Multi Mode Fibers 6

2.3 Other Derived Applications for Fiber Splicing Loss Equations 7

2.4 Choice of Analytical Models for Splice Loss 10

2.5 Classification of Losses in Optical Fiber 10

2.5.1 Intrinsic Loss 10

2.5.2 Extrinsic Loss 11

vii

2.6 Optical Fiber Transmission Rates 13

2.7 The Optical Link Architecture 15

2.7 The Optical Link Architecture 16

Chapter Three Methodology 16

3.1 Assessment of Losses at Optical Fiber Joints 16

3.2. Splicing Preparation Steps 16

3.3 Measurement Using the OTDR 19

3.4 Bit Error Rate 22

3.5 Development of Matlab Simulation Blocks 23

3.5.1 Optical Carrier Source Model 23

3.5.2 MZIM Modulator Model 24

3.5.3 Linear Fiber Propagation Model 24

3.5.4 Receiver Model 26

3.5.5 Optical Splice Joint Model 27

3.6.6 Assumptions and Simulation Parameters 28

Chapter Four Measurement, Simulation Results and Analysis 29

4.1 Measurement Procedure 29

4.2 Measured Splice Losses 29

4.3 Calculated Lateral and Angular Misalignment Values 30

4.4 Result of Splice Loss Inspection 31

4.5 Result of the Reflectance (Return Loss) Measurement 33

4.6 Determination of the Optical Link Power Budget 36

4.7 Simulation Results 36

4.7.1 Signal Distortions at Scope 36

4.7.2 Bit Error Rate (BER) 38

viii

4.8 Results of One-Way Anova Statistical Analysis 41

Chapter Five Conclusion and Suggestions 42

5.1 Conclusion 42

5.2 Suggestions 42

References 44

Appendix A Optical Fiber Cable Drum Data Sheet 49

Appendix B Matlab Optical Simulation Model Without Traffic 50

Appendix C Matlab Optical Simulation Model With Traffic 51

Appendix D Amplifier Datasheet 52

Appendix E Analysis of Variance (ANOVA) for Fiber Tubes and Colours 53

Appendix F Splice Loss Equations for Single Mode Fibers 54

Appendix G Typical System Initialisation MATLAB m-file 60

ix

LIST OF FIGURES

Figure 2.500 Intrinsic loss in optical fiber waveguide

Figure 2.501 (a) Extrinsic loss from microbending (b) extrinsic loss from

macrobending

Figure 2.502 (a) Insertion loss from misaligned core diameters (b) insertion loss

from angular misalignment (c) insertion loss from air gap (d) insertion

loss from contamination

Figure 2.700 General optically amplified DWDM point-to-point link propagtion in

optical fiber

Figure 3.200 Semantic of fusion splicing of optical fibers

Figure 3.201 Flow chart for fiber fusion splicing

Figure 3.300 Nanjing DVP-730 arc fusion splicer machine (courtesy of Astera

Nigeria Ltd)

Figure 3.301 Nanjing DVP-105 cleaving machine (courtesy of Astera Nigeria Ltd)

Figure 3.302 Nanjing KL-6200 OTDR machine (courtesy of Astera Nigeria Ltd)

Figure 3.303 Fusion splicing of fiber lengths

Figure 3.400 Eye pattern

Figure 3.500 Sinewave source from Simulink block

Figure 3.501 Block diagram of the linear fiber model

Figure 4.400 Bar chart of splice loss measurement

Figure 4.401 Bar chart of calculated lateral misalignment versus angular

misalignment measurement

Figure 4.500 Return loss at point AA

Figure 4.501 Return loss at point AB

x

Figure 4.502 Return loss at point AC

Figure 4.503 Return loss at point AD

Figure 4.700 Signal scope at 0.01dB (a) before and (b) after splice joint

Figure 4.701 Signal scope at 0.019dB (a) before and (b) after splice joint

Figure 4.702 Signal scope at 0.05dB (a) before and (b) after splice joint

Figure 4.720 Eye diagram (BER) before filtration (a) without load (b) with 100%

traffic

Figure 4.721 Eye diagram (BER) after filtration (a) without load (b) with 100%

traffic

Figure 4.722 Eye diagram (BER) at the receiver (a) without load (b) with 100%

traffic

xi

LIST OF TABLES

Table 2.500 Sources of transmission loss in optical fibers (waveguides)

Table 2.600 Optical transmission rates

Table 3.300 Simulation parameters

Table 4.200 Measured splice loss at points AA, AB, AC, AD

Table 4.300 Calculated lateral and angular misalignment values

Table 4.400 Summary of OTDR readings and measured splice loss readings

Table 4.401 Summary of attenuation readings recorded by the OTDR and qouted

factory attenuation values of the fiber

Table 4.402 Summary of splice loss contribution to overall optical links loss

xii

LIST OF ABBREVIATIONS

Amp Amplifier

BER Bit Error Rate

dB Decibel

dBm Power level in dB

DCF Dispersion Compensation Fiber

Demux Demultiplxer

DWDM Dense Wavelength Division Multiplexing

EM Electromagnetic

EMI Electromagnetic Interference

EMP Electromagnetic Pulses

FFT Fast Fourier Transform

Gbps Giga bits per second

GHz Giga Hertz

GSM General System for Mobile Telecommunications

HF Holey Fiber

IEC International Electrotechnical Commission

IFFT Inverse Fast Fourier Transform

ITU International Telecommunications Union

ITU-T ITU – Telecommunication Standardization Sector

Kbps Kilo bits per second

km Kilometer

LAN Local Area Networks

LED Ligth Emiting Diode

MAN Metropolitan Area Networks

Mbps Mega bits per second

MFD Mode Field Diameter

MHz Mega Hertz

Mux Multiplexer

mW Milliwatt

MZDI Mach Zehnder Delay Interferometer

MZIM Mach Zehnder Interferometric Modulator

NA Numerical Aperture

xiii

NEC National Electrical Code

OC-1 Optical Carrier- level 1

Opt Optical

OTDR Optical Time Domain Reflectometer

QoS Quality of Service

Regen Regenerator

RFI Radiofrequency Interference

Rx Receiver

SDH Synchronous Digital Hierarchy

SNR Signal-to-Noise Ratio

SONET Synchronous Optical Network

SSMF Standard Single Mode Fiber

STM-1 Synchronous Transport Module-level 1

STS-1 Synchronous Transport Signal-level 1

TAM Power coefficient for angular misalignment

TLM Power coefficient for lateral misalignment

Tx Transmitter

UV Ultra Violet

WAN Wide Area Networks

WDM Wavelength Division Multiplexing

µm Micrometer

xiv

ABSTRACT

This study analyses the characteristics of signal loss at optical splice joints. This

includes the investigation of splicing loss contribution to the links overall loss.

Splicing losses from four different points spread along an optical link were measured.

The lateral and angular misalignment loss equations for single mode fiber were

employed to determine the lateral separation distances and angular deviations of each

splice joint from the measured losses at the spliced joints. A one way ANOVA test

performed on the splice losses at p-value of <0.05, firstly on the tube and fiber

colours, indicated that the differences in the mean values among the treatment groups

are not great enough to exclude the possibilty that the difference is due to random

sampling variability; there is not a statistically significant difference on the tube.

However there is a significant difference among the colours. The statistical minimum,

maximum and average of the values splicing losses obtained were used to run a

MATLAB simulation developed with simulink blocks for optically modulated

transmission system. The developed simulation model was monitored with several

scopes which were tapped in the link and the effects of splicing losses on the link

were viewed and analysed. The simulation results indicate that a high splicing loss

will increase the level of signal distortion. The attenuation level observed for the fiber

length shows a slight difference from the factory quoted values. Thus at a sufficient

traffic volume, the distortions will have a significant effect on the overall integrity of

the link’s signals.

1

CHAPTER ONE INTRODUCTION

1.1 Background of the Study To handle the ever increasing demand for high-bandwidth services by

telecommunication users in Nigeria, communication providers deploy optical fibers as

the choice of transmission medium. The incredible advancements in communication

engineering in the country have opened an appetite for new services and more

bandwidth requirment that the traditional communication network has ran short of

bandwidth capacity [2]. In addition to high bandwidth demand, many new services

demand high quality of service (QoS) indices, reliability, availability and real-time

deliverability as well as bandwidth elasticity, and bandwidth on demand [39]. Again

the conventional method of signal propagation using microwave has some negative

impacts on the environment. This comes from pollution coming from exhaust of

generators mounted at base stations and radioactive emmissions from the base station

masts.

Optical fibers are dielectric wave guiding devices used to confine and guide light. A

simple optical network includes a laser diode as an optical source and fiber optic as a

medium of transmission and detector as a part of receiver. To achieve this, optical

network cables are joined at strategic intervals to have a closed communication link.

Joints are inevitable in optical fiber links as it is not economical and viable to have a

single continuous long haul of optical cable for signal propagation that will link the

various components of the optical communication system over a considerable

distance. The choice of joint to be made is based on whether a permanent bond or an

easily demountable joint is desired. A permanent bond on an optical fiber cable is

called a splice while an easily demountable joint is called a connector.

2

1.2 Statement of Problem

The introduction of optical fiber transmission system for GSM and other

communication sevices in Nigeria came with varying degrees of problems. These

include absence of regulatory framework, unsatable electricity (power) supply, lack of

qualified and skilled manpower, communication system compatiblity issues,

environmental impact assessment issues, cost implications for the new technology and

issues of returns on investment.

To install the optical cables either for long haul transmission (backbone) or short

spans of few kilometers, the cable must be joined to have complete communication

link. Fiber joining techniques are subject to certain conditions that cause varying

degrees of optical power loss at the joints. These losses depend on parameters such as

the input power distribution to the joint, the length of the fiber between the optical

source and the joint, the geometrical and wave guide characteristics of the two fiber

ends at the joint and the fiber end qualities [1]. The optical power that can be coupled

from one fiber to another one is limited to the number of modes that can propagate in

each fiber. For example, if a fiber which has a greater number of modes is coupled

(connected) to another fiber with less number of modes, a percentage loss in optical

power is inherent from the first fiber to the second assuming all the modes were

excited. The considerations of analytical models developed to calculate the level of

loss at the joints have not been exhausted as the mathematical equations developed

are merely pessimistic or addressed only a part of the multiple of the causes

responsible for the loss at the joints [1]. This is because it is difficult to predict the

exact loss at the joints as the signals propagate down the link owing to the

unpredictable nature of light waves as it moves along a medium especially in multi

mode fibers [1]. Asides these, practical field working conditions where these

3

installations are carried out do not give room for complicated and complex methods

for the calculation and determination of signal losses emanating from fiber joints [3].

1.3 Objectives of the Study

Attenuation and signal degradation as light signals propagate along a fiber wave guide

is an important consideration in the design of optical communication system as it will

help in determining the unaided (without amplifiers and repeaters) permissible

transmission distance between a transmitter and the receiver [5].

Since amplifiers and repeaters are expensive to manufacture, install and maintain, the

degree of attenuation and signal degradation from fiber joints has a large influence on

overall system performance. These distortion mechanisms in a fiber cause the optical

signal pulses to broaden as they travel along a fiber [1]. If these pulses travel

sufficiently far, they will eventually overlap with neighboring pulses, thereby creating

errors in the receiver output thus reducing the integrity of the optical fiber network.

The project aims at determining the signal loss at optical spliced joints. The splicing

loss equations for lateral and angular misalignments proposed by Marcuse D. [4] was

used to determine the lateral distances and angular separations of the spliced fiber

ends with a view of establishing the level of influence of spliced losses on a selected

optical link. The influence of splicing joints on the optical communication link was

viewed and analysed using MATLAB simulation tool.

As Nigeria leading telecommunication providers plan massive deployment of optical

fiber cable, the study therefore will help in policy formulations for optical fiber

deployment in the country, determine the level of technical competence of splicers,

determine the contributions of splicing machines (as a result of machine

malfunctioning) and level of errors introduced by optical cable supplied by vendors to

the overall link’s loss.

4

1.4 Scope and Limitations of the Study

Predictions of joint losses in fiber are very difficult. For instance analytical models

can predict instanteneous result but fail to give accurate results because of the nature

and behaviors of light waves as it propagate along a fiber after a considerable distance

[10]. Again considering the fact that in practical optical fiber transmission system, the

optical components have to interact with a number of digital and electronic circuits

that have a different characteristic behavior with the fiber cable, mathematical

analysis of the joint losses invoke a lot of assumptions that may be too pessimistic and

therefore introduce errors that mar the accuracy of the results [4]. Providing a hands-

on experience and laboratory experimentations can be costly especially in the field of

optical communication. Thus relying only on hardware manipulations to analyze

optical joints is not economically viable [3].

The scope and limitations of this work therefore involve measurement of splicing

losses at optical joints and the applications of lateral and angular misalignment

models [4] to determine the separation lateral distance and angular misalignments.

1.5 Thesis Outline

This work is further organized as follows; in chapter two a review of literature is

carried out. In chapter three, the methodology and development of simulation models

for the analysis of losses of spliced joints are considered. Measurement, simulation

and results analysis are considered in chapter four. Chapter five treats the conclusion

and suggestions made for further studies. Lastly, the work concludes with references

and appendices.

5

CHAPTER TWO

LITERATURE REVIEW

2.1 Splicing Loss Equations for Single Mode Fibers

Splice loss theory for single mode fiber is well established with detailed studies by

various reseachers. Marcuse D. [4] determined the splice loss for step index fiber. The

analysis is based on the principle that the mode field of the single mode fiber is nearly

Gaussian in shape hence the splice losess are related to the corresponding losses of the

Gaussian beams [4]. The gaussian beam shape of the mode field of a single mode

fiber theory was colloborated by Miller C.M. [5] but emphasised that the use of

Gaussian power distribution model for splice analysis is difficult since joints are

located at least 1km or less apart in most trunks as power distribution would exist

after several kilometers of fibers.(each segment of the fiber has a slightly different

steady state power distribution.) He went further to suggest that the best way for

splice loss characterisation should be by measuring a typical source power loss and

with typical lengths of fibers and splices or connectors preceeding it.

The mode field radius of a Gaussian beam is defined as the radial distance at which

the amplitudes are at 1/e of their peak. Given mode radii of w1 and w2 in the

respective fibers, the splice loss for lateral misalignment (offset) for a perfect splice

alignment that is at d = 0 for a single mode fiber is given by [4]:

2.100

For a Gaussian shaped beam, the loss between an identical fibers having lateral

misalignment (offset) loss, that is at is given by [4]:

2.101

6

where LLS = splice loss due to lateral misalignment; at d=0 or ∞, W = spot size =

mode field diamter [6] and d is the lateral misalignment(separation distance).

Equation 2.101 can be compressed as [7] to yield

2.102

For angular misalignment (fiber with tilt), the splice loss is given by [4] to be

2.103

Equation 2.103 can be compressed by [7] to yield

2.104

where LAS is the splice loss due to angular misalignment for single mode fiber, is the

angular misalignment in radians, w is the Gaussian spot size =MFD [6], n2 is the

refractive index of the cladding, λ is the wavelength of the light.

2.2 Splicing Loss Equations for Multi Mode Fibers

Young M, [53] assumed multi fibers to be illuminated uniformly across the core and

within the acceptance half angle θ, with joint index matching fluid. Since the

illumination is uniform, the transmission in the one dimensional case by inspection

simply gave a lateral or radial misalignment of

2.106

where b is the width of the core (the diameter in real fibers), δ is the lateral

misalignment distance and Tδ is the transmission connection in the direction of the

light in the misaligned fiber which can be approximated to be the splice loss.

For a multimode fiber, the lateral misalignment splicing loss is given by [6] as

2.105

7

where LLM is the splice loss due to lateral misalignment for multimode fiber, d is the

lateral misalignment distance, ɑ is the diameter of the fiber.

And for multimode fiber applications,the splice loss between identical fibers due to

angular misalignment can be expressed as [52]

2.106

For the angular misalignment, [53] assumed that the acceptance half angle of the fiber

to be θ. The numerical apperture, NA is equal to nsinθ, where n is the index of the

core. If the second fiber is inclined at angle to the first, then some of the rays

emitted from the first fiber will fall on the second with angle of incidence greater

than θ. Given the assumption of uniform illumination with a full angle of 2θ, this

implies that:

2.107

where is the is the transmission connection in the direction of the light in the

misaligned fiber which can be approximated to be the splice loss.

2.3 Other Derived Applications for Fiber Splicing Loss Equations

Nemota S. and Makinto T. [43] derived the connector (coupling) loss between single

mode fibers that have unequal mode field diameters, lateral, longitudinal and angular

offsets plus reflections. The derived equation is given as

2.108

where ρ = (kW1)2

q = G2+(σ +1 )2

u = (σ +1 )F2 +2σFGsinθ + σ(G2+σ +1 )Sin2θ

F =

8

G =

σ =

k =

n1 = core refractive index of fibers

n3 = refractive idex of medium between fiber

λ = wavelenght of optical source

d = lateral offset

s = longitudinal offset

θ = angular misalignment

W1 = 1/e mode field radius of transmitting fiber

W2 = 1/e mode field radius of receiving fiber

The derived equation for the single mode coupling loss gave a good correlation with

experimental investigations as reported by [44].

Kihara M. et al [45] derived the connector return loss equation for index matching

fiber. The equation is given as

2.109

This approximation can be extended to determine the return loss for a mechanically

spliced fiber joint provided the index matching gel provided to reduce return (

reflectance loss) do not shrink during usage and thermal expansivity of the gel is of

permisible limit [46].

Varoius researchers such as Lin T.Y. [6] have applied the fiber splice loss equation as

derived by [4] in the design and modeling of fiber connectors. This indicates that the

splice loss equations can be used as good approximation for the fiber connector loss

9

equation. The assumption for the splice loss approximation for the splice connector

are that

1. The numerical appertures (NA) of the connecting fibers are the same.

2. The diameters of the connecting fibers are identical.

3. Matching fluids are used during connecting and further testing.

4. The end faces of the fibers contact.

Lizier J. [7] used the splice loss equation in the determination of splicing loss, spot-

size conversion and coupling factor of Holey fiber material. The splice loss formulae

are used to predict Holey fiber (HF) parameters.

Ieda Koji et al [10] applied splice loss equation of [4] in the determination of splicing

and bending loss characterizations of hole assisted fiber. The splice loss of the hole

assisted fiber (HAF) was investigated taking into consideration the mode field

diameter (MFD) mismatch and the refractive index of the matching material of the

fiber material.

Nakajima Kazuhide et al [47] also applied the splice loss in the design of the mode

field diameter (MFD) characteristics of a hole assisted fiber (HAF) which is

insensitive to bending loss. The splice loss equation of [4] was used because the

designed hole assisted fiber transmission characteristics is compatible to conventional

single mode fiber (SMF).

As noted by [6], the practical measurement of connector or splice loss can be divided

into two namely insertion loss and return loss. These two terms are defined as

2.110

2.111

(Signal Power)in

(Signal Power)out = Insertion Loss

(Signal Power)reflected

(Signal Power)in = Return (Reflectance) Loss

10

These two equations are useful in the experimental measurements since these can

quantify input and output power however these can not be used in theoritical analysis

as these represent the physical phenomenon but no design parameters.

2.4 Choice of Analytical Models for Splice Loss

The choice of the splice loss models in equations 2.101 and 2.103 developed by [4]

were adopted based on the type of the optical fiber deployed in the transmission link

being considered. Certain assumptions in the developed model are applicable only to

single mode fibers and may be extended in the analysis of connector type of joints

provided that certain conditions clearly spelt out for instance in [6] are met.

The splice loss model for gap is not considered since the fusion splicing machine will

ensure that the fiber ends contact properly. The splice loss models for angular (offset)

and lateral (longitudinal) separation are thus employed to analyze the separations in

the fiber.

2.5 Classification of Losses in Optical Fibers

Losses in optical fibers are classified into two namely intrinsic and extrinsic.

2.5.1 Intrinsic Loss

Loss due to inherent traits within the fiber; for example, absorption and

scattering.

Absorption loss is light energy being absorbed in the glass, or more

specifically, the removal of light by non-reradiating collisions with the atomic

structure of the optical core.

Scattering loss is the removal of light due to light being "scattered" after

colliding with a variation in the atomic structure of the optical material.

Insertion loss is the total power loss caused by the insertion of a component

such as a splice or connector in an optical fiber system. Intrinsic loss can also be

11

caused by impure molecules from processing issues, pure, but rare molecules, or

impurity intentionally introduced during processing (doping) [34].

2.5.2 Extrinsic Loss

Loss that is induced in an optical transmission system by an external source. If an

external source introduces loss to an optical fiber medium, then the following classes

of loss are obtained.

Microbending in optical fiber, sharp but microscopic curvatures that create

local axial displacements of a few microns and spatial wavelength displacements of a

few millimeters. One frequent cause is longitudinal shrinking of the fiber buffer [9].

But it also can result from poor drawing or cable manufacturing methods and

installation.

Macrobending occurs when the fiber is bent into a visible curvature. A

relatively large-radius bend in an optical fiber may be found in a splice organizer tray

or a fiber-optic cable that has been bent. A macrobend will result in no significant

radiation loss if it is of sufficiently large radius. This depends on the type of fiber.

Single-mode fibers have a low numerical aperture, typically less than 0.15 [9], and are

therefore are more susceptible to bend losses than other types.

Figure 2.500 Intrinsic loss in optical fiber wave guide [20]

12

(c)

(b)

d

θ

d 2a1

2a1

Figure 2.501 (a) Extrinsic loss from Microbending (b) Extrinsic loss from macrobending [9]

Insertion loss from misalignment of mismatched core diameters

Insertion loss from angular misalignment

Insertion loss from air gap (there is no physical contact between the fibers)

Insertion loss from contamination

Dirts,scratches or chips

Fiber core

(a)

(d)

Figure 2.502 (a) – (d) Different optical insertion (splicing) loss mechanisms [4,20]

13

Transmission loss

Causes

1. Absorption

Intrinsic

Impurity

Defects

- UV Electronic transitions - IR molecular vibrations - Transition metals - Rare earths - Interstitials - Matrix impurities - OH vibrations - H2 vibrations - Vacancies - Radiation induced - Thermally induced - H2 induced

2. Scattering Rayleigh Bulk imperfections Waveguide imperfections Brillouin, Raman

- Minute density and concentration fluctuations - Bubbles, inhomogeneities, cracks - Core, clad interfacial irregularities - Spontaneous

3. Waveguide Macrobending Microbending Design Stimulated Raman,

Brillouin

- Curvature induced - Perturbation induced - Radiative - Depends on power density

Table 2.500 Sources of transmission loss in optical fibers (lightguides) [21].

2.6 Optical Fiber Transmission Rates

The advent of high capacity fiber transmission lines necessitated the establishment of

standard signal format for service providers. The signal formats are called

synchronous optical network (SONET) in North America and synchronous digital

hierarchy (SDH) in other parts of the world. These standards define a synchronous

frame structure for sending multiplexed digital traffic over optical fiber trunk lines.

The first level of SONET signal hierarchy is called the synchronous transport signal-

level 1 (STS-1) with bit level of 51.84 Mbps. Higher rate SONET signals are obtained

14

by byte-interleaving N of these STS-1 frames, which are then scrambled and

converted to an optical carrier- level (OC-N) signal. Thus the OC-N signal will have a

line rate exactly N times that of an OC-1 signal. For SDH systems the fundamental

building block is the 155.52-Mbps synchronous transport module—Level 1 (STM-1).

Again, higher-rate information streams are generated by synchronously multiplexing

N different STM-1 signals to form the STM-N signal. The test optical link where the

splicing process was done have 155 Mbps transmission rate.

SONET level Electrical level SDH level Line rate, Mbps Common rate name

OC-1

OC-3

OC-12

OC-48

OC-192

OC-768

STS-1

STS-3

STS-12

STS-48

STS-192

STS-768

-

STM-1

STM-4

STM-16

STM-64

STM-256

51.84

155.52

622.08

2,488.32

9,953.28

39,813.12

-

155 Mbps

622 Mbps

2.5 Gbps

10 Gbps

40 Gbps

Table 2.600 Some commonly used Optical SONET and SDH information

transmission rates [1].

2.7 The Optical Link Architecture

A general optical link may contain all or part of the components mentioned above.

The choice of component depends on the nature of the signals to be handled and

design requirements. The Wavelength Division Multiplexing (WDM) is the optical

technology that couples many wavelength carrier light waves transmitting over the

same single mode fiber. This increases the aggregate bandwidth per single fiber to

integrate the bit-rate of all wavelength channels. The Dense Wavelength Division

Multiplexing (DWDM) technology offers larger (denser) number of wavelengths

15

coupled into a fiber compared to WDM with closer spacing between carries of the

channels [17].

Figure 2.700 shows the DWDM architecture adopted in the implementation of the

MATLAB simulation.

In-line OA wide band for multiwavelength

Opt fiber

mux demux Opt ADM

Tx

Tx

Tx

Tx

Regen

Regen

Regen

Regen

Rx

Rx

Rx

Rx

WDM mux WDM demux

amp

Figure 2.700 General optically amplified DWDM point-to-point link [12,15,17]

16

CHAPTER THREE

METHODOLGY

3.1 Assessment of Losses at Optical Fiber Joints

There exist three possibilities in the assessment of losses at optical fiber joints. These

include:

Measurement surveys using appropriate instrumentation like optical time

domain reflectometer, OTDR. Nanjing Model KL-6200 OTDR was used to

measure the attenuation of the fiber cable against the quoted attenuation

results at the point of manufacture. Also splicing losses at selected points

along the test fiber link were measured and used to calculate the lateral

separation values and angular deviations at the measured spliced joints.

Employing computational methods in order to simulate the propagation

scenarios. Due to the absence of optical spectrometer , the Matlab® Simulink®

event environment was used to model and view graphically, the influence of

splicing loss as the signals propagate down the optical link.

By using simplified mathematical analytic methods. The splicing loss

equations 2.101 and 2.103 developed by Marcuse D [4] were used to obtain

the lateral separation distances and angular deviations of the measured spliced

joints once the measured splice loss values were known.

3.2 Splicing Preparation Steps

Fusion splices are made by thermally bonding prepared fiber ends, where the fiber

ends are first aligned and then butted together. This is done either in a grooved fiber

holder or under a microscope with a micromanipulator [40]. The butt joint then is

heated with an electric arc or a laser pulse so that the fiber ends are melted

momentarily and hence bonded.

17

The following steps are taken when splicing joints at fiber ends:

Step 1: Preparing the fiber - Strip the protective coatings, jackets, tubes, strength

members, etc. leaving only the bare fiber showing. The matching gel is

wiped with spirit or any other appropriate cleaning solvent. The main

concern here is cleanliness of the surface of the fiber lengths.

Step 2: Cleave the fiber - the cleave precision is critical. Fiber tip is also kept free

from contamination to help couple the light from one fiber end to the other.

Step 3: Mechanically join the fibers - Simply position the fiber ends together inside

the splice unit and allow the splicing machine to weld the two fibers

together.

Step 4: Protect the fiber - the completed splice is provided with protection by ferrule

which houses the joint and then heated for the proper bonding. The spliced

length is then kept in a protective encapsulation.

Step 5: The encapsulation is then placed firmly using fasteners at the pole or buried

underground in a trench.

Electric arc or laser fusion welder

Figure 3.200 Semantic of fusion splicing of optical fibers [1]

Micromanipulatable fiber holders

18

Yes

No

No

Yes

Fiber cutting/ removal of protective

coating, jacket

Check if fiber is

damaged?

Fiber cleaning with solvents

and removal of matching index

oil

Fiber tip preparationn

Cleaving

Fusion splicing

Is the splice loss ≤ 0.05dB

Ferrule alignment and setting

Tray arrangement and encaspulation

Final cover up and fiber duct protection

End

Figure 3.201 Flow chart for fiber fusion splicing

Start

19

3.3 Measurement Using the OTDR

The optical time domain reflectometer is used to make single ended measurements in

optical link characteristics and faults tracing. Such characteristics include fiber

attenuation, connector and splice losses reflectance levels from link components and

chromatic dispersion [2]. The OTDR fuctions by injecting a series of optical pulses

into the fiber under test. It also extracts, from the same end of the fiber, light that is

scattered (Rayleigh backscatter) or reflected back from points along the fiber. The

strength of the return pulses is measured and integrated as a function of time, and is

plotted as a function of fiber length.

To get the attenuation level of the optical power in the link,the OTDR was connected

by a patch cord to the joined fiber end, the optical power of the OTDR was lauched.

The process is repeated at the end of fiber length to see if there is any significant

differences in the reading. It may be possible to have different readings due to the fact

that adjacent fibers may have different backscatter coefficients, so the second fiber

reflects more light than the first fiber, with the same amount of light travelling

through it. If the OTDR is placed at the other end of this same fiber pair, it will

measure an abnormally high loss at that joint. However if the two signals are then

combined, the correct loss will be obtained.

For this reason, it is common OTDR practice to measure and combine the loss from

both ends of a link, so that the loss of cable joints, and end to end loss, can be more

accurately measured.

The readings obtained were recorded and taken to the PC-based software to perform

easy data collection and sophisticated data analysis. The screen shots of the values

obtained are shown and tabulated in the next chapter.

20

Figure 3.300 Nanjing DVP-730 arc fusion splicer machine (courtesy of Astera Nigeria Ltd)

Figure 3.301 Nanjing DVP-105 cleaving machine (courtesy of Astera Nigeria Ltd)

21

Figure 3.302 Nanjing Model KL-6200 OTDR machine (courtesy of Astera Nigeria Ltd)

Figure 3.303 Fusion splicing of fiber lengths

22

“0”

“1”

3.4 Bit Error Rate

The bit error rate (BER) is used as a performance index for error rate analysis in

digital systems. The developed simulation model system performance BER is

analysed using Q-factor from the eye diagram which is expressed as [16] contained in

[12]

3.400

where is the magnitude of the eye opening shown in figure 3.30. are

fractions of and . The former are defined for Gaussian pulse shape as [16]

contained in [12] by

Figure 3.400 Eye pattern [17]

3.401

One bit Length

µ1- µ0

Signal with noise

Noise margin

Good sampling

period Jitter

Noise

23

3.5 Development of MATLAB Simulation Blocks

The simulation blocks that will be employed in viewing the optical link will be

limited to the transmitter (source and the modulator), splice joint, fiber cable, and the

receiver.

3.5.1 Optical Carrier Source Model

The ideal laser source model in the Simulink block is achieved by selecting the sine

wave block [28]

Figure 3.500 Simulink sine wave source block [35]

The block models the desired sinosoidal optical carrier obtained from an ideal laser

which takes the mathematical form [12]

3.500

where and are the frequency and phase of the optical carrier respectively,A is

the amplitude, with = 2π x 1.93x1014 rad/s corresponding to the 1550 nm

operating wavelength of the laser source. The amplitude is set for unity for simplicity.

Due to the discrete nature in which MATLAB stores and processes data; one needs to

sample this waveform and other signals to ensure synchronization at certain intervals,

T, in order to process the data through the system correctly [12]. The sample time

fields of some blocks are required, the Nyquist sampling time is inserted here. This

technique maintains the integrity of the signals. According to the Nyquist theorem,

this sampling interval is at least twice the highest frequency in the system. Thus:

3.501

3.502

24

where B is highest sampling frequency.

3.5.2 MZIM Modulator Model

The optical laser source is now injected with a modulated MZIM (Mach Zehnder

Interferometric Modulator) carrier frequency which is modeled according to the

equation [12]

3.503

When multiplied by π gives a value between 0 and π. This value is used to implement

the required phase shifting of the optical carrier. The laser source and MZIM

complete the transmitter section of the optical link.

3.5.3 Linear Fiber Propagation Model

The developed model achieves propagation accuracy by implementing fiber

dispersion effects using time-domain digital signal processing and filtering technique

that has been proven to be efficient in its computational resources. The split step

model has been implemented in [13] and as contained in [12].This fiber propagation

model considers the effects of fiber attenuation and dispersion compensation on the

system performance. The mathematical representation is given by

3.504

where

3.505

L is the fiber length, λ the operating wavelength, v the optical frequency and c the

speed of light. From these equations it can be shown that the equivalent model for the

single mode fiber is expressed by the transfer function as [14,26,27,36]:

3.506

25

Hout (f)

Hin (f)

Since equ 3.506 is in the form of a frequency domain transfer function, it is more

convenient to operate in the frequency domain as apposed to taking the convolution in

the time domain. Determining the output of the fiber (f) given an input

modulated signal (f) (where the ^ symbol refers to the Fast Fourier Transform

(FFT) of xin and xout) is found by:

3.507

Figure 3.501 Block diagram of the linear fiber model [13]

Thus by taking the FFT of the input modulated signal in Simulink then multiplying by

H(f) and finally taking the IFFT (inverse FFT) one can accurately represent fiber

propagation with any additional chromatic dispersion, thus making the model linear.

For the standard single mode fiber (SSMF) fiber model one uses D(λ) SSMF =

+16.744 ps/nm.km at 1550 nm wavelength, L = 90km) with no optical amplifiers and

for the dispersion compensation fiber (DCF) model, smaller length is assume where,

D(λ) DCF = -85 ps/nm.km, L = 17 km. This value of dispersion for the DCF cancels

the dispersion effects of the SSMF.

Given the fiber manufacturers specifications quote of an attenuation level of

0.185dB/km attached in appendix A, this implies a total of 15.17dB attenuation of

optical power after 90km. This results in power attenuation (Simulink gain block) of

0.012 approximately. This value is taken into account in the simulations of the SMF

Simulink model via the Gain block at the top of the model.

H (f)

26

The other fiber models are identically the same with modifications to the parameter

values made as desired for dispersion compensation.

3.5.4 Receiver Model

This model of the receiver attempts to simulate, to within Simulink capabilities, some

of the key principles allowing for the successful receipt of signal. The optical carrier

is implemented by the MZDI, (Mach Zehnder Delay Interferometer). A receiver

model (block: Post Tx tap) is also place before fiber propagation to allow for

comparisons between pre and post fiber effects in eye diagram form. Phase offset and

photodiode/ amplifier noise models are incorporated into the receiver component to

represent the optical to electrical conversion performed by the single-ended

photodiode [13].

The MZDI characteristic is modeled according to the expression

3.508

where

The final term, in equation 3.508 is referred to as phase offset.

The detection of transmitted lightwaves is performed primarily by the photodetector.

In most instances, the received optical signal is quite weak and thus electronic

amplification circuitry is used, following the photodiode, to ensure that an optimized

power signal-to-noise ratio (SNR) is achieved [12]. This power signal to noise ratio is

calculated as follows

3.509

where Isig denote the photocurrent and as the mean squared noise

contributions from the photodetector. Three sources of optical receiver noise include

shot noise ish, the PD dark current noise idk and the thermal (Johnson noise) ith. The

27

total current generated by the photodiode when optical power falls on it is expressed

by [12]

3.510

where

It has been demonstrated that both the shot noise and dark current noise contributions

from the bulk material of the photodiode follow a Poisson process, and is thus random

[12]. The noise sources are expressed mathematically as

3.511

The photodiode amplifier datasheet shown in appendix D as used by [12,15] specify

the values for simulation.

Exact signal recovery is not the major concern of the simulation, hence observed

disparity between the input wave form at the scope of the source and the receiver.

However, inclusion of optical demodulator would have taken care of that.

3.5.5 Optical Splice Joint Model

The model for the splice joint was developed using constant block in Simulink. The

value of the constant block represents distance of the optical link. The gain block

which represents the measured splice loss value was used to multiply the constant

block thus allowing the value of the measured splice loss with respect to optical link

distance value to be represented. For instance, if the link distance is 90km; a constant

block with the value 90 was used and at splice loss value of 0.05dB, a gain block with

value 0.05 was also used to develop the splice joint model.

28

3.3.6 Assumptions and Simulation Parameters

Field Measurement

1. The Numerical Apertures (NA) of the connecting fibers are identical to

allow complete coupling of light.

2. The diameters of the connecting fibers are identical since the fibers ends

were once in the same length.

3. The fibers did not expand in any form as no environmental factor affected

the fiber. This is however too pessimistic as fibers both those buried

underground and those kept on open surface continually under

deformation due to several factors including temperature changes, applied

force on the fiber bundle, etc

Simulations

1. Exact signal recovery was not the major concern of the simulation.

2. There are no transmitter losses.

3. Actual system design configurations in fiber communications are different

from the arrangement of some developed block models in the simulation.

Parameter Magnitude Level of distortion

SSMF (fiber) 90 km (length) +16.744ps/nm.km

DCF (fiber) 17 km (length) -85ps/nm.km

Carrier Frequency 2*pi*1.93*10^14 rad/s -

Wavelength 1550 nm -

Bit Number 256 b -

Speed of Light 3*10^8 m/s -

Sampling Time 2.59*10^-15 sec -

Simulation Time 2.59*10^-12 sec -

Table 3.300 Simulation parameters. CHAPTER FOUR

MEASUREMENT, SIMULATION RESULTS AND ANALYSIS

29

4.1 Measurement Procedure

A Nanjing DVP-105 cleaver was used for the cleaving process. The cleaver machine

has error margin of ± 0.05%. Positioning accuracy and precision were achieved

during cleaving operation by placing well cleaned fiber ends appropriately at the

cutting edge (position) of the cleaver. The fiber ends were inspected for proper

cleaves and bad ones re-cleaved again. The cleaver was wiped intermittently to

remove fiber ends as this may contaminate new fiber lengths being cleaved.

A Nanjing DVP-730 fusion splicer with splice time of 1800mS was used for the

optical fiber fusion splicing. The output of the completed fusion splicing process was

indicated by the LCD panel of the splicing machine. A threshold value of splice loss

of ≤0.05dB was implemented. This was adopted to reduce the splice loss contribution

to the link’s loss. Several values exceeded this value and were discarded. The splicing

process was repeated again using the flow chart shown in figure 3.201 until the

splicing of the fiber lenghts were completed.

The splicing machine was switched off and the splicing programme initialised. This

was done when the machine was recording exceedingly high splicing loss values. The

end power setting of the arc of the splicing machine was steadly maintained as this

ensured that heated fibers melted and bonded homogeneously. This ensured that

splices with un-optimised splicing paramters (errors) such as fuse current too hot, fuse

time being too long, low and high auto fed were avoided. By inspection the lateral and

angular misaligned fiber spliced joints were separated. The splicing loss values

obtained at the cut sections of the fiber cable are shown in table 4.200.

30

4.2 Measured Splice Losses

Tube Number

F.No Fiber Colour

Splice Points AA(dB) AB(dB) AC(dB) AD(dB)

A(Blue) 1 Blue 0.01 0.01 0.02 0.02 2 Orange 0.02 0.02 0.02 0.02 3 Green 0.02 0.02 0.03 0.02 4 Brown 0.04 0.02 0.04 0.02 5 Grey 0.01 0.02 0.01 0.02 6 White 0.02 0.02 0.01 0.02 7 Red 0.03 0.03 0.01 0.02 8 Black 0.03 0.03 0.01 0.02 9 Yellow 0.02 0.03 0.01 0.01 10 Violet 0.01 0.02 0.01 0.03 11 Pink 0.02 0.01 0.01 0.02 12 Turquoise 0.01 0.01 0.01 0.01

B(Orange) 13 Blue 0.02 0.02 0.02 0.02 14 Orange 0.03 0.01 0.02 0.03 15 Green 0.01 0.02 0.03 0.02 16 Brown 0.02 0.03 0.01 0.01 17 Grey 0.02 0.03 0.01 0.01 18 White 0.03 0.02 0.02 0.01 19 Red 0.03 0.02 0.02 0.01 20 Black 0.02 0.03 0.03 0.01 21 Yellow 0.05 0.03 0.03 0.01 22 Violet 0.02 0.03 0.01 0.01 23 Pink 0.03 0.04 0.02 0.01 24 Turquoise 0.01 0.01 0.04 0.01

C(Green) 25 Blue 0.03 0.02 0.03 0.02 26 Orange 0.02 0.01 0.02 0.02 27 Green 0.03 0.01 0.02 0.01 28 Brown 0.01 0.02 0.01 0.01 29 Grey 0.01 0.02 0.01 0.02 30 White 0.01 0.03 0.03 0.03 31 Red 0.01 0.03 0.01 0.03 32 Black 0.01 0.03 0.02 0.02 33 Yellow 0.02 0.04 0.01 0.01 34 Violet 0.03 0.01 0.01 0.02 35 Pink 0.04 0.02 0.02 0.01 36 Turquoise 0.02 0.02 0.01 0.01

D(Brown) 37 Blue 0.02 0.01 0.01 0.01 38 Orange 0.02 0.01 0.03 0.03 39 Green 0.02 0.01 0.02 0.03 40 Brown 0.03 0.01 0.02 0.03 41 Grey 0.03 0.02 0.03 0.02 42 White 0.01 0.03 0.03 0.02 43 Red 0.02 0.03 0.03 0.01 44 Black 0.01 0.02 0.04 0.02 45 Yellow 0.01 0.01 0.01 0.02 46 Violet 0.02 0.02 0.01 0.01 47 Pink 0.02 0.01 0.01 0.02 48 Turquoise 0.02 0.01 0.01 0.02 Max 0.05 0.04 0.04 0.03 Min 0.01 0.01 0.01 0.01 Avg 0.0208 0.0204 0.0187 0.0175

Table 4.200 Measured splice loss at points AA, AB, AC and AD

31

4.3 Calculated Lateral and Angular Misalignment Values Tube Number

Fiber colour

F No

d1 (nm) d2 (nm) d3 (nm) d4 (nm) θe1 (0) θe2 (0) θe3 (0) θe4 (0)

A (Blue)

Blue 1 0.48 0.48 0.68 0.68 - - - - Orange 2 0.49 0.69 0.69 0.69 - - - - Green 3 0.69 0.69 - 0.69 - - 0.03 - Brown 4 - 0.69 - 0.69 0.04 - 0.04 - Grey 5 0.49 0.69 0.49 0.69 - - - - White 6 0.69 0.69 0.49 0.69 - - - - Red 7 - - 0.49 0.69 0.03 0.03 - - Black 8 - - 0.49 0.69 0.03 0.03 - - Yellow 9 0.69 - 0.49 0.49 - 0.03 - - Violet 10 0.49 0.69 0.49 - - - - 0.03 Pink 11 0.69 0.49 0.49 0.69 - - - - Turquoise 12 0.49 0.49 0.49 0.49 - - - -

B (Orange)

Blue 13 0.68 0.68 0.68 0.68 - - - - Orange 14 - 0.48 0.68 - 0.03 - - 0.03 Green 15 0.48 0.69 - 0.69 - - 0.03 - Brown 16 0.69 - 0.48 0.48 - 0.03 - - Grey 17 0.69 - 0.49 0.49 - 0.03 - - White 18 - 0.69 0.69 0.48 0.03 - - - Red 19 - 0.69 0.69 0.49 0.03 - - - Black 20 0.69 - - 0.49 - 0.03 0.03 - Yellow 21 - - - 0.49 0.04 0.03 0.03 - Violet 22 0.70 - 0.49 0.49 - 0.04 - - Pink 23 - - 0.69 0.49 0.03 0.02 - - Turquoise 24 0.50 0.50 - 0.50 - - 0.04 -

C (Green)

Blue 25 - 0.69 - 0.69 0.03 - 0.03 - Orange 26 0.69 0.49 0.69 0.69 - - - - Green 27 - 0.49 0.69 0.49 0.03 - - - Brown 28 0.49 0.69 0.49 0.49 - - - - Grey 29 0.49 0.69 0.49 0.69 - - - - White 30 0.49 - - - - 0.03 0.03 0.03 Red 31 0.49 - 0.49 - - 0.03 - 0.02 Black 32 0.49 - 0.69 0.69 - 0.04 - - Yellow 33 0.69 - 0.49 0.49 - 0.02 - - Violet 34 - 0.49 0.49 0.69 0.03 - - - Pink 35 - 0.69 0.69 0.49 0.04 - - - Turquoise 36 0.69 0.69 0.49 0.49 - - - -

D (Brown)

Blue 37 0.70 0.50 0.50 0.50 - - - - Orange 38 0.70 0.50 - - - - 0.02 0.03 Green 39 0.70 0.50 0.70 - - - - 0.03 Brown 40 - 0.50 0.70 - 0.03 - - 0.03 Grey 41 - 0.71 - 0.71 0.03 - 0.03 - White 42 0.50 - - 0.71 - 0.03 0.03 - Red 43 0.71 - - 0.50 - 0.03 0.03 - Black 44 0.50 0.71 - 0.71 - - 0.03 - Yellow 45 0.50 0.50 0.50 0.71 - - - - Violet 46 0.71 0.71 0.50 0.50 - - - - Pink 47 0.72 0.50 0.50 0.72 - - - - Turquoise 48 0.72 0.50 0.50 0.72 - - - -

Table 4.300 Calculated lateral and angular misalignment values Table 4.300 was generated using excel worksheet. where the values of d and are obtained for the various splice points respectively.

32

Recall that:

from equ 3.281 and 3.282

from equ 3.287 an 3.288

π = 3.1415, n2 = 1.457 (for silica based fiber)

w = MFD [6] (see appendix A)

4.4 Result of Splice Loss Inspection

The results of splice loss measurements (figure 4.400) and calculated lateral and

angular misalignment(figure 4.401) values are shown in accordance with [6,10,11].

The total measurement samples was 240 which corresponds to the total number of

splice joints. The splice loss recorded 0.02dB as the highest occuring value indicating

a good splicing workmanship. However splicing should be geared towards achieving

no loss. The maximum and minimum value of 0.05dB and 0.01dB were recorded

respectively. The calculated average for the splice loss inspection was 0.019dB.

Loss (dB)

0.00 0.01 0.02 0.03 0.04 0.05

Freq

uenc

y (n

umbe

r of o

ccur

ence

)

0

20

40

60

80

nm240 Samplesmax = 0.05dBavg = 0.019dBmin = 0.01dB

Figure 4.400 Bar chart of splice loss measurement

33

Angular misalignment Lateral misalignment

Freq

uenc

y (n

umbe

r of o

ccur

ence

)

0

20

40

60

80

100

120

140

160

Figure 4.401 Bar chart of calculated lateral misalignment versus angular

misalignment measurement.

From the bar chart in figure 4.401 for the splice loss inspection, it can be seen that

lateral misalignment occurred more frequently than the angular misalignment.

Possible reasons for this are the level of positioning accuracy achieved by the

cleaving machine which is used in cutting the fiber and fusion efficiency of the

splicing machine.

Achieving lower splicing loss may be hard due to time factor and avoidance of

material wastage. The former is of extreme importance especially during emergency

repairs operation in the network to reduce loss of revenue due to service down time.

34

4.5 Result of the Reflectance (Return Loss) Measurement

The return (reflectance) loss measurement test was carried out using the optical time

domain reflectometer (OTDR) machine on tube A of the fiber. The colour of the fiber

is blue. This is only the link currently in use as the others are redundant or awaiting

leasing.

Figure 4.500 Return loss at point AA

It is observed that the splice loss recorded is 0 dB while the measured splice value

was 0.01dB. The discrepancy in the loss is the error introduced by the patchcord. The

slope with high spike indicates splice joint(s) with dirts (contaminations).

Figure 4.501 Return loss at point AB

35

The screen shot at point AB shows that the splice loss is 0.085 dB at reference

kilometer of about 10km.

Figure 4.502 Return loss at point AC

Figure 4.503 Return loss at point AD

As with the observed trend, the measured average at point AB is 0.02 dB. The return

loss is 0.149 dB at a reference distance of about 12km. At 40km, the return loss is

0.077dB. The induced error can be attributed to marginal errors introduced by the

OTDR machine, chromatic dispersion losses from the fiber cable, micro and macro

36

bending losses emanating from the fiber. Table 4.500 shows the difference between

OTDR readings (first reference) and measured splice loss values

S/No Location OTDR reading (dB) Measured splice loss (dB) Difference (%)

1 AA - 0.01 -

2 AB 0.085 0.01 17.64

3 AC 0.106 0.02 0.57

4 AD - 0.02 -

Table 4.500 Summary of OTDR readings and measured splice loss readings

Similarly, table 4.501 shows the the summary of the attenuation readings recorded by

the OTDR and fiber drum quoted values (see appendix A)

S/No Location OTDR attenuation (dB) Quoted attenuation value (dB) Difference (%)

1 AA 0.192 0.186 3.22

2 AB 0.189 0.186 1.61

3 AC 0.187 0.186 0.53

4 AD 0.186 0.186 0.00

Table 4.501 Summary of Attenuation readings recorded by the OTDR and qouted

factory values of the fiber (see appendix A)

S/No Location Links loss (dB) Splice Loss (dB) Contribution (%) 1 AA 1.821 0 -

2 AB 1.605 0.085 5.20

3 AC 6.625 0.106 1.60

4 AD 2.310 0.149 6.45

Table 4.502 Summary of Splice loss contribution to overall optical links loss

37

4.6 Determination of the Optical Link Power Budget

The optical link power buget is determined by establishing the minimum power to fall

on the photodiode in order to ensure a certain bit error rate (BER). The light coupling

efficiency of the transmitter, the loss of the fiber and the sequntial loss contributions

of each element in the link determine the power received at the detector. Power

budget can be expressed by [54] as :

Ptr = Prec + Ploss + Msys 4.600

where Ptr is the average transmitted power, Prec is the average received power, Ploss is

the system lost power and Msys is the system margin or safety factor. Ptr is also

referred to as minimum transmit power and Prec minimum receive sensitivity [55].

The system lost power, Ploss is given by [54] as

Ploss = α f L + αcon + αsplice 4.601

where α f L is the attenuation of the fiber in dB/km (given in appendix A), L is the

fiber length , αcon is the connector losses and αsplice is the splice losses.

Given that Ptr = 32.366dBm and Prec =1.821dBm

Ploss = (4*0.05dB + 0.019*90 + 0.185*90) =18.36dB

Msys = 32.366-18.36-1.821 = 12.185dB

This value will help to determine the transmission power threshold and replacement

policy of fiber cable in the link.

4.7 Simulation Results

4.7.1 Signal Distortions at Scope

The statistical averages obtained in the field measurement were used to model the

magnitude of signals of the splice loss at the splice points in the absence of optical

spectrometer. The mininum, average and maximum values obtained from readings at

38

the different splice points were simulteneously changed in the simulation model.

Signal scopes were attached before and after the splice joints to observe the signal

behaviour as it enter and leaves the joints.

Figure 4.700 Signal scope at 0.01dB before and after spliced joints

Figure 4.601 Signal scope at 0.019dB before and after spliced joints

The magnitude (strength) of the signal at the scope was the major distinguishing

factor for the various splice points. As shown in figures 4.700 (a) and (b) through

4.702 (a) and (b), the signal distortion magnitude increases as the value of splice loss

4.700(a)

4.700(b)

4.701 (a)

4.701 (b)

39

increases. This is because an increased splice loss value will increase the distortion

level of the optical link. When there is traffic in the link, the scopes can be

discriminated and viewed by increasing the signal amplitude in the source lest there

will be no significant differences.

Figure 4.702 Signal scope at 0.05 dB before and after spliced joint.

4.7.2 Bit Error Rate (BER)

Figure 4.720 Eye diagram (BER) before filtration (a) without load and (b) with 100%

Traffic

4.702 (a)

4.702(b)

4.720(a)

4.720 (b)

40

Figure 4.721 Eye diagram (BER) after filtration (a) without load and (b) with 100%

traffic

Figure 4.722 Eye diagram (BER) at the receiver (a) without load and (b) with 100%

traffic

From equations 3.400 and 3.401 in section 3.4 the bit error rate of optical signal in the

link were determined. The BER for figures 4.720 and 4.721 respectively are 10-8 and

10-8. The values were obtained after the increment in the amplitude and gain blocks in

4.721 (a)

4.721 (b)

4.722 (a)

4.722 (b)

41

the Simulink Matlab library. This is also the process through which a proper view of

eye diagram scopes can be seen for better discrimination. The BER for the receiver

can not be readily determined owing to distortions introduced in the link by the fiber

propagation models. A remedy to this is to design a demodulator block capable of

exact signal demodulation.

4.8 Results of One-Way Anova Statistical Anaysis

A one way ANOVA statistical analysis test was performed on the splice losses at p-

value of <0.05, firstly on the tube and fiber colours, using SPSS version 17 as shown

in appendix E. The loss values obtained at cut section AA of the transmission link was

arbitrarly chosen as the control group while the values obtained in the other cut

sections were chosen as treatment groups. The results indicated that the differences in

the mean values among the treatment groups are not great enough to exclude the

possibilty that the difference is due to random sampling variability; there is not a

statistically significant difference on the tube. However there is a significant

difference among the colours. This is understandable due to the large numbers of the

fiber colours which are forty eight in direct contrast of the numbers of the tube which

are four.

This is to say that the errors obtained in the splicing process at the cut section of the

optical link were marginal and could have reduced significantly the overal splicing

loss contributions to the links total loss if the same approach were adopted in splicing

other joints in the link by the field splicers and installers.

However significant improvement can also be obtained in the performance of the

transmission link by transmission engineers during continous monitoring of signal

loss caused by splicing loss as the cable is damaged or cut if optimal replacement

policy for aging splicing machine is implemented.

42

CHAPTER FIVE

CONCLUSION AND SUGGESTIONS

5.1 Conclusion

The design of powerful systems is increasingly becoming a complex problem as long

as the parameters influencing the performance of each component are complex

[26,36,41]. Installed fiber systems have good reliabilty as most fiber failures are due

to complete cable cut. Owing to the emergence of fibers with multi core

configuration, service time restoration to a cut or damaged section of an optical link

can be repaired with minimal downtime rate. Avoidable errors due to improper fiber

splice installation can be reduced in an optical link by proper training and following

established good practices.

Unlike copper cable connectors where electrical isolation is an important design

parameters, the factors affecting the design of fiber splices are mechanical and

environmental. All forces whether axial or radial, acting on an optical fiber cable or

splice will cause the transmission characteristics to deviate [37]. To prevent this, the

design of the fiber strength and splice tray encaspulation must substantially isolate

the fiber spilce joints so that the forces are not converted into serious deformations

[1]. Under a laboratory controlled condition, it is possible to maintain a lossfree

system in a complex system like the optical link. However such environment is not

obtainable in the field of operation, hence network modelling tools in conjuction with

analytical methods are applied to view the performance of such a complicated system

[38,42]. In practice, the mismatch between the two fiber ends having different angular

or lateral misalignment in a single spliced joint is insignifant. Even if alignment is

achieved, the existence of air gaps in the fiber joint result in multiple beam interfernce

that can cause fluctuations in the joint loss of more 1dB [42]. Thus at a sufficient

43

distance the cummulative effects of these individual splice losses can mar the

transmission integrity of an optical link.

In this project, the influence of signal loss at optical splice joints of damaged sections

of an optical cable in a link were measured with the loss parameters determined

analytically. The values obtained were used to view propagating signals of the optical

link using the MATLAB simulation software.

5.2 Suggestions

The absence of an optical laboratory, optical measuring instruments and simulation

tools tailored to the analysis of optical communication greatly limited the scope of

this work. Again the data classification protocol at Astera Nigeria Ltd, on the volume

of traffics carried by the link means that the quality of service parameters of the link

can not be determined, analysed and compared with the simulated result. The

challenges faced in this research work were enormous and the following can be

considered for improvement:

Determination of the QoS parameters of an optical link at spliced joints and a

comparism of this with a simulated result.

Design of a demodulator in block in MATLAB© so that the transmitted signals

can be recovered at the receiver of the optical link and hence lost signals can

be determined.

Since the manipulations of optical parameters in MATLAB© can be fastidious

and engaging, the simulation can better be performed using Optisim©,

Optiwaves© and or Labview© simulation packages. These packages are

tailored for the analysis of optical communication hence the performance

effects of the splice loss in a network can also be noted when auxillary

components of an optical link are included in the design.

44

REFERENCES

[1] Gerd Keiser. (2003) Optical Fiber Communications 3rd Ed. McGraw Hill

Publishers, New York, USA.

[2] Kartalopoulos S. V. (2008) Next Generation Intelligent Optical Networks: From

Access to Backbone. Springer Science + Business Media LLC,New York,

USA.

[3] Koontz Warren L. G. and Mandloi Divya. (2000) Application of Optical System

Simulation Software in a Fiber Optic Telecommunications Program.

Rochester Institute of Technology, Rochester, New York, USA. Pp. 1-2.

[4] Marcuse D. Loss Analysis of Single-Mode Fiber Splices. American Telephone and

Telegraph Company; The Bell System Technical Journal Vol. 56, May –

June 1977, Pp. 703-718.

[5] Calvin M. Miller. Optical Fiber Cables and Splices. IEEE Journal on Selected

Areas in Communication, Vol. SAC-1, No. 3, April 1983, Pp. 533-540.

[6] Lin T. Y. Design Considerations for Multi – Fiber Ferrule Manufacturing. Elsevier

Science Direct, Optical Fiber Technology Vol.12 (2006), Pp. 255-261.

[7] Joseph Lizier. (2000) Applications of Holey Fibre: Splicing, Spot-size Conversion

and Coupling, Unpublished Bachelor of Engineering (Electrical -

Information Systems) Degree Thesis, School of Electrical and Information

Engineering, the University of Sydney.

[8] Senior John. (1985) Optical Fiber Communication, Prentice-Hall International

Inc; London, United Kingdom.

[9] Gerd Keiser. (2004) Optical Communications Essentials. The McGraw-Hill

Companies. Downloaded from McGraw-Hill Digital Engineering Library,

Available online at www.digitalengineeringlibrary.com

[10] Koji Ieda, Kazuhide Nakajima, Takashi Matsui, et al. Characteristics of Bending

Loss Optimized Hole Assisted Fiber, Elsevier Science Direct, Optical Fiber

Technology Vol.14 (2008), Pp. 1-9.

[11] Koichi Inada, Basic Components and Fiber Optic Passive Components: Status

and Trends in Japan. IEEE Journal on Selected Areas in Communications,

Vol. SAC-4, No 4, July 1986, Pp. 472-479.

[12] Binh L. N. and Laville B. (2005) Simulink Models for Advanced Optical

Communications: Part IV- DQPSK Modulation Format,Technical

45

Report(MECSE-5-2005), Department of Electrical and Computer Systems

Engineering, Monash University, Clayton, Australia.

[13] Armstrong J. (2003) “Simulink Optical Simulator”, in Electrical and Computer

Systems Engineering, Monash University, Clayton, Australia. Pp. 62.

[14] Elrefaie A.E. Chromatic Dispersion Limitations in Coherent Lightwave

Transmission Systems, IEEE Journal of Lightwave Technology, Vol. 6,

May, 1988.

[15] Humayun Kabir, Asaduzzamann All Faruq and Tanvir Reza. Span Analysis of

Optical Fiber Transmission Based on WDM, DWDM, DQPSK.

Unpublished Degree Thesis, Submitted to the Department of Computer

Science and Engineering, BRAC University, May 2008.

[16] Agrawal G. P. (2002) Fiber- Optic Communication Systems, 2nd ed. Academic

Press.

[17] Binh L. N. and Chenung Y. L. (2005). DWDM Optically Amplified

Transmission Systems –Simulink Models and Test-Bed. Technical Report

(MECSE-4-2005), Department of Electrical and Computer Systems

Engineering, Monash University, Clayton, Australia.

[18] Surasak Sanguanpong. (2000) Fiber Optics Fundamentals; Applied Network

Research Group, Department of Computer Engineering Kasetsart

University, Thailand.

[19] Arumugam M. Optical Fiber Communications-An Overview; Pramana Journal

of Physics, Indian Academy of Sciences, Vol.57, Nos.5 and 6, Nov and Dec,

2001, Pp. 849-869.

[20] JDSU. (2008) Best Practices for Ensuring Fiber Optic System Performance:

Inspection, Cleaning and Testing.

[21] Suzanne R. Nagel. Optical Fiber - the Expanding Medium, IEEE

Communications Magazine, April 1987 Vol. 25, No. 4, Pp. 33-43.

[22] Hart W. H. Jr. (1989) Engineering Electromagnetics, McGraw - Hill, New York,

5th ed.

[23] Kraus J. D. (1992) Electromagnetics, McGraw – Hill, New York, 4th ed.

[24] Paul C.R. and Nasar S. R., (1987) Introduction to Electromagnetic Fields,

McGraw – Hill, New York, 2nd ed.

46

[25] Moller K.D. (2007) Optics: Learning by Computing with Examples Using

Mathcad®, Matlab®, Mathematica®, and Maple®, Springer

Science+Business Media, LLC, New York, 2nd ed.

[26] Le Nguyen Binh. MATLAB© Simulink Simulation Platform for Photonic

Transmission Systems. I. J. Communications, Network and System

Sciences, Scientific Research Publishing, 2009, 2, Pp. 91-168.

[27] Claudio F. de Melo Jr., Ceasar A. Lima, Licinius D. S. de Alcantara et al. A

Simulink™ Toolbox for Simulation and Analysis of Optical Fiber Links. In

sixth International Conference on Education and Training in Optics and

Photonics, edited by J. Javier Sanchez- Mondragon. SPIE, Vol. 3831

(2000), Pp. 240-251.

[28] Nihal Shastry, Uday Madireddy and Nitin Ravi. “Simulation of an Fiber Point to

Point Communication Link using Simulink”.

[29] Hisashi Tanji. Optical Fiber Cabling Technologies for Flexible Access Network.

Elsevier Science Direct, Optical Fiber Technology Vol.14 (2008), Pp.177-

184.

[30] Pieter Matthijsse and Willem Griffioen. Matching Optical Fiber Lifetime and

Bend Loss Limits for Optimized Local Loop Fiber Storage. Elsevier

Science Direct, Optical Fiber Technology Vol.11 (2005), Pp. 92-99.

[31] Mohammad Ilyas and Hussein T. Mouftah. (2003) The Handbook of Optical

Communication Networks. CRC Press LLC, Boca Raton; Florida- U. S.

[32] Mike Gilmore. (2008) An Overview OF Singlemode Optical Fibre

Specifications, Fiberoptic Industry Association, Buntingford, U.K.

[33] Hirofumi Takai and Osamu Yamauchi. Optical Fiber Cable and Wiring

Techniques for Fiber to the Home (FTTH), Elsevier Science Direct, Optical

Fiber Technology Vol.15, (2009), Pp. 380-387.

[34] Kyozo Tsujikawa, Katsusuke Tajima and Jian Zhou. Intrinsic Loss of Optical

Fibers. Elsevier Science Direct, Optical Fiber Technology Vol.11, (2005),

Pp. 319-331.

[35] MATLAB© Simulink©, (1984-2007) The Mathworks Inc., US.

[36] Ghezal H. Ahmed and Ouchar Ali, Design and Conception of Optical Links

Simulator for Telecommunication Applications under Simulink©

Environment, 5th WSEAS Conference on Applied Electromagnetics,

47

Wireless and Optical Communications, Tenerife, Spain, Dec.,14-16 2007,

Pp. 52-57.

[37] Otto I. Szentesi. Reliability of Optical Fibers , Cables and Splices. IEEE Journal

on Selected Areas in Communications, Vol. SAC-4, No 9, December 1986,

Pp. 1502-1508.

[38] Mieghem Van Piet., ( 2006) Performance Analysis of Communications Networks

and Systems. Cambridge University Press, New York, USA.

[39] Visawanathan Thiagarajan., (2006) Telecommunication Switching Systems and

Networks., Prentice Hall Ltd, New Delhi India.

[40] Agarwal D. C. (2003) Fiber Optic Communication, S. Chand and Company Ltd;

Reprint ed., Ram Nagar, New Delhi, India.

[41] Tetsuhiro Yamashita and Akio Hasemi. A Construction Support System for

Optical Fiber Networks, Furukawa Review, No. 18. 1999, Pp. 85-89.

[42] Nachum Gilboa. “Fiber Optic Connectors and Losses in Fiber Joints”. Light

Applications, the Fast Laser Group, Hod-Hasharon, Israel.

[43] Nemota S. and Makimoto T. Analysis of Splice Loss in Single mode Fibers using

a Gaussian Field approximation. Opt. Quantum Electronic.,vol 11, no 5,

Pp. 447-457, Sept 1979.

[44] Young W. C. and Frey D. R. Fiber Connectors, in S.E. Miller and I. P.

Kaminow, eds., Optical Fiber Telecommunications- II, Academic, New

York,1988.

[45] Kihara M., Nagasawa S. and Tanifuji T. Return Loss Characteristics of Optical

Fiber Connectors, J. Lightwave Tech., Sept. 1996,vol.14, Pp. 1986-1996.

[46] Priyadarshi A., Fen L. H. et al Fiber Misalignment in Silicon V-groove Based

Optical Modules. Elsevier Science Direct, Optical Fiber Technology vol.

12, Pp. 170-184, 2006.

[47] Nakajima Kazuide, Shimizu Tomaya et al. Single-mode Hole Assisted Fiber as a

Bending-loss Insensitive Fiber. Elsevier Science Direct, Optical Fiber

Technology, Article in Press, 2010.

[48] Gregg Elizabeth “Fiber Optic Splice Optimization,” Naples Central.

[49] The Fiber Optic Association Inc., “Outside Plant Fiber Splicing and

Termination” available online at www.theFOA.org.

48

[50] Guanhai Jin. “Advanced Fiber Optic Connectors for Condition Based

Maintenance”. Agiltron Inc. Woburn MA. Available online at

www.agiltron.com

[51] The Fiber Optic Association- Tech Topics “Guidelines on what Loss to Expect

when Testing Fiber Optic Cables for Insertion Loss.” Available online at

www.theFOA.org

[52] Gloge D. Offset and tilt loss in optical fiber spilces, Bell System Technical

Journal vol; 55, Sept. 1976, Pp. 905-916.

[53] Young M. Geometrical Theory of Multimode Optical Fiber -to- Fiber

Connectors, Optics communications Journal vol; 7, no 3, Sept. 1973, Pp.

25-255.

[54] Kawaya Shaka Saleh Dispersion (2004),Compensation in Wavelength Division

Multiplexed Optical Fiber Links. Unplished Master in Engineering Thesis

Rands University, Johanesburg South Africa.

[55] Optical Power Budgets (1999) Transition Networks Inc; Minneapolis, MN

55344 USA, available online at http://www.transition.com.

49

APPENDIX A

OPTICAL FIBER CABLE DRUM DATA SHEET [Courtesy of Astera Nigeria Ltd]

50

APPENDIX B

OPTICAL QPSK MODEL WITHOUT TRAFFIC

51

APPENDIX C

OPTICAL QPSK MODEL WITH TRAFFIC

52

APPENDIX D

AMPLIFIER DATASHEET [12,15,17]

53

APPENDIX E ANALYSIS OF VARIANCE (ANOVA) FOR FIBER TUBES

Sum of Squares df Mean Square F Sig.

Splice Point A Between Groups .000 3 .000 .675 .572

Within Groups .004 44 .000

Total .004 47

Splice Point B Between Groups .000 3 .000 2.056 .120

Within Groups .003 44 .000

Total .004 47

Splice Point C Between Groups .000 3 .000 1.126 .349

Within Groups .004 44 .000

Total .004 47

Splice Point D Between Groups .000 3 .000 1.929 .139

Within Groups .002 44 .000

Total .002 47

ANALYSIS OF VARIANCE (ANOVA) FOR FIBER COLOURS

Sum of Squares df Mean Square F Sig.

Splice Point A Between Groups .001 11 .000 .569 .841

Within Groups .004 36 .000

Total .004 47

Splice Point B Between Groups .001 11 .000 2.195 .038

Within Groups .002 36 .000

Total .004 47

Splice Point C Between Groups .001 11 .000 .890 .558

Within Groups .003 36 .000

Total .004 47

Splice Point D Between Groups .000 11 .000 .522 .876

Within Groups .002 36 .000

Total .002 47

54

v

APPENDIX F

Splice Loss Equations for Single Mode Fibers

The incident electric field E at the input end of the fiber can be expressed in terms of

fiber modes as stated by [4]

6.001

where the summation symbol indicates symbollically summation over guided modes

(one for single mode fibers).

Ev is the electric field vectors of the modes (guided and radiation modes) of the fiber

and integration over radiation modes. The symbol v labels the mode (if v = 0 as the

label of the guided mode of the single mode fiber).

Mode orthogonality allows for c0 to be obtained from equ.(6.001)

6.002

H0 is the magnetic field vector of the guided mode, ez is a unit vector in the direction

of the fiber axis , and r and Ø are cylindrical coordinates in the plane at right angles to

the axis of fiber.

The power transmission coefficient finally is obtained from equ. (6.002) by the

relation

T = │c0│2 6.003

The electric field vector of the input field consists of one dorminant transverse

component. If the input field is gaussian; then

6.004

The refractive index n2 equals the cladding index of the fiber, P is the power carried

by the field and is identical to the P parameter in equ. (6.002), w is the width

55

parameter of the gaussian field, β is its propagation constant, μ0 and ϵ0 are the

magnetic susceptibility and the dielectric permitivity of vacuum.

We wish to compare the gaussian field to the mode of the step index fiber,then

6.005

The P parameter is identical to those in equations (6.002) and (6.004), W and U are

related to the important V parameter by

U2 + W2 = V2 = ( )k2ɑ2 6.006

The free space propagation constant of plane waves is k = and ɑ is the core

radius of the fiber. J0 and J1 the Bassel functions and K0 is the modified Hankel

function. The parameter U can be related to the propagation constant βs as follows

U = ( . 6.007

The r- integral in equ.(6.002) must be evaluated numerically. The value of T depends

on the width parameter w of the gaussian beam; T assumes a maximum as a function

of w. At V = 2.4, T = 0.9965, this value of V is close to the largest value where the

fiber supports only one mode. The next larger value ot T comes at V = 2.405, the best

match for fiber mode gaussian field distribution occurs at 2.4.

It can be shown that the optimum value of w divided by the core radius is only a

function of V. This function can be approximated very closely by the empirical

formula in equ 6.008. The accepatable range of values are 1.2 ≤ V ≤ 2.405

6.008

56

For large values of V the emprical approximation w divide by the core radius can be

expressed as

6.009

If a different approach is adopted and the approxiamation of guided mode of a single

mode fiber with refractive index distribution n(r) for r < ɑ and n(r) = n2 for r > ɑ, and

substitute equ (6.004) into wave equation

6.010

and obtain

6.011

for a graded index distribution

6.012 with g = 2, equ. (6.011) can be satisfied.

Equation (6.012) is an infinitely extended parabolic index profile. In this case, we can

find

6.013

And

6.014

We define the V parameter for any value of g by the equation

6.015

This expression is also a good approximation of (6.006), if we use

6.016

57

Equations (6.013) and (6.014) are not correct for actual parabolic index fibers whose

refractive index distributions are given by (6.012) (with g = 2) only for r < ɑ, but

assume the form n(r) = n2 for r > ɑ. Such profiles are referred to as truncated index

distributions.

For the different fiber defects shown in figures 2.501 (a) and 2.501 (b), [4] the

relevant formulae can be obtained by using equations (6.002) and (6.003) with the

field of both fibers represented by gaussian field distributions of the form in (6.004).

For analysis each fiber is represented by the width parameter of the optimum gaussian

field distribution, w1 which belongs to the fiber with radius ɑ1 and w2 belongs to the

fiber with radius ɑ2.

For splice loss with lateral misalignment, the power transmission coefficient can be

expressed as

6.017

The normalised fiber separation distance is defined as

6.018

At d = 0,

6.019

For d → ∞, we obtain asymptotically

6.020

58

For identical fibers, w1 = w2 = W and noting that W = n2kw, then

6.021

6.022

A condensed as expressed by [7] is given as

6.023

where TLM is the power transmission coefficient which reperesent the spilce loss for

lateral misalignment, d is the lateral misalignment and W is the gaussian spot size.

For a fiber with tilt (angular misalignment), the power transmission coefficient is

obtained by

6.024

When the tilt angle becomes large enough to make the exponent of the exponential

function in (6.024) to unity,the transmittted power decreases to 1/e of its maximum

value.

Then this angle is given by the expression

6.025

For identical fibers, w1 = w2 = W and noting that the terms in bracket dimishes faster

than the later, the expression becomes

6.026

The expression for TAM becomes

59

6.027

6.028

A condensed expressed by [7] is given by

6.029

where TAM is the power transmission coefficient which reperesent the spilce loss for

angular misalignment, is the angular misalignment,W is the gaussian spot size, n2

is the refractive index of the cladding and λ is the wavelength of fiber.

60

APPENDIX G

TYPICAL SYSTEM INITIALISATION MATLAB m-file

Initialize opticalmojexsimulation.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%

%%%%%%%%%%%%%%%%

% simulation run-time. keep the eye diagram windows on top

% during simulation run-time,

% allow simulations to conclude to view full eye diagram

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%

%%%%%%%%%%%%%%%%

%standard system parameters

bitrate=10*10^9 %bitrate in b/s

bitnum=256 %number of bits in data string,

lambda=1550e-9 %operating wavelength in m

%FIBER PARAMETERS

Dsmf=17e-6 %SMF dispersion factor in s/m^2

Ddcf=-85e-6 %DCF dispersion factor in s/m^2

Lsmf=90000 %SMF fiber length in m

Ldcf=17000 %DCF fiber length in m

speedlight=3*10^8 %speed of light in m/s

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%

%%%%%%%%%%%%%%%%