Photonic Crystal Fibres

303 Pages·2003·20.673 MB·English

by  Anders Bjarklev, Jes Broeng, Araceli Sanchez Bjarklev (auth.)

Photonic Crystal Fibres
Photonic Crystal Fibres
By
Anders Bjarklev
Jes Broeng
Araceli Sanchez Bjarklev
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication
CIP info or:
Title: Photonic Crystal Fibres
Author (s): Anders Bjarklev, Jes Broeng and Araceli Sanchez Bjarklev
ISBN 978-1-4613-5095-8 ISBN 978-1-4615-0475-7 (eBook)
DOI 10.1007/978-1-4615-0475-7
Copyright © Springer Science+Business Media Dordrecht 2003
Softcover reprint of the hardcover 1st edition 2003
Originally published by Kluwer Academic Publishers 2003
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CONTENTS
Preface IX
Acknowledgements Xl
1. Introduction 1
1.1 Fromclassicalopticsto photonic bandgaps 1
1.2 Microstructures in nature 3
1.3 Photonic crystals andbandgaps in fibres 5
1.4 Developmentofthe researchfield 6
1.5 Differentclasses ofmicrostructuredoptical fibres 9
1.6 Organisationofthebook 11
References 13
2. Fundamentals ofphotonic crystalwaveguides 19
2.1 Introduction 19
2.2 The developmentfrom ID over2D to 3Dphotonic crystals 20
2.2.1 One-dimensionalphotonic crystals 20
2.2.2 Two- and three-dimensionalphotonic crystals 23
2.2.3 Fabricationofphotonic crystals for the optical domain 25
2.2.4 Spatial defects inphotonic crystals 26
2.3 Terms involved inphotonic crystal fibre technology 29
2.4 Efficient structures for creatingphotonicbandgaps in fibres 30
2.4.1 In-plane photonic crystals 31
2.4.2 Fromin-planeto out-of-planephotonic crystals 34
2.4.3 The supercell approximation andefficient
plane-wavemethod 37
2.5 Summary 42
References 42
VI Contents
3. Theoryand modelling ofmicrostructuredfibres 53
3.1 Introduction 53
3.2 The effective-index approach 55
3.3 Themethod oflocalizedbasis functions 61
3.4 Full-vectorialplane-wave expansionmethod 67
3.4.1 SolvingMaxwell's equationusing aplane-wave
expansionmethod 68
3.4.2 Two-dimensionalphotoniccrystalwithhexagonal
symmetry 71
3.5 Thebiorthonormal-basis method 75
3.5.1 The basic equations ofthebiorthonormal-basis method 77
3.5.2 Biorthonormal-basismethodwithperiodical
boundary conditions 80
3.6 The multipole method 81
3.7 TheFourierdecomposition method 85
3.8 TheFinite-Difference method 90
3.8.1 TheFinite-DifferenceTime-Domainmethod 90
3.8.2 The Finite-DifferenceFrequency-Domainmethod 94
3.9 TheFinite-ElementMethod 97
3.10TheBeam-propagationmethod 99
3.11 The equivalentaveragedindexmethod 101
3.12Summary 104
References 106
4. Fabricationofphotonic crystal fibres 115
4.1 Introduction 115
4.2 Production ofphotonic crystal fibre preforms 116
4.3 Drawingofphotonic crystal fibre 119
4.4 Photonic crystal fibres innew materials ormaterial
combinations 123
4.4.1 Fabricationofhole-assistedlightguide fibres 124
4.4.2 Cha1cogenide fibres with microscopic air-hole
structures 124
4.4.3 Microstructuredpolymeroptical fibres 125
4.4.4 Extrudednon-silicaglass fibres 126
4.5 Summary 128
References 128
5. Properties ofhigh-index core fibres 131
5.1 Introduction 131
5.2 Background-"Single-material"fibres 132
Contents vii
5.3 Fibreswithperiodic cladding structures 134
5.3.1 Basicproperties ofhigh-indexcore photonic crystal
fibres 135
5.3.2 Cut-offproperties ofindex-guidingphotonic crystal
fibres 138
5.3.3 Macro-bending losses ofindex-guidingPCFs 146
5.3.4 Dispersionproperties ofindex-guidingPCFs 148
5.4 Fibreswithnon-periodic ornon-circularcladding structures 151
5.5 Hole-assisted lightguidingfibres 154
5.6 Summary 155
References 156
6. Low-indexcore fibres - the truephotonicbandgap approach 161
6.1 Introduction 161
6.2 Silica-airphotonic crystals 162
6.2.1 Simpletriangularstructures 162
6.2.2 Effective-index considerations 164
6.2.3 Hexagonal orhoneycomb structures 167
6.2.4 Modifiedtriangularandhoneycomb photonic crystals 170
6.3 Designing large-bandgapphotonic crystals 173
6.4 The first experimental demonstrationofwaveguidance
byphotonicbandgap effect atopticalwavelengths 177
6.4.1 Considerations on fabrication ofhoneycomb fibres 177
6.4.2 Basicproperties ofhoneycomb-basedfibres 178
6.4.2.1 Thewaveguidingprinciple ofhoneycomb fibres 179
6.4.2.2 Simple core designconsiderations ofPBG fibres 183
6.4.3 Basic characterisationofthe first honeycomb fibres 185
6.4.4 Modellingofrealisticphotonicbandgap fibres 187
6.5 Properties ofPBG-guidingfibres 191
6.5.1 Dispersionproperties ofhoneycomb-basedfibres 191
6.5.1.1 Single-mode fibres withhighanomalous
dispersionandstrongly shiftedzero
dispersionwavelength 192
6.5.1.2 Single-mode fibres withbroadband,
near-zero, dispersion-flattenedbehaviour 194
6.5.2 Polarizationproperties ofhoneycomb-based fibres 197
6.5.2.1 Polarizationeffects from non-uniformities 198
6.5.2.2 High-birefringentfibres andsingle-polarization
state fibres 200
6.6 Air-guiding fibres 206
6.6.1 Claddingrequirements for obtaining
leakage-free waveguidance inair 206
Vlll Contents
6.6.2 Corerequirements ofair-guiding fibres 208
6.6.3 Advancedproperties ofair-guidingphotonic crystal
fibres 210
6.6.4 Lossproperties ofair-guiding fibres 213
6.7 Summary 214
References 215
7. Applications andfuture perspectives 219
7.1 Introduction 219
7.2 Large-mode-areaphotonic crystal fibres 221
7.2.1 Characteristics oflarge-mode-area
photonic crystal fibres 222
7.2.2 Keyparameters indescribing large-mode-area
photonic crystal fibres 225
7.2.3 Newapproaches andrecentimprovements of
large-mode-areaphotonic crystal fibres 227
7.3 Highly nonlinearphotonic crystal fibres 232
7.3.1 Design considerations ofhighly nonlinearPCFs 233
7.3.2 Dispersionmanagementin highlynonlinear
photonic crystal fibres 234
7.3.3 Supercontinuum generation in silica-based
index-guidingphotonic crystal fibres 238
7.3.4 Device demonstrations 241
7.3.5 Comparison ofkeyparameters ofhighlynonlinear
fibres 242
7.4 High numerical aperture fibres 245
7.5 Photonic crystal fibre amplifiers 247
7.6 Tuneablephotonic crystal fibre components 250
7.7 Highlybirefringentfibres 252
7.8 Dispersionmanagedphotonic crystal fibres 255
7.9 Coupling andsplicing 259
7.10Lossproperties ofphotonic crystal fibres 260
7.11 Summary 264
References 265
Acronyms 277
Listofvariables (includingdimensions) 279
Index 285
PREFACE
Photonic crystal fibres represent one of the most active research areas
today in the field of optics. The diversity of applications that may be
addressed by these fibres and their fundamental appeal, by opening up the
possibility ofguiding light in aradically new way compared to conventional
optical fibres, have spun an interest from almost all areas of optics and
photonics. The aim of this book is to provide an understanding of the
different types of photonic crystal fibres and to outline some of the many
new and exciting applications that these fibres offer. The book is intended
for both readers with a general interest in photonic crystals, as well as for
scientists who are entering the field and desire abroad overview as well as a
solid starting point for further specialized studies. The book, therefore,
covers both general aspects such as the link from classical optics to photonic
bandgap structures and thoughts of inspiration from microstructures in
nature, as well as classification of the various photonic crystal fibres,
theoretical tools for analysing the fibres and methods of their production.
Finally, the book points toward some ofthe many future applications, where
photonic crystal fibres are expectedtobreaknew grounds.
ACKNOWLEDGEMENTS
The authors would like to express a few personal feelings concerning the
work leading to the present book. The work in the area ofphotonic crystal
fibres has been extremely rewarding and we feel in many respects thankful
for being able to participate in a tremendously exciting research area where
pioneering work in both optical fibre technology and fundamental physics
have been- andstill is being- achieved.
Our work would not have been possible without the collaboration and
support from a large number ofpersons; most importantly we would like to
express our appreciation to our colleagues at COM, Technical University of
Denmark, and Crystal Fibre AlS. We would further like to acknowledge the
financial and academic support of several companies and institutions,
including NKT AIS, DTU Innovation AlS, the Danish Research Council,
University ofBath, the EuropeanOptical Society (awardingthe "EOS Optics
Prize 1999"),the DanishOptical Society (awardingthe "DOPS Annual Prize
1999"), andDanaLimAlS (awardingthe "DanaLimPrisen2000").
Finally, we would like to thank our families for loving support and
patience.
Chapter 1
INTRODUCTION
1.1 FROM CLASSICALOPTICS TO PHOTONIC
BANDGAPS
In the world ofscientific investigations, we are often facing the situation
that a complex problem or the fascination ofa given idea forces us to focus
so much that we have a tendency to overlook the things, which should have
been the true inspiration of our work. Many times, it is first at the point,
when we have determined a solution to a simple sub-problem that we might
generalize the finding and obtain a wider perspective. Then the situation
becomes even more rewarding, when we from the more general theory
become able to solve new and unforeseen problems, which at first glance
hadvery littleto do withthe first sub-problem.
If we look at the subject ofthis book - the photonic crystal fibre - it is
possible to recognize the same kind of pattern, and we will in this
introduction sketch some ofthe elements ofthis.
We will start by taking offset in the widespread application of guided
wave optics. Here, it is clear that optical fibres and integrated optical
waveguides today are finding extensive use, covering areas such as
telecommunications, sensor technology, spectroscopy, and medicine [1.1
1.3]. Their operation usually relies on light being guided by the physical
mechanism known as total internal reflection, or index guiding. In order to
achieve total internal reflection in these waveguides (which are normally
formed from dielectrics or semiconductors), a higher refractive index ofthe
core comparedto the surrounding media is required. Total internalreflection
A. Bjarklev et al., Photonic Crystal Fibres
© Kluwer Academic 2003