All fibre devices for WDM optical communications

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Faculty of Engineering and Applied Science Department of Electronics and Computer Science

All-Fibre Devices for WDM Optical Communications

by

Carlos Feio Gama Alegria

A thesis submitted for the degree of Doctor of Philosophy

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Doctor of Philosophy

ALL-FIBRE DEVICES FOR WDM OPTICAL COMMUNICATIONS by Carlos Feio Gama Alegria

This thesis is concerned with the study of two key technologies for enabling wavelength division multiplexed optical communication systems. The first is gain equalisation of the erbium-doped fibre amplifier and the second is the routing of optical channels through the network by means of all-fibre add-drop multiplexer configurations.

Firstly, in order to flatten dynamically the EDFA gain spectrum, an AO filter based on a multi-tapered fibre structure was demonstrated. The controlled taper profile was used as another degree of freedom for tailoring the filter loss spectrum. The coupling between the fundamental and several cladding modes was investigated by studying the evolution of the resonance conditions as the fibres are progressively tapered both theoretically and experimentally. The filter was demonstrated by equalising the EDFA gain spectrum for different saturation levels. The main advantage of this novel design when compared to alternative AO filters is its simplicity due to the reduced number of tuning parameters. Furthermore, a method of determining the ideal filter loss spectrum and correct placement within the amplifier was analysed. This is based on calculating the EDF wavelength dependent background loss necessary to equalise the amplifier gain spectrum, and integrating it into a discrete number of filters placed within the EDFA. Configurations based on one and two equalising filters were compared. Additionally, this method allowed novel complex filter designs, which could compensate for their own insertion losses as well as the insertion losses of other devices distributed along the amplifier, while achieving a flat gain spectrum.

Secondly, all-fibre OADMs based on the inscription of Bragg gratings in the waist of fused fibre-couplers were investigated. Design considerations of devices based on half- and full-cycle couplers were presented and their performances compared. In both these configurations the exact positioning of the gratings within the fused coupler waist is critical to achieve optimum performance. An all-fibre compact add-drop multiplexer based on a novel non-uniform half-cycle fused coupler is presented, providing an alternative OADM design with optimised symmetric operation, which is insensitive to the position of the grating in the coupler waist. The spectral performance of this 3cm long device is similar to that of a device based on a meter-long uniform half-cycle coupler. Finally, a technique for the non-destructive characterisation of couplers is proposed, in order to determine the 3dB points within the couplers waist. A CO2 laser beam is scanned along the coupler

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Acknowledgments

………..…..viii

I

INTRODUCTION

CONTENTS...III 1 THESIS OVERVIEW... 2

1.1 WAVELENGTHDIVISIONMULTIPLEXING... 3

1.2 MOTIVATION... 4

1.3 MAINACHIEVEMENTS... 5

1.4 SUMMARY OF THE THESIS... 6

2 INTRODUCTION TO THE EDFA... 8

2.1 EDFA OVERVIEW... 9

2.2 THEORY... 10

2.2.1 Energy levels ... 10

2.2.2 Numerical modelling of spectral properties... 13

2.3 NOISE FIGURE... 15

2.4 LARGER BANDWIDTH... 17

2.5 GAIN EQUALISATION... 18

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3 INTRODUCTION TO ADD-DROP MULTIPLEXERS... 21

3.1 OPTICALADD-DROPTECHNOLOGY... 22

3.2 ADD-DROPCONFIGURATIONS... 23

3.2.1 Reconfigurable Add-Drops ... 27

3.3 ADD-DROPPERFORMANCE... 28

3.3.1 Isolation and Crosstalk ... 28

3.3.2 Insertion losses... 29

3.3.3 Back-reflections... 30

3.4 SUMMARY... 31

4 INTRODUCTION TO FIBRE-COUPLERS... 32

4.1 COUPLERTECHNOLOGY... 33

4.2 THEORETICALCOUPLERDESCRIPTION... 33

4.3 FABRICATION OFFUSEDFIBRECOUPLERS... 37

4.3.1 Flame-Brush Technique ... 37

4.3.2 CO2Laser... 40

4.3.3 Heating Oven... 41

4.3.4 Shape of the Tapered Region ... 41

4.3.5 Effect of the tapered transition on the coupler power evolution... 44

4.3.6 Coupler cross section ... 48

4.4 SUMMARY... 48

5 INTRODUCTION TO FIBRE BRAGG GRATINGS... 50

5.1 PHASEMATCHINGCONDITIONS... 51

5.2 MATHEMATICALDESCRIPTION OFBRAGGGRATINGS... 53

5.2.1 Coupled mode equations ... 53

5.3 APODISATION... 57

5.4 TRANSFERMATRIX... 60

5.5 PHOTOSENSITIVITY... 61

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II

EDFA GAIN EQUALISATION

6 ACOUSTO-OPTIC TUNABLE FILTER DESIGN ... 63

6.1 ACOUSTO-OPTICTECHNOLOGY... 64

6.2 THEORY... 66

6.2.1 Propagation of the acoustic wave ... 66

6.2.2 Optical modes in tapered fibres ... 68

6.2.3 Acousto-optic interaction ... 71

6.3 EXPERIMENTS... 77

6.3.1 Characterisation of the dispersion relations... 78

6.3.2 Flattening the EDFA ASE spectrum... 81

6.4 SUMMARY... 86

7 IDEAL FILTER DESIGN FOR EDFA GAIN EQUALISATION... 88

7.1 INTRODUCTION... 89

7.1.1 Theoretical Model ... 90

7.2 THEORETICAL FILTER DESIGN: ... 90

7.2.1 Effect of the fibre background loss... 92

7.3 DESIGN OF PRACTICAL FILTERS... 97

7.3.1 Ideal filter – No insertion loss... 97

7.3.2 Inclusion of the filter insertion loss... 108

7.3.3 Filter designs compensating the device own insertion loss ... 113

7.3.4 EDFA Equalisation by using the inverse of the gain spectrum... 120

7.3.5 Conclusions ... 122

7.4 GAIN FLATTENING FILTERS COMPENSATING FOR THE INSERTION LOSSES OF OTHER DEVICES... 124

7.4.1 Equalisation of the EDFA with a lump loss positioned at Z=2m ... 125

7.4.2 Equalisation of a (EDFA + isolator) structure: ... 132

7.4.3 Conclusions ... 137

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III

Add-Drop Multiplexers

8 ALL-FIBRE ADD-DROP MULTIPLEXERS... 139

8.1 OVERVIEW... 140

8.2 NUMERICALMODEL... 140

8.3 ADD-DROPCONFIGURATIONS... 143

8.3.1 Grating-based uniform half-cycle fibre coupler OADM... 144

8.3.2 Grating-based uniform full-cycle fibre coupler OADM... 160

8.3.3 Grating-based non-uniform fibre coupler OADM. ... 165

8.4 SUMMARY... 176

9 CHARACTERISATION OF FIBRE-COUPLERS ... 178

9.1 INTRODUCTION... 179

9.2 LOCALPERTURBATIONCOUPLERCHARACTERISATIONTECHNIQUE... 180

9.2.1 General Description of the Proposed Method ... 180

9.3 THEORETICALMODEL... 182

9.3.1 Coupler Description... 182

9.3.2 Effect of External Perturbation ... 183

9.3.3 Asymmetric perturbations of non-ideal couplers ... 191

9.3.4 Output Relative Phase Measurements... 193

9.4 NUMERICALSIMULATIONS... 194

9.4.1 Overlap integrals between the coupler eigenmodes and the perturbation profile. ... 194

9.4.2 Coupler Perturbation Results... 200

9.4.3 Perturbations of non-ideal couplers ... 206

9.4.4 Output Phase Perturbation ... 212

9.5 EXPERIMENTALRESULTS... 213

9.5.1 Characterisation of a half-cycle coupler [

φ

(L)=

π

] ... 215

9.5.2 Characterisation of a full-cycle coupler [

φ

(L)=2

π

] ... 217

9.5.3 Characterisation of a complex non-uniform

π

coupler... 220

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IV

SUMMARY

10 SUMMARY OF THESIS ... 224

10.1 EDFAGAIN EQUALISATION... 225

10.2 ADD-DROP MULTIPLEXERS... 226

10.3 FUTUREWORK... 226

Appendix A… … … ..… … .228

Appendix B… … … ..… … … … ..… ...230

Appendix C… … ..… … … ...232

Appendix D… … … ...… … … .… … ...240

References… … … … ..… … … .244

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Acknowledgements

During my studies at the ORC of the University of Southampton I have had the pleasure to work and discuss different aspects of optoelectronics with extraordinary people. I am grateful to Prof. D. Payne for giving me the opportunity of studying at the ORC and to the Portuguese Fundação para a Ciência e Tecnologia for funding my PhD.

Among other people that have passed by, or are still at the ORC, I’d like to thank Prof. D. Richardson, Prof R. Eason and Dr. E. Tarbox for giving me confidence in my work, M. Ibsen, Dr. Y. S. Kim, Dr. C. Renaud for useful discussions, R. Haaksman for all his logistical help, the ORC secretaries Eve Smith and Heather Spencer for helping me in numerous situations. I’d also like to thank everyone which whom I have worked directly in the laboratories from whom I have acquired many technical skills, namely, F. Ghiringhelli, G. Brambilla, M. Ibsen, Dr. R. Feced, Dr. M. Gunning, Dr. M. Durkin, Niel P. Fagan and Simon Butler.

In particular I couldn’t thank enough Dr. R. Feced for all his help during the initial stages of my PhD and J. Mackenzie and Dr. E. Tarbox for going out of their way, taking the task of proofreading my thesis. I am also grateful to Prof. M. N. Zervas, for his excellent supervision of the work and comments on the thesis, and Richard Laming for originally accepting me as his PhD student.

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1

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1.1 Wavelength Division Multiplexing

The advent of the Internet and global spread of personal computers has revolutionised our way of life in the last 10 years. The ability to communicate, shop, travel, find information, listen to radio, get medical support, and so many other aspects of the day by day life, are accessible with a simple mouse-click. The demand for better multimedia services and the increasing number of Internet users has given rise to an increased demand on the optical network capacity and efficiency, in all sectors - local area networks (LAN), metropolitan networks (METRO), and long-haul systems. Consequently, the need to transmit greater amounts of information via a single optical fibre, coupled with the need for low cost and more efficient distribution nodes in LAN [1], has led to the increasing importance of wavelength division multiplexed (WDM) systems. These networks transmit several channels corresponding to different wavelengths in the same optical fibre as illustrated in Figure 1.1. Different channels are launched in a single fibre by means of a multiplexer and after transmission through an amplified link, separated using a demultiplexer. For the practical implementation of these multi-wavelength networks several network key technologies have to be available; which include equalised optical amplifiers, optical switches and cross-connects, and add-drop multiplexers.

Figure 1.1- Basic representation of a WDM transmission link.

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availability and relatively low cost of optical fibres; consequently significant research has been aimed at this area. However, in long-haul transmission systems, emphasis is given to long-term stability and performance of the technologies employed. Recently the utilisation of fibre amplifiers operating at different wavelength bands (S, L and C) led to a system trial that demonstrated a record transmission capacity of 6.4Tbits/s using WDM technology [2]. In contrast, for optical time domain multiplexing (OTDM) systems the maximum bit rate achieved was 1.28Tbit/s [3].

This thesis is aimed mainly at investigating two components used in WDM systems namely; gain equalised erbium-doped fibre amplifiers (EDFAs) and all-fibre add-drop multiplexer configurations. An acousto-optic tunable filter for the dynamic equalisation of the EDFA gain spectrum is demonstrated and a theoretical study of the ideal filter shape and placement in the amplifier is performed. Different add-drop configurations based on the inscription of gratings in the waist of fused fibre-couplers are investigated and a novel device based on a non-uniform fibre coupler is demonstrated. The sensitivity of the performance of these devices on the position in the coupler waist where the grating is written, has led to the development of a novel technique for the characterisation of fibre couplers.

1.2 Motivation

The main motivation for this research was to develop an understanding of the aspects related to EDFA gain flattening and routing of signals in WDM optical communications and to demonstrate novel devices or methods that may be used in such networks. The key topics underlying this work can be summarised as follows:

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• To develop an understanding of EDFA gain equalising filters and configurations and to demonstrate an acousto-optic tunable filter for equalising the EDFA gain spectrum for different amplifier saturations.

• To demonstrate a compact all fibre add-drop multiplexer with symmetric operation.

• To develop personal experimental, research, engineering and software skills.

1.3 Main Achievements

This thesis is focused mainly on two aspects of WDM optical communications: First the need for the equalisation of the EDFA gain spectrum and secondly the selective routing of different optical channels by means of add-drop multiplexers.

Chronologically the work was initiated by developing an acousto-optic tunable filter for equalising the EDFA gain spectrum under different saturation conditions. This device was demonstrated as a simple (easier to reconfigure) although less flexible alternative to solving the problem. Secondly, a theoretical study of ideal filters for the EDFA gain equalisation was performed giving an insight into the possibilities and limitations for extrinsic filters placed either outside or within the EDFA.

The second aspect of the work was directed towards the demonstration of novel add-drop multiplexer designs based on inscription of gratings in the waist of fibre couplers. This project has led to an understanding of aspects related to the performance of these devices and how they can be addressed practically. Firstly, a novel method for characterising fibre-couplers based on a local perturbation induced by a CO2 laser beam was developed and secondly, a novel add-drop multiplexer

design was demonstrated.

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the fibre couplers from the time of fabrication was optimised during the work according to the facilities available. A considerable amount of time has also been spent modelling fibre propagation characteristics, add-drop multiplexers based on fibre couplers with a grating inscribed in the waist, and the local perturbation of fibre couplers.

1.4 Summary of the thesis

This thesis investigates two technologies essential for the deployment of WDM networks. The first is equalisation of the EDFA gain spectrum, and the second is the routing of channels through all-fibre add-drop multiplexer configurations. The thesis is divided in four sections:

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- Section II addresses the equalisation of the EDFA gain spectrum. In chapter 6 a novel technique for tailoring the loss spectrum of an acoustooptic (AO) filter is proposed. The application of the technique is demonstrated by dynamically equalising the amplified spontaneous emission (ASE) spectrum of an EDFA for different saturating input signals. The operation of the device relies on simpler tuning conditions compared to similar alternative technologies. Chapter 7 presents a theoretical and numerical study of ideal filters for the equalisation of the EDFA gain spectrum. It discusses a method for determining the required ideal filter shapes and placement position in the amplifier in order to obtain the best performance whilst equalising the EDFA gain spectrum. It is shown that the optical filter can be properly designed in order to compensate for its own insertion loss as well as of other devices incorporated in the EDFA.

- Section III is dedicated to all-fibre add-drop multiplexer configurations. It addresses three compact all-fibre configurations based on the inscription of Bragg gratings in the waist of fibre-couplers. Design and fabrication issues for each of these configurations are addressed in chapter 8. The need for an experimental method for characterising the fibre-couplers, in order to correctly position the Bragg gratings within the coupler waist, led to the development of a novel technique for the non-destructive characterisation of fibre-couplers. This technique is based on scanning a locally induced perturbation along the coupler waist to obtain the taper and waist profile and determine the evolution of power along the coupler, as well as, the shape of the coupler waist and coupling constant distribution. This is addressed theoretically and experimentally in chapter 9.

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2

Introduction to the EDFA

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2.1 EDFA Overview

The invention of the EDFA in the late eighties [4, 5] was one of the major events in the history of optical communications. It provided new life to the optical fibre transmission window centred at 1.55µm and the consequent research into technologies that allow high bit-rate transmission over long distances. High bit-rates were also possible with the aid of different dispersion compensation schemes. The basic configuration for incorporating the EDFA in an optical fibre link is shown in Figure 2.1. The signals and pump are combined through a WDM coupler and launched into an erbium-doped fibre. The amplified output signals can be transmitted through 60-100km before further amplification is required.

Figure 2.1- Basic configuration for the incorporation of an EDFA in an optical fibre link.

In general the EDFA has a narrow high gain peak centred close to 1532nm and a broad peak with lower gain centred at 1550nm. The initial WDM schemes used few wavelengths (typically 4) across the broad flat amplification region. In order to take advantage of the whole amplification band provided by the EDFA gain spectrum early equalisation schemes where employed [6]. However, the use of an increased number of channels in the present DWDM optical networks requires a flat gain spectrum across the whole usable bandwidth. Different EDFA equalisation schemes are discussed in section 2.5.

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new dopants and glasses to provide amplification at different wavelength bands (see section 2.4) or by using Raman amplifiers.

EDFAs have been used successfully in WDM transmission systems as all-optical lumped amplifiers at which the gain is boosted at a point of the transmission line. On the other hand, the fibre amplifiers based on Raman effect also have attracted huge research attention nowadays due to its tunability of amplification band by simply changing pump wavelength, since ever-increasing demand of optical data transmission capacity expansion in telecommunications has generated enormous interest in optical communication bands (S-, L-band) [7, 8] outside of a conventional EDFA gain bandwidth (C-band). The principle of the Raman amplifier is based on the stimulated emission process associated with Raman scattering in fibre for the amplification of signals. The inelastic non-linear effects can be regarded as scattering of a pump beam off phonon (molecular vibrational state) and the transfer of energy into a lower energy beam. The Stokes shift corresponds to the Eigen-energy of an optical phonon, which is approximately 13.2 THz for optical fibres. In Raman amplifiers, signal wavelength is longer than pump wavelength by the equivalent amount of the frequency shift. By using multiple pumps across the target gain window, over 100nm band Raman amplifiers can be achieved [9]. The major drawbacks of this technology are the requirement of high pump power or long length of fibre and the related Rayleigh scattering issue. However, availability of cheap and high power pump lasers, and highly non-linear fibres enables fibre Raman amplifiers to be a promising technology for the increase of transmission capacity of current and future WDM networks.

2.2 Theory

2.2.1 Energy levels

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medium the energy levels are modified by local electric fields through Stark-splitting. These levels are in thermal equilibrium due to rapid nonradiative transitions between these levels. The amplifier is assumed to have homogeneous broadening but if the local electric field is different at various sites along or across the fibre due to impurities, clustering effects, or other glass structural disorders, then inhomogeneous broadening occurs resulting in different electronic transitions at respective sites. The incorporation of a network modifier such as Aluminium (Al) to enhance the solubility of the Er3+ ions in the glass structure changes each energy level’ s Stark-splitting and increases the inhomogeneity of the medium. The energy transitions typically associated with Er3+ in a silicate glass are the 4I11/2, 4I13/2, and 4

I15/2states, and are illustrated in Figure 2.2.

Figure 2.2 – a) Energy level diagram for Er3+ ions showing the dominant transitions. b)

Stark-splitting of the energy levels due to the crystal or glass electric field.

W12, W21 are the rates for the stimulated transitions while A32 and A21 are the rates

for the spontaneous emission. A32 is assumed to be essentially nonradiative and A21

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Generally the EDFA is pumped with 980nm radiation, exciting electrons from the ground state 4I15/2 to level 4I11/2 or at 1480nm by exciting electrons from the

ground state to a high-energy Stark-split sublevel of the 4I13/2manifold. Rigorously

this implies, when pumping the EDFA using a wavelength of 980nm, that the amplifier corresponds to a three-level system while when using a 1480nm pump the amplifier is a quasi three-level system (as pumping is to a higher-energy Stark-split state within the I13/2 manifold). However, both pumping schemes can be described

effectively in terms of the populations of two levels. This approximation is justified in the 980nm pumping case due to the nonradiative decay rate A32being much larger

than the stimulated emission rate from 3 to 1, and therefore the population of level 3 (4I11/2) can be neglected. In the case of 1480nm pumping the two-level system is

justified due to the rapid thermalisation decay that transfers the higher-energy electrons of the 4I13/2manifold to lower-energy Stark sublevels. The rate equations

for the populations of a two-level system are written as:

2 21 2 21 1 12 2

n A n W n W dt dN

− −

= (2.1a)

2

1 n

n

nt = + (2.1b)

where nt is the Er3+ion density and n1 and n2the fractional density of the lower and

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2.2.2 Numerical modelling of spectral properties

The wavelength dependent properties of EDFAs can be modelled following the method proposed by [11] in which the spatial characteristics of the amplifier are integrated. This model involved dividing the EDFA spectrum into discrete optical channels of frequency bandwidth, ∆νk, centred at the optical wavelength λk.

Assuming homogeneous broadening and a uniform distribution of the Er3+ ions across the fibre core, the amplifier can be characterised by introducing four measurable fibre parameters: The absorption spectrum,αk, the gain spectrum g*k, the

fibre saturation power, PkSat, and the fibre background loss, lk, that are given by:

t k ek

k n

g* =σ Γ (2.2a)

t k ak

k =

σ

Γ n

α

(2.2b)

* *

)

( k k

k

k k

t eff k Sat

k

g h g

n A h P

+ = +

=

α

ν

ξ

τ

α

ν

(2.2c)

Where; σak and σek are respectively the wavelength dependent absorption and

emission cross sections, nt is the total concentration of the erbium ions,

ξ

=Aeffnt/

τ

is

the ratio of the linear density of erbium ions to the fluorescence lifetime, Aeff=πb2eff

is the effective area of the doped region,τ is the metastable level 2 lifetime, andΓk

is the overlap integral between the dopant and optical mode distributions that in the case of uniform doping of the erbium ions (beff=b) is given by:

=

Γ 2π

φ

φ

0 0

) , ( b

k

k I r rdrd (2.3)

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above overlap integral depends in general on the wavelength channel, k, for which it is calculated. Under steady-state operation, assuming a uniform distribution for the excited lower state and upper state populations (n1 and n2 respectively), the excited

upper state population density for the EDFA is given by [11]:

+ + = k Sat k k k Sat k k k k k t P z P P z P g n n ) ( 1 ) ( * 2

α

α

(2.4a) 2 1 n n

nt = + (2.4b)

The equations that describe the propagation of the beams of wavelength λk and the

pump through the fibre are [10]:

(

+

)

+ ∆ −

(

+

)

= * 2 ( ) * 2 ( )

z P l mh n n g z P n n g u dz dP k k k k k t k k t k k k

k

α

ν

ν

α

(2.5a)

(

+

)

(

+

)

= * 2 ( ) ( )

z P l z P n n g u dz dP pump pump pump pump t pump pump k

pump

α

α

(2.5b)

Pk(z) is the signal power at frequency λk at a certain position along the amplifier

length; uk represents the direction of the travelling beam uk=1 for a forward

propagating beam and uk=-1 for backward propagation; the term mh

ν

k

∆ν

k is the

contribution of the spontaneous emission from the local excited state population n2, with m=2 corresponding to the number of polarisation modes supported by the fibre,

and h the Plank constant; lk is a wavelength dependent background loss. Thus the two-level amplifier system can be fully characterised using equations (2.5a) and

(2.5b) that describe the propagation of the signal, ASE and pump along the

erbium-doped fibre and equation (2.4.a) describing the population inversion and saturation

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gain coefficient is null g*980 =0 and equation (2.5b) describing the pump evolution

along the EDF can be simplified.

Details of the model used herein for numerical simulations of the EDFA performance are described in Chapter 7. Briefly though it was implemented by dividing the full EDFA bandwidth (from 1420nm to 1620nm) into equal segments. The wavelength dependence of α(λ) and g*(λ) were obtained by digitising absorption and gain parameters measured for an actual EDF as illustrated in Figure 2.3. Using the measured value for the fibre background loss lbgand the ratio of ion

density to the fluorescence lifetime ξ, the rate and propagation equations were solved until the specified convergence parameters were reached.

0 1 2 3 4 5 6 7

1420 1470 1520 1570 1620

Wavelength (nm)

Absorption/Gain(dB/m

)

g*(λ)

α(λ)

Figure 2.3 – Measured absorption and gain parameters for the fibre used in the numerical simulations.

2.3 Noise figure

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to discuss the effect on the EDFA performance, in terms of a noise figure, when the concept of gain equalising filters is introduced. The optical noise figure is a parameter used for quantifying the noise penalty added to a signal due to the insertion of an optical amplifier. That is, before light enters an amplifier the signal to noise ratio is SNR(0), after amplification it is SNR(z). Thus, optical noise figure can be defined as:

) (

) 0 (

z SNR SNR

NFOpt = (2.6)

If the noise figure of the amplifier were 1, then the initial signal to noise ratio would be maintained throughout amplification. However it has been shown that the quantum limit for an optical amplifier [10] is 3dB, therefore the signal to noise ratio after amplification is half (50%) of the original value. For real optical amplifiers the noise figure can be as high as 6dB whereby the signal quality is sufficiently deteriorated that the detector’ s ability to discriminate signal from noise is compromised.

The signal to noise ratio can be described as the ratio between the average signal intensity and the standard deviation of intensity fluctuations from that average. The definition follows in terms of the average number of photons <n(z)> and the varianceσ2=<n(z)2>-<n(z)>2:

) (

) (

2 2

z z n SNR

σ

= (2.7)

where z is the position along the amplifier or fibre link. It has also been shown, [10]

that the noise figure of an optical amplifier can be described as:

) ( 1 )

( 1 ) ( 2

z G z G

z G n NF

k k

k sp

Opt +

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where Gk(z) is the amplifier gain at a given position, z, at a wavelengthλkand where

nspis the spontaneous emission factor that takes the form:

1 2

2

N N

N n

ek ak sp

σ

σ

= (2.9)

Here, N1 and N2 are the populations of the ground and excited energy levels

respectively. For a total population inversion N1=0, nsp=1 and therefore the noise

figure is close to 2, which is the quantum limit for the amplifier noise. The spontaneous emission factor is related to the total power of the amplified spontaneous emission PASE within the bandwidth,∆νk, by the following expression

[10]:

(

k

)

k

ASE sp

h G

P n

ν ν∆ − =

1

2 (2.10)

2.4 Larger bandwidth

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1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62

Wavelength (µm)

L-Band

S-Band

C-Band

Figure 2.4– Wavelength bandwidth covered by the amplifiers.

2.5 Gain equalisation

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characteristic equalisation properties and insertion losses that can be as low as the splicing loss between the EDF fibre and the filter fibre or as high 8-9dB as reported in [24, 25].

In chapter 6 an acousto-optic tunable filter based on the profile of a multi-tapered optical fibre and its spectral transmission properties [18, 19], is discussed. The amplified spontaneous emission spectrum of an EDFA was equalised for different saturation levels in order to demonstrate the potential of the device. The tunable parameters of the device were, the acoustic wave frequency and the filter loss shape, which was dependent upon the tapered fibre profile. Although this filter lacks the flexibility of reshaping the spectral profile, it is very easy to tune depending only on 2 to 4 parameters as opposed to the 12 tuning parameters of other designs [17].

Figure 2.5 – Basic EDFA gain flattening configurations. Top: Filter placed outside the

amplifier. Bottom: Filter placed within the amplifier.

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type of filter and the fabrication procedure, can be up to 8-9dB [24, 25], and therefore another amplification stage is usually required after the filter. If however, the filter is placed at a certain position inside the EDFA (configuration 2 in Figure 2.5), the penalty in amplifier loss can be reduced but the exact filter shape and placement is not known. Liaw [20] used the loss spectrum of a samarium-doped fibre and found the best position at which it should be placed in a given amplifier by splicing it at different positions along the amplifier. Acoustooptic tunable filters [26] have also been used in this configuration and optimised by tuning the filter shape until the desired performance is reached. This is an iterative process and quite time consuming, as the filters may not be placed in the optimum position along the amplifier. A solution to these problems is proposed in chapter 7, where the theoretical design of ideal filters that in addition to gain flattening also compensate for insertion losses, and their position within an amplifier for equalising the EDFA gain spectrum is discussed. Performance of the above filter configurations is compared.

2.6 Summary

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3

Introduction to Add-Drop

Multiplexers

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3.1 Optical Add-Drop Technology

The evolution of single wavelength point-to-point transmission lines to wavelength division multiplexed optical networks has introduced a demand for wavelength selective optical add-drop multiplexers (OADM) to separate/route different wavelength channels. They can be used at different points along the optical link to insert/remove or route selected channels increasing the network flexibility. This feature is particularly important in metropolitan WDM lightwave services where offices or sites can be connected by different add-drop channels, for example in an interoffice ring. Additionally there is flexibility of transmitting different data rates in different WDM channels according to the capacity needs. Figure 3.1 illustrates the basic operation of an add-drop multiplexer where a stream of 16 channels with central wavelengths λ1 through λ16 are launched into the input (port 1) and 8

channels are dropped at port 4, the rest go through port 2. Simultaneously, 4 channels are launched into port 3 and added to the signal stream at port 2. The channels that are added or dropped at that node depend on the network requirements.

Figure 3.1- Basic operation of an optical add-drop multiplexer.

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bypassing faulty connections, allowing minimal service disruption and the ability to adapt or upgrade the optical network to different WDM technologies.

Configurations presented in the literature to perform the required add or drop functions use both planar and fibre technology. Planar devices [28-36] provide compact solutions with the possibility of adding or dropping many channels using only one integrated optical circuit using arrayedwaveguidegrating (AWG) [34] or -waveguide-grating-router (WGR) technology [35, 36]. The main drawbacks of planar devices are their high insertion loss, which can be as high as 7dB, and their polarisation dependence. Alternatively, all-fibre devices [37-47] are attractive solutions due to their low insertion losses, polarisation insensitivity (depending on the fibre and configuration) and ease of coupling between device output and inputs of the optical network using simple splices and pigtails. Typically, due to their larger dimensions these devices are sensitive to environmental variations, dependent upon the configuration. Devices based in free space optics (micro mirrors and gratings) have also been used successfully to perform add-drop operations with good performance [48]. Although, these devices are in general more expensive and have relatively high insertion losses. Finally thin film filter devices have been traditionally used for multiplexing/demultiplexers purposes. Fibre and planar add-drop configurations and their respective performance are discussed in the following section.

3.2 Add-Drop Configurations

Excellent performance and compactness offered by four-port planar-waveguide-based devices can be rivalled by the simple all-fibre add-drop configuration, as shown in Figure 3.2. It consists of a 3dB splitter and a grating in one of the output arms; light launched into port1 is split in two, λG is reflected by the grating then

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and drop port. An optical isolator at port 1 protects the input network from the back-reflected signal. The dropped signal is 6dB weaker than the original input signal. In transmission, a second 3dB coupler splits the signal that was not reflected by the grating. The add function is performed by launching a signal into port 3 which is reflected by the grating and thus added to the signal at port 2, as illustrated in Figure 3.2. An isolator is also required to isolate the Add port from the signal transmitted from the input. When using the two isolators, at the input and Add ports, this non-interferometric configuration provides excellent add-drop performance. In this configuration there are no limitations on the length, position, or apodisation of the written grating. Ideal grating filters may be designed using an inverse scattering method [49, 50]. The primary drawback of this configuration is the insertion loss to all the channels that is at least 6dB. However, when comparing with planar-waveguide-based devices, it has similar insertion losses but has increased flexibility in writing and tuning ideal gratings. Notwithstanding, planar devices have the advantage of compactness and are easier to stabilise with respect to environmental changes.

Figure 3.2–Add-drop multiplexer configuration based on a grating and two 3dB couplers.

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Theoretically this device is symmetric and can yield excellent performance in terms of insertion loss, back-reflection and cross-talk.

Figure 3.3. illustrates the principle of operation for this configuration: A 3dB coupler splits light launched into port 1 and a specific wavelength, λG, is reflected

by the two identical gratings. These reflected signals interfere in the 3dB coupler in such a way that the signal is dropped and the back-reflected light intensity arriving at port1 is zero, providing the coupler is well matched (50% splitter). The transmitted wavelengths are made to interfere in the second 3dB coupler such that they arrive at the output port with no residual light at the Add port, again for a well-matched coupler. This configuration is based on the splitting and interference of light and is therefore quite sensitive to changes in the signals path length, the characteristics of the identical gratings, and the matching of the 3dB couplers. Therefore environmental stabilisation, UV trimming of the individual paths [47] and identical couplers and gratings are essential for good device performance. The stability and tolerances for achieving practical WDM performance using this configuration were analysed by Erdogan [31]. This configuration in planar technology has shorter path lengths and therefore is easier to stabilise. Also, identical gratings can be written with one exposure simply by using a small separation between the interferometer arms. Alternative configurations based on the dual-core fibres that present shorter interferometer arms and avoid the need for UV trimming have been demonstrated as practical devices using the MZ interferometer configuration [40, 45].

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Another example of a symmetric four-port add-drop multiplexer is similar to configuration 1 shown in Figure 3.2, with the 3dB couplers replaced by optical circulators. Theoretically the operation of this non-interferometric device is ideal: The spectral properties depend principally on the performance of the grating that can be designed as an ideal square filter using inverse scattering techniques; the insertion loss and cross-talk are mainly dependent on the performance of the optical circulators. Figure 3.4 illustrates this configuration. Light launched into port 1 is directed into a fibre Bragg grating with resonant wavelength, λG, reflected back to

the circulator and dropped to port 4 with the remaining optical channels being transmitted to arrive at port 2. Another signal of wavelength, λG, is launched in port

3, reflected by the grating and added to the optical stream at port 2.

The main drawback of this configuration is that circulators are expensive and bulky devices. However, with the advent of cheaper circulators and with low insertion losses, it will be a very attractive add-drop multiplexer solution, due to its inherent stability and performance [51].

Figure 3.4– Add-drop multiplexer configuration based on a grating and two circulators.

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This is only possible by using very short and strong gratings or very long couplers. Figure 3.5 shows schematically this configuration. Light launched into port 1 is transferred to the even and odd eigenmodes of the coupler. A grating is placed at the centre of the coupler where the phase difference between the eigenmodes isπ/4 i.e., where light is equally split between the two coupled waveguides (see chapter 4 for the eignemode description of a fused coupler). The channel at the grating resonance wavelength λG is reflected and the remaining signals propagate through the coupler

arriving at the output port. In reflection, the eigenmodes reach the beginning of the coupler with a π/2 total phase difference and therefore, the channel is dropped to port 4. In principle, the stabilisation of this interferometric device is improved with respect to the Mach-Zehnder (configuration 2) due to the point-like reflection point and the interference achieved through the beating between the propagating coupler eigenmodes. However, limitations in the grating strength and the length of fabricated couplers compromise the expected performance. Optimisation and discussion of different schemes using configuration 4 are addressed in Chapter 8.

Figure 3.5– Add-drop multiplexer configuration based on grating inscribed in the waist of a coupler.

3.2.1 Reconfigurable Add-Drops

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it on or off [32, 34]. Even though low cross-talk is achievable with multiple passes through the multiplexer, these devices have unavoidably high insertion losses.

On the other hand, all-fibre add-drop configurations have potentially no cross talk (depending on the filter design) with very low insertion loss. When using the non-interferometric add-drop configurations 1 or 3, wavelength selection is achievable by straining [52] or heating [53] the Bragg grating. Whilst using the interferometric configuration 2, both fibre gratings should be affected equally and therefore wavelength tuning is not practicable. However, switching is possible by unbalancing the interferometer by straining or heating only one of the arms.

3.3 Add-Drop Performance

The analogue performance of add-drop multiplexers is characterised by using scattering parameters Sij for each pair of ports [54]. The first subscript, i, refers to

the destination port and the second subscript, j, the input port. Several properties may be characterised using the scattering parameter namely; the insertion loss, polarisation dependent loss (PDL), dropped channel isolation, channel uniformity, frequency accuracy and bandwidth considerations. In appendix A system application characteristics for the isolation of the optical ports achievable with current 50, 100, 200 and 400 GHz channel-spacing technologies as well as, cross-talk, back-reflection and insertion loss requirements are given. The remaining parameters are defined to in [54].

3.3.1 Isolation and Crosstalk

The two main parameters related to the isolation of channels in an add-drop multiplexer are the through-port isolation of a dropped channel (S21 parameter) and

the drop-port isolation of through channels (S43parameter). Note that in a symmetric

device S43=S21. These two parameters represent the sources of the interchannel

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highlighted. If the amount of power launched into port 1, P1, and the dropped power

to port 4, P4, the remaining transmitted power, P2, emerges at port 2 as interchannel

crosstalk. The measure of isolation is given by -10log(P1/P2).

Figure 3.6– Example of the S21isolation of the through port of a dropped channel.

The second kind of crosstalk is due to unwanted signals transferred from neighbouring channels to the filtered one, and is named intrachannel crosstalk [55]. It can appear in the interferometric configurations as a result of an incorrect splitting ratio in the 3dB (50%-50%) couplers. This kind of crosstalk however, has a low power penalty in the performance of the WDM system.

3.3.2 Insertion losses

Insertion losses are the attenuation in the optical power of the channels due to the insertion of the device. The effect of the device insertion loss is schematically illustrated in Figure 3.7 where both the dropped channel and the output channels are attenuated.

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The insertion loss, linscorresponding to the transfer efficiency of light from port i to

port j affects all the channels equally and is described by

=

j i ins

P P l 10log

Pi and Pj are the powers of a given signal channel at the respective ports assuming

there is no cross-talk or polarisation-dependent loss (PDL).

3.3.3 Back-reflections

Back-reflections are defined by the scattering parameters Sii. The subscript i is 1 or 3

corresponding to the input or add ports respectively. Figure 3.8 shows schematically the effect described by these parameters. If the channel selection is based on a Bragg grating with a resonance wavelength λG(as in configurations 1 to 4), then when that

channel is launched into either port 1 or port 3 it will be reflected to either the drop or out port respectively. However, there is also a percentage of light, which is reflected back to the original ports P’1 or P’3, thus the Sii back-reflection parameter

is defined as 10log(Pi/P’i). The effect of the back-reflections can be avoided by

introducing isolators into both of these ports (as shown in Figure 3.2). However, the problem can be avoided by adequate add-drop multiplexer balancing.

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3.4 Summary

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4

Introduction to

Fibre-Couplers

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4.1 Coupler Technology

Fibre- and integrated-optic couplers are extremely important components in a number of photonics applications. They are generally four-port devices and their operation relies on the distributed coupling between two individual waveguides in close proximity, which results in a gradual power transfer between modes supported by the two waveguides. This power transfer and cross-coupling at the coupler output ports can be viewed also, as a result of the beating between eigenmodes of the composite two-waveguide structure along the length of the composite coupler waist [56]. The most common use of fibre- and integrated-optic couplers is as a power splitter, this is, the fibre-optic equivalent of a free space optic beam-splitter. They can be used to split the optical power of an optical channel (of certain wavelength) between the output ports [57]. Another application is to combine or split the power of different channels, corresponding to different wavelengths (wavelength-division-multiplexing (WDM) splitters/combiners) [58]. Lately fibre- and integrated-optic couplers, have been combined with reflective Bragg gratings written in their waist, to provide selective adding and dropping of different channels in WDM systems [41, 42].

4.2 Theoretical Coupler Description

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by an overlap integral of the fields associated with each of the individual guides. Fused couplers are obtained by fusing together and stretching two parallel uncoated fibres. As the fibres are stretched the core sizes decrease until the modes (at the wavelength of interest) are no longer guided by the core but by the composite cladding-air structure. If the taper is adiabatic only the two lowest-order eigenmodes of this structure will be excited and the power exchange is due to the beating between these two eigenmodes. In the work presented here only fused fibre couplers are discussed.

Figure 4.1 - Four-port coupler schematic showing the coupling region (LC), which is comprised of two taper regions (LT1, LT2) and the coupler waist (LW).

Consider the 2x2 coupler shown schematically in Figure 4.1. When light is launched into port 1, the normalised field amplitudes of the even (Ae) and odd (Ao)

eigenmodes at the coupler input (z=0) can be approximated by [56]:

2 ) 0 ( ) 0 ( ) 0 ( ; 2

) 0 ( ) 0 ( ) 0

( A1 A2 A A1 A2

Ae = + o = − (4.1)

where A1(0) and A2(0) are the normalised amplitudes of the fields launched into the

two input ports 1 and 2, respectively. For single port excitation, A1(0)=1 and A2(0)=0

and, through Equation (4.1), Ae(0)=Ao(0)=1/ 2. Therefore, light launched into one

of the input ports of a 2x2 coupler excites equally the two lowest-order (even and odd) eigenmodes along the coupling region. The two eigenmodes propagate adiabatically along the entire coupling region with propagation constants βe(z) and

βo(z) respectively. The beating between these two modes then provides the coupling

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Even

+ + +

Odd

∆φeo 0 3π/2 2π

P1

P1

P2 P2

π π/2

Figure 4.2 -Schematic of even and odd eigenmode beating and total power evolution along a 2x2 full-cycle (∆φeo=2π) coupler.

The propagating total electric field at any point along the coupler is described by:

+ =

+

= − −

z

o z

e i d

o d i

e o

e

t z E z E z A z e A z e

E 0 0

) ( )

(

) ( )

( ) ( ) ( ) (

ζ ζ β ζ

ζ β

(4.2)

During adiabatic propagation, the even and odd eigenmodes retain their

amplitude (Ae(z)=Ae(0) and Ao(z)=Ao(0)) and change only their relative phase. This results in spatial beating along the coupler waist and power redistribution between

the two individual waveguides comprising the optical coupler. The peak field

amplitudes for each individual waveguide, along the coupling region, can be

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[ ] [ ] − = − = = + = + − + − z o e z o e d i o e d i o e e z i z E z E z E e z z E z E z E 0 0 ) ( ) ( 2 1 2 ) ( ) ( 2 1 1 ) ( 2 1 sin 2 ) ( ) ( ) ( ) ( 2 1 cos 2 ) ( ) ( ) ( ζ ζ β ζ β ζ ζ β ζ β

φ

φ

(4.3)

where = = ∆ =

[

]

z

o e

z

eo

eo z d d

z 0 0 ) ( ) ( ) ( ) ( )

(

φ

β

ζ

ζ

β

ζ

β

ζ

ζ

φ

is the relative

accumulated phase difference between the even and odd eigenmodes. βe andβoare

the propagation constants of the even and odd eigenmodes, respectively. The

corresponding normalised peak power carried by the individual waveguides is given

by P1(2)=|E1(2)|2, namely

= = ) ( 2 1 sin ) ( ) ( 2 1 cos ) ( 2 2 2 1 z z P z z P

φ

φ

(4.4)

At the points along the coupler, where

φ

is zero or a multiple of 2π, the total power is concentrated predominantly around waveguide#1 (P1=1 and P2=0). At the

points along the coupler, where

φ

is multiple ofπ, on the other hand, the total power is concentrated predominantly around waveguide#2 (P1=0 and P2=1). Finally, at the

points where

φ

is multiple of π/2, the total power is equally split between the two waveguides (P1=P2). The even/odd eigenmode beating and total power evolution

along a full-cycle coupler (

φ

=2π) is shown schematically in Figure 4.2. The coupling coefficient k(z) describing the strength of the interaction between the eigenmodes

and is given by:

2 ) ( ) ( )

(z z z

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The coupler beat length LB is defined as the minimum interaction length the two

eigenmodes, initially in phase, must travel in order to interfere constructively i.e., to be again in phase:

o e B

L

β β −π

= 2 (4.6)

4.3 Fabrication of Fused Fibre Couplers

4.3.1 Flame-Brush Technique

The flame-brush technique for the fabrication of fibre couplers is based on the scanning of a point-like flame while pulling the fibres [59]. Two fibres are clamped parallel to each other and the flame is scanned over a given interaction region. Figure 4.3 shows the experimental configuration of such a rig for fabricating fibre tapers or couplers.

Figure 4.3– Flame brush technique experimental setup

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controlled Aerotech stages. The flame is scanned using a third Aerotech stage. The flame gas consists of a mixture of isobutene and oxygen. Both cleaning and alignment of the fibres is crucial for fabricating uniform tapers or couplers with low insertion losses. Air draughts or gas pressure variations can severely affect the quality of the devices, due to variations in the flame temperature and consequent local non-uniformities along the tapers/couplers. During the pulling of the fibres the output power is monitored and the process halted at the desired fibre radius (in the case of taper fabrication) or extinction ratio (in the case of coupler fabrication). Figure 4.4 shows the power at both the output ports (Port 3 and Port 4) during the pulling process for a half-cycle coupler fabricated using this technique. Coupler elongation of 46mm represents the point at which coupling of light between the waveguides starts to occur, corresponding to the monomode regime [60]. As illustrated, the power at port 3 drops to 0V while the power in port 4 increases to around 7V. The pulling process was halted when Port 3 reached its minimum, producing this way a half-cycle coupler.

0 2 4 6 8

46 51 56 61 66 71

Coupler Elongation (mm)

C

ou

pl

ed

po

w

er

(a

.u

.)

Port 4 Port 3

50% splitter 100% coupler

Figure 4.4 – Power evolution of a coupler fabricated using the flame-brush technique at λ=1.55µm during pulling process.

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the output ports with an Optical Spectrum Analyser (OSA). Figure 4.5 illustrates the spectral characteristics of a 20mm long full-cycle coupler fabricated using this technique. It is observed that the extinction ratio was better than 30dB and the meausurement was noise-limited due to insufficient input power. The pulling process was halted so that the full-cycle resonance peak was at λ=1.55µm. The

resonance at λ=1.175µm is the half-cycle resonance corresponding to a total phase displacement ofφ(L)=π.

Disadvantages of this fabrication method are; the possible contamination of the tapers/couplers by the combustion by-products, the variations of the burner temperature, and the flame size, that may not be approximated to a point like source. Notwithstanding, throughout this work very good quality tapers and couplers were obtained. In fact, the quality of the couplers produced with the rig, as illustrated in Figure 4.5, provided confidence in the uniformity of the tapers and stability of the flame during the fabrication process. For example, using a standard telecommunications single mode fibre, typical insertion losses of the fabricated tapers were only 0.1dB.

-90 -80 -70 -60 -50

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Wavelength (µµµµm)

P

ow

er

(d

B

m

)

Port 3

Port 4

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4.3.2 CO

2

Laser

Recently Dimmick et. al. [61] reported the development of a fused-fibre coupler and fibre taper rig that uses a scanning, focused, CO2 laser beam as the heat source,

instead of the gas burner. The setup is similar to that of the flame-brush technique, with two pulling stages that stretch the fibre at a desired speed whilst the CO2 laser

radiation is scanned across the fibres by a rotating mirror. The beam is focused using a ZnSe lens with a 30mm focal length giving a spot size of 820µm. An experimental setup used to fabricate fibre-couplers using a CO2laser is illustrated in Figure 4.6.

Figure 4.6 – Experimental setup of the fabrication of fibre tapers/couplers using the radiation of a focused CO2laser.

This setup provides a better control of the shape of the taper/coupler tapered region due to the smaller hot spot produced by the focused CO2laser when compared to the

flame-brush technique. It also allows greater control in producing non-uniform tapers or couplers due to the possibility of rapid positioning of the laser spot and fast switching of the laser beam power with a shutter.

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(which depends on the fibre radius and temperature), and the laser spot size. To overcome this problem the laser power has to be adjusted constantly in order to maintain a constant temperature during the fibre pulling. In contrast, when heating with a flame burner, the presence or not of the fibre has little or no effect on the temperature of the heat source due to the mechanism of heat generation.

4.3.3 Heating Oven

Another technique used in industry for fabricating fibre couplers and tapers relies on heating the whole uniform section using an oven or resistive electrical heater while pulling the fibres. Due to the long heat zone this technique has no control over the shape of the tapered region although the sensitivity to environmental factors is reduced. The quality of the tapers/couplers is essentially dependent on the oven design, and the temperature uniformity along the length of waist region.

4.3.4 Shape of the Tapered Region

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The shape of fibre tapers/couplers produced by using scanning point-like heating sources has been extensively studied by Birks el al. [64]. Assuming that the localised heating of the fibre makes the glass soft enough to be stretched whilst not being so soft that it falls under its own weight, the shape of the tapers can be calculated without having to recur to fluid mechanics beyond the principle of conservation of mass. A tapered fibre, at any given time (or elongation) of the pulling process, can be characterised by the parameters shown in figure 4.7a). ro is

the initial fibre radius corresponding to a transition length, z0, and r(z) the radius of

the taper transition at a given position z. The length of the uniform taper waist lw(t)

is equal to the length of the hot-zone L(t) at that time. The size of the hot-zone L(t) may vary with time but is subject to the constraints L≥0 and dL/dx≤1. This second constraint ensures that the hot-zone does not overtake the pulled transitions. The time change is proportional to the extension or elongation of the taper i.e., the pulling speed is constant. Figure 4.7b) shows the equivalent untapered fibre where the initial hot spot length (at t=0) is L0and x is the total pulling extension at a given

time. Comparing the tapered with the untapered fibre it may be observed that points A and B are elongated by x. In the particular case where the hot-zone is constant during the pulling, the waist length is constant lw(x)=L0 and the taper transition is

equal to half of the extension z=x/2.

Figure 4.7 - Schematic representation of a fibre taper structure. a) At a time t during the

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From the conservation of mass principle, the following expression can easily be derived:

L r dx

drw w

2

= (4.7)

Secondly, the extension x can be related to the taper transition length z by comparing the initial length AB at t=0, with the total taper length AB at any given time:

0

2z+L=x+L (4.8)

The particular case where the hot-zone remains constant during the fibre extension has been analysed by [64-66]. In this case L(z)=L0 and z=x/2. Integrating

(4.7) gives the waist shape for a total fibre extension x.

( 0)

0 2

0 ) ' (

' 2 / 1

0

)

( L x x L

dx

w x re re

r

x

− −

=

= (4.9)

The taper profile is calculated by substituting x=2z in (4.9), resulting in the well-known exponential decay profile. All the taper and coupler devices discussed in this thesis were fabricated using a constant hot-zone, thus expression (4.9) is sufficient to describe the profiles of the tapered regions. Further examples of interest are discussed in [64] where equation (4.7) is demonstrated as well.

In order to minimize losses between the fundamental and the nearest cladding modes, the taper angle |dr/dz| has to obey the adiabatic criterion [63].

( )

( )

(

)

πβ β

2

2

1 z z

r dz

dr

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Where β1(z) and β2(z) are respectively the local propagation constants of the

fundamental mode and the closest cladding modes, and r is the local core radius. Experimentally it was observed that intrinsic loss of the fabricated couplers and tapers using the flame-brush technique were very low and justify the use of the above parameters describing smooth adiabatic transitions.

4.3.5 Effect of the tapered transition on the coupler power

evolution

The long transition regions in couplers fabricated using the flame-brush technique with constant hot zone, play a role in the way the power evolves along the coupler. For a full-cycle coupler with a constant hot zone of L0=30mm fabricated with

standard telecommunications single mode fibre, the evolution of the power at the output ports is illustrated in Figure 4.8. Light from a DFB-LD at a wavelength of 1.55µm is launched in port 1 and monitored at port 3 and port 4 during the pulling

process. The power evolution is only plotted from an extension of x=47mm (from x=0 to x=47 there was no coupling) in order to emphasise the coupling process.

0 1 2 3 4 5

47 52 57 62 67 72 77

Coupler Elongation (mm)

M

ea

su

re

d

o

ut

pu

t(

V

)

Port 4 Port 3

50% splitter

πcoupler 2πcoupler

x1

∆x

x3

x2

x0 xm xN

. . . .

. . . .

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Light starts to be coupled between the two fibres for a coupler extension around x=51mm, the half-cycle point is reached at around x=73.5mm when all the light is in Port 4 and the pulling process was halted after one full-cycle, i.e., when all light was coupled back to Port 3. Using the information plotted in Figure 4.8 and the fact that dL/dx=0 (constant hot-zone pulling), an iterative method to extract the coupling strength profile due to the tapered transition region can be developed. After a given extension, x, where coupling starts to occur, all the interaction is due to the waist section with length L0. The coupling coefficient, k(x), can be evaluated for that

extension (or equivalently for that waist radius) assuming that the hot-zone section is uniform and constant during the fabrication process, by solving equation (4.4) in order to determine φ(x)=∆β(x)L0=2k(x)L0. Now the phase displacement between the

even and odd eigenmodes corresponding to the coupled power P1(x0) at extension x0

is given by:

[

1 0

]

0 1

0) cos ( )

(x = − P x L

β

(4.11)

and the value of∆β(x1) at the next extension x1=x0+∆x can be calculated iteratively

using;

[

1 1

]

0 1 0

1

1) cos ( ) ( )

(x = P x L −∆ xx L

ββ , (4.12)

finally at the mthsection, xm=x0+m∆x, it yields;

[

]

=

=

∆ 1

0 0 0 1

1

) ( )

( cos )

(

m

n

n m

m x

L x L x P

x

β

β

(4.13)

The reader is reminded that z=x/2 and therefore, ∆β(z)=∆β(x)/2. Using this general

recursive expression and the coupler power evolution Port 3 (blue line in Figure

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compared to the ideal coupler (dashed line) without a tapered transition region. The origin of the graph in Figure 4.9 corresponds to a coupler extension of x=47mm and therefore a transition length of z=23.5mm. At this position the normalised coupler radius can be calculated using (4.9) yielding r(z=23.5)/r0=exp(-z/L0)≈0.457.

The ideal coupler has a higher coupling strength along the uniform waist than the fabricated coupler; although the total coupler phase displacement φ(L) corresponding to the integration of the coupling strength along the whole length, is the same in both couplers at λ=1.55µm. By comparing the power coupling in the transition regions with that in the uniform region of the fabricated coupler, it is realised that 22.1% of the total phase displacement along the coupler is due to the tapered transition regions and 77.9% due to the uniform waist. Therefore, when optimising add-drop multiplexers based on full-cycle couplers with gratings inscribed in the waist, by placing them between the exact points along the coupler where the power is equally split between the fibres, the coupler transition region has to be taken into account. However, the non-destructive coupler characterisation method presented in Chapter 9 overcomes this problem.

0 0.5 1 1.5

0 7.5 15 22.5 30 37.5 45 52.5 60

Coupler Position (mm)

k(

z)

(x

10

4

m

-1 )

Ideal coupler

Real coupler

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The effect of the tapered transition region on the power evolution along the coupler length is illustrated directly in Figure 4.10. Both the output coupler ports (Port 3 and Port 4) are shown. The dashed line refers to the ideal coupler and the solid line to the fabricated coupler. It is observed that the fabricated coupler is longer and the coupling smoother corresponding to the transition regions. The coupler positions where the power is equally distributed in both the waveguides (50-50% points) are shifted towards the tapered regions. Identification of these coupler positions is critical for the optimisation of add-drop multiplexers based on gratings inscribed in the coupler waist and will be discussed in Chapter 8.

The accuracy of expression (4.13), in determining the coupling strength and hence the 50-50% points of the coupler, depends on the uniformity of the hot-zone length and the adiabatic evolution of the tapered transition region during the pulling process. In order to characterise the coupler and determine its 50-50% points a novel non-destructive characterisation technique for fibre couplers was developed and is discussed in Chapter 9.

0 0.5 1

0 7.5 15 22.5 30 37.5 45 52.5 60

Coupler Position (mm)

N

or

m

al

is

ed

P

ow

er

P1(z)

P2(z)

Figure

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