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Foundations Of Photonic Crystal Fibres (2nd Edition) 2nd Revised edition [Kõva köide]

(Univ Of Sydney, Australia), (Aix-marseille Univ, France), (Univ Montpellier Ii, France), (Aix-marseille Univ, France), (Aix-marseille Univ, France), (Univ Of Sydney, Australia), (U), (Aix-marseille Univ, France & Liverpool Univ, Uk)
  • Formaat: Hardback, 552 pages
  • Ilmumisaeg: 21-Aug-2012
  • Kirjastus: Imperial College Press
  • ISBN-10: 1848167288
  • ISBN-13: 9781848167285
Teised raamatud teemal:
Foundations Of Photonic Crystal Fibres (2nd Edition) 2nd Revised editionSuurem pilt
  • Formaat: Hardback, 552 pages
  • Ilmumisaeg: 21-Aug-2012
  • Kirjastus: Imperial College Press
  • ISBN-10: 1848167288
  • ISBN-13: 9781848167285
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781848167285.html
Märksõnad:
The focus of this book lies at the meeting point of electromagnetic waveguides and photonic crystals. Although these are both widely studied topics, they have been kept apart until recently. The purpose of the first edition of this book was to give state-of-the-art theoretical and numerical viewpoints about exotic fibres which use “photonic crystal effects” and consequently exhibit some remarkable properties.Since that first edition, photonic crystal fibres have become an important and effective optical device. In this second edition, the description of the theoretical and numerical tools used to study these fibres is enhanced, whilst up-to-date information about the properties, applications and fabrication of these fibres is added.
Forewords to the First Edition v
Forewords to the Second Edition ix
Preface xxi
Acknowledgements xxxvii
1 Introduction
1(58)
1.1 Conventional Optical Fibres
2(11)
1.1.1 Guidance mechanism
2(1)
1.1.2 Fibre modes
3(3)
1.1.3 Main properties
6(7)
1.2 Photonic Crystals
13(5)
1.2.1 One dimension: Bragg mirrors
13(1)
1.2.2 Photonic crystals in two and three dimensions
14(2)
1.2.3 Guiding light in a fibre with photonic crystals
16(2)
1.3 High-index Core Photonic Crystal Fibres
18(17)
1.3.1 A bit of history
18(1)
1.3.2 Guidance mechanism
19(3)
1.3.3 Number of modes
22(2)
1.3.4 Endlessly single-mode fibres
24(2)
1.3.5 Dispersion
26(3)
1.3.6 Non-linearity
29(3)
1.3.7 Birefringence
32(1)
1.3.8 High-bandwidth multimode fibres
32(1)
1.3.9 High NA fibres
33(2)
1.4 Low-index Cores
35(16)
1.4.1 Bragg fibres
36(1)
1.4.2 Two-dimensional bandgap guiding fibres
37(7)
1.4.3 Non-bandgap guiding fibres: inhibited coupling
44(3)
1.4.4 Application of bandgap and hollow-core fibres
47(1)
1.4.5 Applications (A hole is a hole until you fill it)
48(3)
1.5 A Few Words on Leaky Modes
51(8)
1.5.1 Confinement losses
51(1)
1.5.2 Modes of a leaky structure
52(1)
1.5.3 Heuristic approach to physical properties of leaky modes
53(2)
1.5.4 Mathematical considerations
55(2)
1.5.5 Spectral considerations
57(2)
2 PCF Fabrication and Post-processing
59(28)
2.1 Introduction
59(1)
2.2 Optical Fibre Materials
59(2)
2.3 Fabrication of PCFs
61(15)
2.3.1 Stacking
62(5)
2.3.2 Drilling
67(2)
2.3.3 Extrusion and casting
69(4)
2.3.4 PCF drawing
73(3)
2.4 Post-processing of PCF
76(7)
2.4.1 Tapcring PCFs
76(3)
2.4.2 Differential hole inflation in PCFs
79(4)
2.5 Splicing of PCFs
83(4)
3 Electromagnetism --- Prerequisites
87(72)
3.1 Maxwell's Equations
87(7)
3.1.1 Maxwell's equations in vacuo
87(2)
3.1.2 Maxwell's equations in idealised matter
89(5)
3.2 The Monodimensional Case: Propagation Modes and Dispersion Curves
94(22)
3.2.1 A first approach
94(6)
3.2.2 Localisation of constants of propagation
100(1)
3.2.3 How can one practically find the dispersion curves and the modes?
101(9)
3.2.4 Spectral approach
110(6)
3.3 The Monodimensional Case: Leaky Modes and Dispersion Curves
116(4)
3.3.1 Pole hunting: the tetrachotomy method
117(3)
3.4 A First Foray into the Realm of the Finite Element Method
120(1)
3.5 Leaky Modes of Perot-Fabry Structures
121(2)
3.6 The Two-dimensional Vectorial Case (General Case)
123(8)
3.6.1 curlβ operator
123(1)
3.6.2 Three different kinds of modes: basic definitions
124(1)
3.6.3 Some useful relations between the transverse and axial components
125(2)
3.6.4 Equations of propagation involving only the axial components
127(2)
3.6.5 What are the special features of isotropic microstructured fibres?
129(2)
3.7 The Two-dimensional Scalar Case (Weak Guidance)
131(1)
3.8 Spectral Analysis for Guided Modes
132(8)
3.8.1 Preliminary remarks
132(1)
3.8.2 A brief vocabulary
133(1)
3.8.3 Posing the problem
134(1)
3.8.4 Continuous formulation
135(5)
3.9 Non-finiteness of Energy of Leaky Modes
140(2)
3.10 Bloch Wave Theory
142(17)
3.10.1 The crystalline structure
142(1)
3.10.2 Waves in a homogeneous space
143(1)
3.10.3 Bloch modes of a photonic crystal
144(4)
3.10.4 Computation of the band structure
148(3)
3.10.5 A simple one-dimensional illustrative example: the Kronig-Penney model
151(8)
4 Finite Element Method
159(76)
4.1 Finite Elements: Basic Principles
159(19)
4.1.1 A one-dimensional naive introduction
160(3)
4.1.2 Multi-dimensional scalar elliptic problems
163(5)
4.1.3 Mixed formulations
168(2)
4.1.4 Vector problems
170(2)
4.1.5 Eigenvalue problems
172(6)
4.2 The Geometric Structure of Electromagnetism and its Discrete Analogue
178(14)
4.2.1 Topology
179(1)
4.2.2 Physical quantities
180(1)
4.2.3 Topological operators
181(3)
4.2.4 Metric
184(4)
4.2.5 Differential complexes: from de Rham to Whitney
188(4)
4.3 Some Practical Questions
192(11)
4.3.1 Building the matrices (discrete Hodge operator and material properties)
192(2)
4.3.2 Reference element
194(2)
4.3.3 Change of coordinates
196(2)
4.3.4 Nedelec edge elements versus Whitney 1-forms
198(2)
4.3.5 Infinite domains and leaky modes
200(3)
4.4 Propagation Mode Problems in Dielectric Waveguides
203(11)
4.4.1 Weak and discrete electric field formulation
204(5)
4.4.2 Numerical comparisons
209(2)
4.4.3 Variants
211(3)
4.5 Periodic Waveguides
214(8)
4.5.1 Bloch modes
214(2)
4.5.2 The Bloch conditions
216(3)
4.5.3 A numerical example
219(2)
4.5.4 Direct determination of the periodic part
221(1)
4.6 Perfectly Matched Layers (PMLs) and the Computation of Leaky Modes
222(10)
4.6.1 Finite element method and PMLs
223(5)
4.6.2 Numerical results
228(4)
4.7 Conclusion
232(3)
5 The Multipole Method
235(44)
5.1 Introduction
235(1)
5.2 The Multipole Formulation
236(13)
5.2.1 The geometry of the modelled microstructured optical fibre
236(2)
5.2.2 The choice of the propagating electromagnetic fields
238(1)
5.2.3 A simplified approach for the multipole method
238(5)
5.2.4 Rigorous formulation of the field identities
243(4)
5.2.5 Boundary conditions and field coupling
247(1)
5.2.6 Derivation of the Rayleigh identity
248(1)
5.3 Symmetry Properties of MOF
249(5)
5.3.1 Symmetry properties of modes
249(5)
5.4 Implementation
254(6)
5.4.1 Finding modes
255(1)
5.4.2 Dispersion characteristics
256(1)
5.4.3 Using the symmetries within the multipole method
257(1)
5.4.4 Another way to obtain Jm(β)
257(2)
5.4.5 Software and computational demands
259(1)
5.5 Validation of the Multipole Method
260(3)
5.5.1 Convergence and self-consistency
260(2)
5.5.2 Comparison with other methods
262(1)
5.6 First Numerical Examples
263(13)
5.6.1 A detailed C6υ example: the six-hole MOF
263(9)
5.6.2 A C2υ example: a birefringent MOF
272(1)
5.6.3 A C4υ example: a square MOF
272(4)
5.7 Conclusion
276(3)
6 Rayleigh Method
279(26)
6.1 Genesis of Baron Strutt's Algorithm
279(1)
6.2 Common Features of the Multipole and Rayleigh Methods
280(3)
6.3 Specificity of Lord Rayleigh's Algorithm
283(1)
6.4 Green's Function Associated with a Periodic Lattice
283(2)
6.5 Some Absolutely Convergent Lattice Sums
285(2)
6.6 The Rayleigh Identities
287(2)
6.7 The Rayleigh System
289(1)
6.8 Normalisation of the Rayleigh System
290(2)
6.9 Convergence of the Multipole Method
292(1)
6.10 Limit Cases: Asymptotics for High-contrast, βΛ << 1 and rc << A (Long-wave Limit and Dilute Composite)
293(7)
6.10.1 Effective boundary conditions for total internal reflection or high-contrast (ARROW) fibres
293(2)
6.10.2 Estimate of the cut-off curve
295(3)
6.10.3 Dipole approximation and effective parameters
298(2)
6.11 Higher-order Approximations, Photonic Bandgaps for Out-of-plane Propagation
300(2)
6.12 Conclusion and Perspectives
302(3)
7 A la Cauchy Path for Pole Finding
305(22)
7.1 A Simple Extension: Poles of Matrices
308(9)
7.1.1 Degenerate eigenvalues
312(1)
7.1.2 Multiple poles inside the loop
313(1)
7.1.3 Miracles sometimes happen
314(3)
7.2 Cauchy Integrals for Operators
317(1)
7.3 Numerical Applications
318(8)
7.4 Conclusion
326(1)
8 Main Properties of Microstructured Optical Fibres
327(62)
8.1 Types of Microstructured Optical Fibres or Types of Modes?
327(1)
8.2 Main Linear Properties of Modes in High-index Microstructured Optical Fibres with Low-Index Inclusions
328(33)
8.2.1 Solid-core microstructured fibre with low-index inclusions and band diagram point of view
328(4)
8.2.2 Basic properties of the losses
332(4)
8.2.3 Single-modedness of high-index core Csv MOF
336(10)
8.2.4 Modal transition without cut-off of the fundamental mode
346(7)
8.2.5 Chromatic dispersion
353(8)
8.3 Two Examples of Hollow-core MOFs with Air-guided Modes
361(18)
8.3.1 A hollow-core MOF made of silica and the band diagram point of view
361(8)
8.3.2 An optimised hollow-core MOF made of high-index glass for the far infrared
369(10)
8.4 A Detailed Example of an ARROW MOF
379(8)
8.4.1 Guiding in ARROW microstructured optical fibres and interpretation
379(1)
8.4.2 The ARROW model and its application to MOFs
380(2)
8.4.3 ARROW MOFs and band diagrams
382(1)
8.4.4 ARROW MOFs and avoided crossings
383(4)
8.5 Conclusion
387(2)
9 Twisted Fibres
389(16)
9.1 Introduction
389(1)
9.2 Helicoidal Coordinates
390(5)
9.2.1 Twisted PML
394(1)
9.3 Finite Element Modelling of Twisted Waveguides
395(3)
9.4 Quadratic Eigenvalue Problem
398(2)
9.5 Numerical Example
400(4)
9.6 Conclusion
404(1)
10 Conclusion
405(2)
Appendix A From Change of Coordinates in Maxwell's Equations to Transformation Optics
407(12)
A.1 Change of Coordinates in Maxwell's Equations
407(6)
A.2 The Geometric Transformation --- Equivalent Material Properties Principle
413(2)
A.3 Useful Jacobian Matrices
415(2)
A.4 Transformation Optics
417(2)
Appendix B A Formal Framework for Mixed FEMs
419(4)
Appendix C Some Details of the Multipole Method Derivation
423(8)
C.1 Derivation of the Wijngaard Identity
423(2)
C.2 Change of Basis
425(1)
C.2.1 Cylinder-to-cylinder conversion
425(1)
C.2.2 Jacket-to-cylinder conversion
425(1)
C.2.3 Cylinder-to-jacket conversion
426(1)
C.3 Boundary Conditions: Reflection Matrices
426(5)
Appendix D Integration by Parts
431(4)
Appendix E Six-hole Plain-core MOF Example: Supercells
435(6)
Appendix F A Potpourri of Mathematics
441(30)
Bibliography 471(34)
Index 505