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.

• Series Preface xiiiPreface xv1 Introduction 11.1 Contents and Organisation of the Book 21.2 Step-Index Subwavelength Waveguides Made of Isotropic Materials 31.3 Field Enhancement in the Low Refractive Index Discontinuity Waveguides 51.4 Porous Waveguides and Fibres 61.5 Multifilament Core Fibres 71.6 Nanostructured Waveguides and Effective Medium Approximation 81.7 Waveguides Made of Anisotropic Materials 91.8 Metals and Polar Materials 101.9 Surface Polariton Waves on Planar and Curved Interfaces 121.10 Metal/Dielectric Metamaterials and Waveguides Made of Them 161.11 Extending Effective Medium Approximation to Shorter Wavelengths 182 Hamiltonian Formulation of Maxwell Equations for the Modes of Anisotropic Waveguides 212.1 Eigenstates of a Waveguide in Hamiltonian Formulation 212.2 Orthogonality Relation between the Modes of a Waveguide Made of Lossless Dielectrics 232.3 Expressions for the Modal Phase Velocity 262.4 Expressions for the Modal Group Velocity 272.5 Orthogonality Relation between the Modes of a Waveguide Made of Lossy Dielectrics 292.6 Excitation of the Waveguide Modes 303 Wave Propagation in Planar Anisotropic Multilayers, Transfer Matrix Formulation 393.1 Planewave Solution for Uniform Anisotropic Dielectrics 393.2 Transfer Matrix Technique for Multilayers Made from Uniform Anisotropic Dielectrics 413.3 Reflections at the Interface between Isotropic and Anisotropic Dielectrics 444 Slab Waveguides Made from Isotropic Dielectric Materials. Example of Subwavelength Planar Waveguides 474.1 Finding Modes of a Slab Waveguide Using Transfer Matrix Theory 474.2 Exact Solution for the Dispersion Relation of Modes of a Slab Waveguide 504.3 Fundamental Mode Dispersion Relation in the Long-Wavelength Limit 534.4 Fundamental Mode Dispersion Relation in the Short-Wavelength Limit 554.5 Waveguides with Low Refractive-Index Contrast 574.6 Single-Mode Guidance Criterion 574.7 Dispersion Relations of the Higher-Order Modes in the Vicinity of their Cutoff Frequencies 574.8 Modal Losses Due to Material Absorption 584.9 Coupling into a Subwavelength Slab Waveguide Using a 2D Gaussian Beam 644.10 Size of a Waveguide Mode 695 Slab Waveguides Made from Anisotropic Dielectrics 755.1 Dispersion Relations for the Fundamental Modes of a Slab Waveguide 755.2 Using Transfer Matrix Method with Anisotropic Dielectrics 775.3 Coupling to the Modes of a Slab Waveguide Made of Anisotropic Dielectrics 786 Metamaterials in the Form of All-Dielectric Planar Multilayers 816.1 Effective Medium Approximation for a Periodic Multilayer with Subwavelength Period 816.2 Extended Bloch Waves of an Infinite Periodic Multilayer 826.3 Effective Medium Approximation 846.4 Extending Metamaterial Approximation to Shorter Wavelengths 866.5 Ambiguities in the Interpretation of the Dispersion Relation of a Planewave Propagating in a Lossy Metamaterial 897 Planar Waveguides Containing All-Dielectric Metamaterials, Example of Porous Waveguides 917.1 Geometry of a Planar Porous Waveguide 917.2 TE-Polarised Mode of a Porous Slab Waveguide 917.3 TM-Polarised Mode of a Porous Slab Waveguide 998 Circular Fibres Made of Isotropic Materials 1038.1 Circular Symmetric Solutions of Maxwell’s Equations for an Infinite Uniform Dielectric 1048.2 Transfer Matrix Method 1078.3 Fundamental Mode of a Step-Index Fibre 1108.4 Higher-Order Modes and their Dispersion Relations Near Cutoff Frequencies 1158.5 Dispersion of the Fundamental m = 1 Mode 1228.6 Losses of the Fundamental m = 1 Mode 1238.7 Modal Confinement and Modal Field Extent into the Cladding Region 1259 Circular Fibres Made of Anisotropic Materials 1379.1 Circular Symmetric Solutions of Maxwell’s Equations for an Infinite Anisotropic Dielectric 1379.2 Transfer Matrix Method to Compute Eigenmodes of a Circular Fibre Made of Anisotropic Dielectrics 1399.3 Fundamental Mode of a Step-Index Fibre 1419.4 Linearly Polarised Modes of a Circular Fibre 14610 Metamaterials in the Form of a Periodic Lattice of Inclusions 15510.1 Effective Dielectric Tensor of Periodic Metamaterials in the Long-Wavelength Limit 15610.2 Bloch Wave Solutions in the Periodic Arrays of Arbitrary-Shaped Inclusions, Details of the Planewave Expansion Method 16411 Circular Fibres Made of All-Dielectric Metamaterials 16711.1 Porous-Core Fibres, Application in Low-Loss Guidance of THz Waves 16711.2 Multifilament Core Fibres, Designing Large Mode Area, Single-Mode Fibres 17511.3 Water-Core Fibres in THz, Guiding with Extremely Lossy Materials 18212 Modes at the Interface between Two Materials 18512.1 Surface Modes Propagating at the Interface between Two Positive Refractive Index Materials 18512.2 Geometrical Solution for the Bound Surface Modes 18812.3 Modes at the Interface between a Lossless Dielectric and an Ideal Metal, Excitation of an Ideal Surface Plasmon 19112.4 Modes at the Interface between a Lossless Dielectric and a Lossy Material (Metal or Dielectric) 19413 Modes of a Metal Slab Waveguide 20913.1 Modes of a Metal Slab Waveguide Surrounded by Two Identical Dielectric Claddings 21013.2 Long-Range Plasmon Guided by Thin and Lossy Metal Slab 22113.3 Modes of a Metal Slab Surrounded by Two Distinct Lossless Claddings. Leaky Plasmonic Modes 22614 Modes of a Metal Slot Waveguide 23314.1 Odd-Mode Dispersion Relation Near the Light Line of the Core Material neff ∼ no. Visible–Mid-IR Spectral Range 23514.2 Odd-Mode Dispersion Relation near the Mode Cutoff neff ∼ 0. Visible–Mid-IR Spectral Range 23814.3 Fundamental Mode of a Metal Slot Waveguide. Visible–Mid-IR Spectral Range 24014.4 Fundamental Mode Dispersion Relation at Low Frequencies ω → 0. Far-IR Spectral Range 24315 Planar Metal/Dielectric Metamaterials 24715.1 Extended Waves in the Infinite Metal/Dielectric Periodic Multilayers (Long-Wavelength Limit) 24715.2 Extending Metamaterial Approximation to Shorter Wavelengths 25016 Examples of Applications of Metal/Dielectric Metamaterials 25316.1 Optically Transparent Conductive Layers, Case of ε_ > 0, ε⊥ > 0 25316.2 Perfect Polarisation Splitter, Case of ε_ > 0, ε⊥ < 0 25616.3 Surface States at the Interface between Lossless Dielectric and Metal/Dielectric Metamaterials 26016.4 Surface Plasmons in a Two-Material System εi = εd 26216.5 Practical Application of Surface Plasmons Supported by Metamaterials 1, 2, 3 27117 Modes of MetallicWires, Guidance in the UV–near-IR, Mid-IR and Far-IR Spectral Ranges 28117.1 Guidance by the Metallic Wires with Diameters Smaller than the Metal Skin Depth 28117.2 Guidance by the Metallic Wires with Diameters Much Larger than the Metal Skin Depth 28517.3 Wire Plasmons in the Visible–Near-IR Spectral Range 28617.4 Wire Plasmons in the Mid-IR–Far-IR Spectral Range 29118 Semianalytical Methods of Solving Nonlinear Equations of Two Variables 30118.1 Polynomial Solution of a Nonlinear Equation in the Vicinity of a Known Particular Solution 30118.2 Method of Consecutive Functional Iterations 30218.3 Method of Asymptotics 304References 307Index 311

“Coverage of material is both rigorous and transparent and thus this volume is likely to be used extensively by researchers in these rapidly developing subject areas.”  (Optics & Photonics News, 9 November  2012)