Nanostructured and Subwavelength Waveguides

Maksim Skorobogatiy is Professor in the Department of Engineering Physics at the Ecole Polytechnique de Montréal, Canada. He arrived at Polytechnique in 2003 after completing his PhD at MIT.He has worked in the area of optical waveguides for over 12 years, and has published over 70 papers. Maksim is an expert on photonic crystal waveguides, and has recently authored a book on this topic for CUP (2009).His research group is active in disseminating their results in the public media. Most recently their research on photonic textiles was featured on a national TV station TéleQuébec, and a Discovery channel documentary about electronic textiles will be broadcast soon.

Optical waveguides take a prominent role in photonics because they are able to trap and to transport light efficiently between a point of excitation and a point of detection. Moreover, waveguides allow the management of many of the fundamental properties of light and allow highly controlled interaction with other optical systems. For this reason waveguides are ubiquitous in telecommunications, sensing, spectroscopy, light sources, and high power light delivery. Nanostructured and subwavelength waveguides have additional advantages; they are able to confine light at a length scale below the diffraction limit and enhance or suppress light-matter interaction, as well as manage fundamental properties of light such as speed and direction of energy and phase propagation.
 
This book presents semi-analytical theory and practical applications of a large number of subwavelength and nanostructured optical waveguides and fibers operating in various regions of the electromagnetic spectrum including visible, near and mid-IR and THz. A large number of approximate, while highly precise analytical expressions are derived that describe various modal properties of the planar and circular isotropic, anisotropic, and metamaterial waveguides and fibers, as well as surface waves propagating on planar, and circular interfaces. A variety of naturally occurring and artificial materials are also considered such as dielectrics, metals, polar materials, anisotropic all-dielectric and metal-dielectric metamaterials.
 
Contents are organized around four major themes:
* Guidance properties of subwavelength waveguides and fibers made of homogeneous, generally anisotropic materials
* Guidance properties of nanostructured waveguides and fibers using both exact geometry modelling and effective medium approximation
* Development of the effective medium approximations for various 1D and 2D nanostructured materials and extension of these approximations to shorter wavelengths
* Practical applications of subwavelength and nanostructured waveguides and fibers
 
Nanostructured Subwavelengths and Waveguides is unique in that it collects in a single place an extensive range of analytical solutions which are derived in various limits for many practically important and popular waveguide and fiber geometries and materials.

Optical waveguides take a prominent role in photonics because theyare able to trap and to transport light efficiently between a pointof excitation and a point of detection. Moreover, waveguides allowthe management of many of the fundamental properties of light andallow highly controlled interaction with other optical systems.

Series Preface xiii
 
Preface xv
 
1 Introduction 1
 
1.1 Contents and Organisation of the Book 2
 
1.2 Step-Index Subwavelength Waveguides Made of Isotropic Materials 3
 
1.3 Field Enhancement in the Low Refractive Index Discontinuity Waveguides 5
 
1.4 Porous Waveguides and Fibres 6
 
1.5 Multifilament Core Fibres 7
 
1.6 Nanostructured Waveguides and Effective Medium Approximation 8
 
1.7 Waveguides Made of Anisotropic Materials 9
 
1.8 Metals and Polar Materials 10
 
1.9 Surface Polariton Waves on Planar and Curved Interfaces 12
 
1.10 Metal/Dielectric Metamaterials and Waveguides Made of Them 16
 
1.11 Extending Effective Medium Approximation to Shorter Wavelengths 18
 
2 Hamiltonian Formulation of Maxwell Equations for the Modes of Anisotropic Waveguides 21
 
2.1 Eigenstates of a Waveguide in Hamiltonian Formulation 21
 
2.2 Orthogonality Relation between the Modes of a Waveguide Made of Lossless Dielectrics 23
 
2.3 Expressions for the Modal Phase Velocity 26
 
2.4 Expressions for the Modal Group Velocity 27
 
2.5 Orthogonality Relation between the Modes of a Waveguide Made of Lossy Dielectrics 29
 
2.6 Excitation of the Waveguide Modes 30
 
3 Wave Propagation in Planar Anisotropic Multilayers, Transfer Matrix Formulation 39
 
3.1 Planewave Solution for Uniform Anisotropic Dielectrics 39
 
3.2 Transfer Matrix Technique for Multilayers Made from Uniform Anisotropic Dielectrics 41
 
3.3 Reflections at the Interface between Isotropic and Anisotropic Dielectrics 44
 
4 Slab Waveguides Made from Isotropic Dielectric Materials. Example of Subwavelength Planar Waveguides 47
 
4.1 Finding Modes of a Slab Waveguide Using Transfer Matrix Theory 47
 
4.2 Exact Solution for the Dispersion Relation of Modes of a Slab Waveguide 50
 
4.3 Fundamental Mode Dispersion Relation in the Long-Wavelength Limit 53
 
4.4 Fundamental Mode Dispersion Relation in the Short-Wavelength Limit 55
 
4.5 Waveguides with Low Refractive-Index Contrast 57
 
4.6 Single-Mode Guidance Criterion 57
 
4.7 Dispersion Relations of the Higher-Order Modes in the Vicinity of their Cutoff Frequencies 57
 
4.8 Modal Losses Due to Material Absorption 58
 
4.9 Coupling into a Subwavelength Slab Waveguide Using a 2D Gaussian Beam 64
 
4.10 Size of a Waveguide Mode 69
 
5 Slab Waveguides Made from Anisotropic Dielectrics 75
 
5.1 Dispersion Relations for the Fundamental Modes of a Slab Waveguide 75
 
5.2 Using Transfer Matrix Method with Anisotropic Dielectrics 77
 
5.3 Coupling to the Modes of a Slab Waveguide Made of Anisotropic Dielectrics 78
 
6 Metamaterials in the Form of All-Dielectric Planar Multilayers 81
 
6.1 Effective Medium Approximation for a Periodic Multilayer with Subwavelength Period 81
 
6.2 Extended Bloch Waves of an Infinite Periodic Multilayer 82
 
6.3 Effective Medium Approximation 84
 
6.4 Extending Metamaterial Approximation to Shorter Wavelengths 86
 
6.5 Ambiguities in the Interpretation of the Dispersion Relation of a Planewave Propagating in a Lossy Metamaterial 89
 
7 Planar Waveguides Containing All-Dielectric Metamaterials, Example of Porous Waveguides 91
 
7.1 Geometry of a Planar Porous Waveguide 91
 
7.2 TE-Polarised Mode of a Porous Slab Waveguide 91
 
7.3 TM-Polarised Mode of a Porous Slab Waveguide 99
 
8 Circular Fibres Made of Isotropic Materials 103
 
8.1 Circular Symmetric Solutions of Maxwell's Equations for an Infinite Uniform Dielectric 104
 
8.2 Transfer Matrix Meth