Photonic crystal fibers: properties and applications

245 Pages·2007·5.44 MB·English

by  Federica Poli, Annamaria Cucinotta, Stefano Selleri

SpringerSeriesin
materials science
102
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F. Poli A. Cucinotta S. Selleri
Photonic Crystal Fibers
Properties and Applications
With129Figures
123
FedericaPoli AnnamariaCucinotta
DipartimentodiIngegneriadell’Informazione DipartimentodiIngegneriadell’Informazione
UniversitadegliStudidiParma UniversitadegliStudidiParma
VialeG.P.Usberti181/A-CampusUniversitario VialeG.P.Usberti181/A-CampusUniversitario
I-43100Parma,Italy I-43100Parma,Italy
StefanoSelleri
DipartimentodiIngegneriadell’Informazione
UniversitadegliStudidiParma
VialeG.P.Usberti181/A-CampusUniversitario
I-43100Parma,Italy
SeriesEditors:
ProfessorRobertHull ProfessorJürgenParisi
UniversityofVirginia UniversitätOldenburg,FachbereichPhysik
Dept.ofMaterialsScienceandEngineering Abt.Energie-undHalbleiterforschung
ThorntonHall Carl-von-Ossietzky-Strasse9–11
Charlottesville,VA22903-2442,USA 26129Oldenburg,Germany
ProfessorR.M.Osgood,Jr. ProfessorHansWarlimont
MicroelectronicsScienceLaboratory InstitutfürFestkörper-
DepartmentofElectricalEngineering undWerkstofforschung,
ColumbiaUniversity Helmholtzstrasse20
SeeleyW.MuddBuilding 01069Dresden,Germany
NewYork,NY10027,USA
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Contents
Preface ix
Acknowledgements xi
Introduction 1
1 Basics of photonic crystal fibers 7
1.1 From conventional optical fibers to PCFs . . . . . . . . . . . . 8
1.2 Guiding mechanism . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.1 Modified total internal reflection . . . . . . . . . . . . . 11
1.2.2 Photonic bandgap guidance . . . . . . . . . . . . . . . . 13
1.3 Properties and applications . . . . . . . . . . . . . . . . . . . . 14
1.3.1 Solid-core fibers. . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 Hollow-core fibers . . . . . . . . . . . . . . . . . . . . . 20
1.4 Loss mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.1 Intrinsic loss . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.2 Confinement loss . . . . . . . . . . . . . . . . . . . . . . 28
1.4.3 Bending loss . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5 Fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.5.1 Stack-and-draw technique . . . . . . . . . . . . . . . . . 34
1.5.2 Extrusion fabrication process . . . . . . . . . . . . . . . 37
1.5.3 Microstructured polymer optical fibers . . . . . . . . . . 39
1.5.4 OmniGuide fibers. . . . . . . . . . . . . . . . . . . . . . 41
1.6 Photonic crystal fibers in the market . . . . . . . . . . . . . . . 42
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
v
vi Contents
2 Guiding properties 53
2.1 Square-lattice PCFs . . . . . . . . . . . . . . . . . . . . . . . . 54
2.1.1 Guidance . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.1.2 Cutoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Cutoff of large-mode area triangular PCFs . . . . . . . . . . . . 70
2.3 Hollow-core-modified honeycomb PCFs . . . . . . . . . . . . . 79
2.3.1 Guidance and leakage . . . . . . . . . . . . . . . . . . . 79
2.3.2 Birefringence . . . . . . . . . . . . . . . . . . . . . . . . 84
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3 Dispersion properties 99
3.1 PCFs for dispersion compensation . . . . . . . . . . . . . . . . 100
3.2 Dispersion of square-lattice PCFs . . . . . . . . . . . . . . . . . 109
3.3 Dispersion-flattened triangular PCFs . . . . . . . . . . . . . . . 114
3.3.1 PCFs with modified air-hole rings . . . . . . . . . . . . 114
3.3.2 Triangular-core PCFs . . . . . . . . . . . . . . . . . . . 119
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4 Nonlinear properties 129
4.1 Supercontinuum generation . . . . . . . . . . . . . . . . . . . . 129
4.1.1 Physics of supercontinuum generation . . . . . . . . . . 130
4.1.2 Highly nonlinear PCFs . . . . . . . . . . . . . . . . . . . 130
4.1.3 Dispersion properties and pump wavelength . . . . . . . 133
4.1.4 Influence of the pump pulse regime . . . . . . . . . . . . 138
4.1.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . 140
4.2 Optical parametric amplification . . . . . . . . . . . . . . . . . 142
4.2.1 Triangular PCFs for OPA . . . . . . . . . . . . . . . . . 143
4.2.2 Phase-matching condition in triangular PCFs . . . . . . 145
4.3 Nonlinear coefficient in hollow-core PCFs . . . . . . . . . . . . 150
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5 Raman properties 159
5.1 Raman effective area and Raman gain coefficient . . . . . . . . 161
5.2 Raman properties of triangular PCFs . . . . . . . . . . . . . . 165
5.2.1 Silica triangular PCFs . . . . . . . . . . . . . . . . . . . 165
5.2.2 Tellurite triangular PCFs . . . . . . . . . . . . . . . . . 172
5.2.3 Enlarging air-hole triangular PCFs . . . . . . . . . . . . 173
Contents vii
5.3 Raman properties of honeycomb PCFs . . . . . . . . . . . . . . 175
5.4 PCF Raman amplifiers . . . . . . . . . . . . . . . . . . . . . . . 178
5.4.1 Model for PCF Raman amplifiers . . . . . . . . . . . . . 179
5.4.2 Triangular PCF Raman amplifiers . . . . . . . . . . . . 182
5.5 Impact of background losses on PCF Raman amplifiers . . . . . 189
5.6 Multipump PCF Raman amplifiers . . . . . . . . . . . . . . . . 192
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6 Erbium-doped fiber amplifiers 203
6.1 Model for doped-fiber amplifiers . . . . . . . . . . . . . . . . . 204
6.2 EDFAs based on honeycomb and cobweb PCFs . . . . . . . . . 205
6.3 EDFAs based on triangular PCFs . . . . . . . . . . . . . . . . . 207
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
A Finite Element Method 219
A.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.2 PCF parameter evaluation . . . . . . . . . . . . . . . . . . . . . 221
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Index 227
Preface
Photonic crystal fibers, also known as microstructured or holey fibers, have
recently generated great interest in the scientific community thanks to the
new ways provided to control and guide light, not obtainable with conven-
tional optical fibers. Proposed for the first time in early 90’s, photonic crystal
fibers have driven an exciting and irrepressible research activity all over the
world, starting in the telecommunication field and then touching metrology,
spectroscopy, microscopy, astronomy, micromachining, biology and sensing.
A variety of very interesting publications and high level books have been
alreadypresented,describingthedifferentkindsofthesenewfibers,thephysics
of their behavior, as well as a huge range of design tools. These aspects will
not be considered again in this work.
This book, instead, is intended to provide an expert guidance through the
properties of photonic crystal fibers, with a specific focus on the telecommu-
nication aspects. Although standard fibers for telecommunication can rely on
a well-established technology and standard fiber based devices and systems
represent a consolidated reality, hardly replaceable, the authors believe that
photonic crystal fibers can revolutionize the field of guided optics and its ap-
plications, evenifmuch easierand closeopportunities canbe foreseenin many
otherfields.Thisbeliefgetsfirmerwhenconsideringsignalprocessingandspe-
cific functions rather than the usage of photonic crystal fibers in long distance
transmission.
The long expertise of the authors in fiber based device analysis is reflected
in a deep analysis aimed to practically understand how the physical and geo-
metrical characteristics of these new fibers can be tailored to achieve the goal
of ad hoc performances. The study, mainly performed with the help of the
finite element method, a powerful numerical approach the authors are very
expert in, has enabled to understand how best to optimize the fiber design,
ix
x Preface
always keeping in mind actual possibilities and limits of photonic crystal fiber
fabrication technology.
This book will thus benefit researchers approaching this very dynamic and
evolving subject with the interest to explore this field of telecommunication,
looking at current as well as emerging applications.