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E-raamat: Nanostructured and Subwavelength Waveguides: Fundamentals and Applications

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Nanostructured and Subwavelength Waveguides: Fundamentals and ApplicationsSuurem pilt
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"This book presents semi-analytical theory and practical applications of a large number of subwavelength and nanostructured optical waveguides. The contents are organized around four major themes: guidance properties of subwavelength waveguides made of homogeneous anisotropic materials; description of guidance by nanostructured waveguides using effective media approximation; operation of nanostructured waveguides at shorter wavelength at the limit of validity of effective medium approximation; and practical applications of subwavelength and nanostructured waveguides.What makes the book unique is that it collects in a single place a large number of analytical solutions which are derived in a long wavelength regime for a plethora of practically important waveguides and fibers than researchers currently use or study worldwide. The waveguides considered include planar and circular isotropic and anisotropic waveguides, as well as surface waves on planar, and circular surfaces, and the waveguide materials include dielectrics, metals and polar materials. After analysis of the basic waveguide structures it considers waveguides made of the nanostructured materials. Many practical applications are then rigorouslydetailed including low-loss low-dispersion guidance using porous THz waves, long-range propagation of plasmons in thin metallic films, and leakage spectroscopy of leaky plasmonic modes propagating on thin metallic films.A companion website (password-protected) provides a fully functional transfer matrix code PolyTMat (Matlab) which is able to treat any multilayer waveguide of planar or circular geometry made of anisotropic dielectrics. "--



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.

Arvustused

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)

 

 

 

Series Preface xiii
Preface xv
1 Introduction
1(20)
1.1 Contents and Organisation of the Book
2(1)
1.2 Step-Index Subwavelength Waveguides Made of Isotropic Materials
3(2)
1.3 Field Enhancement in the Low Refractive Index Discontinuity Waveguides
5(1)
1.4 Porous Waveguides and Fibres
6(1)
1.5 Multifilament Core Fibres
7(1)
1.6 Nanostructured Waveguides and Effective Medium Approximation
8(1)
1.7 Waveguides Made of Anisotropic Materials
9(1)
1.8 Metals and Polar Materials
10(2)
1.9 Surface Polariton Waves on Planar and Curved Interfaces
12(4)
1.9.1 Surface Waves on Planar Interfaces
12(2)
1.9.2 Surface Waves on Wires
14(2)
1.9.3 Plasmons Guided by Metal Slab Waveguides
16(1)
1.9.4 Plasmons Guided by Metal Slot Waveguides
16(1)
1.10 Metal/Dielectric Metamaterials and Waveguides Made of Them
16(2)
1.11 Extending Effective Medium Approximation to Shorter Wavelengths
18(3)
2 Hamiltonian Formulation of Maxwell Equations for the Modes of Anisotropic Waveguides
21(18)
2.1 Eigenstates of a Waveguide in Hamiltonian Formulation
21(2)
2.2 Orthogonality Relation between the Modes of a Waveguide Made of Lossless Dielectrics
23(3)
2.3 Expressions for the Modal Phase Velocity
26(1)
2.4 Expressions for the Modal Group Velocity
27(2)
2.5 Orthogonality Relation between the Modes of a Waveguide Made of Lossy Dielectrics
29(1)
2.6 Excitation of the Waveguide Modes
30(9)
2.6.1 Least Squares Method
32(1)
2.6.2 Using Flux Operator as an Orthogonal Dot Product
33(1)
2.6.3 Coupling into a Waveguide with Lossless Dielectric Profile
33(3)
2.6.4 Coupling into a Waveguide with Lossy Dielectric Profile
36(3)
3 Wave Propagation in Planar Anisotropic Multilayers, Transfer Matrix Formulation
39(8)
3.1 Planewave Solution for Uniform Anisotropic Dielectrics
39(2)
3.2 Transfer Matrix Technique for Multilayers Made from Uniform Anisotropic Dielectrics
41(3)
3.2.1 TE Multilayer Stack
41(2)
3.2.2 TM Multilayer Stack
43(1)
3.3 Reflections at the Interface between Isotropic and Anisotropic Dielectrics
44(3)
4 Slab Waveguides Made from Isotropic Dielectric Materials. Example of Subwavelength Planar Waveguides
47(28)
4.1 Finding Modes of a Slab Waveguide Using Transfer Matrix Theory
47(3)
4.2 Exact Solution for the Dispersion Relation of Modes of a Slab Waveguide
50(3)
4.3 Fundamental Mode Dispersion Relation in the Long-Wavelength Limit
53(2)
4.4 Fundamental Mode Dispersion Relation in the Short-Wavelength Limit
55(2)
4.5 Waveguides with Low Refractive-Index Contrast
57(1)
4.6 Single-Mode Guidance Criterion
57(1)
4.7 Dispersion Relations of the Higher-Order Modes in the Vicinity of their Cutoff Frequencies
57(1)
4.8 Modal Losses Due to Material Absorption
58(6)
4.8.1 Waveguides Featuring Low Loss-Dispersion
61(1)
4.8.2 Modal Losses in a Waveguide with Lossless Cladding
62(1)
4.8.3 Modal Losses in a Waveguide with Low Refractive-Index Contrast
63(1)
4.9 Coupling into a Subwavelength Slab Waveguide Using a 2D Gaussian Beam
64(5)
4.9.1 TE Polarisation
64(3)
4.9.2 TM Polarisation
67(2)
4.10 Size of a Waveguide Mode
69(6)
4.10.1 Modal Size of the Fundamental Modes of a Slab Waveguide in the Long-Wavelength Limit
72(2)
4.10.2 Modal Size of the Fundamental Modes of a Slab Waveguide in the Short-Wavelength Limit
74(1)
5 Slab Waveguides Made from Anisotropic Dielectrics
75(6)
5.1 Dispersion Relations for the Fundamental Modes of a Slab Waveguide
75(2)
5.1.1 Long-Wavelength Limit
76(1)
5.1.2 Single-Mode Guidance Criterion
77(1)
5.2 Using Transfer Matrix Method with Anisotropic Dielectrics
77(1)
5.3 Coupling to the Modes of a Slab Waveguide Made of Anisotropic Dielectrics
78(3)
6 Metamaterials in the Form of All-Dielectric Planar Multilayers
81(10)
6.1 Effective Medium Approximation for a Periodic Multilayer with Subwavelength Period
81(1)
6.2 Extended Bloch Waves of an Infinite Periodic Multilayer
82(2)
6.3 Effective Medium Approximation
84(2)
6.4 Extending Metamaterial Approximation to Shorter Wavelengths
86(3)
6.5 Ambiguities in the Interpretation of the Dispersion Relation of a Planewave Propagating in a Lossy Metamaterial
89(2)
7 Planar Waveguides Containing All-Dielectric Metamaterials, Example of Porous Waveguides
91(12)
7.1 Geometry of a Planar Porous Waveguide
91(1)
7.2 TE-Polarised Mode of a Porous Slab Waveguide
91(8)
7.2.1 Effective Refractive Index and Losses of the Fundamental TE Mode
91(4)
7.2.2 Single-Mode Propagation Criterion, TE Modes
95(1)
7.2.3 Dispersion of the Fundamental TE Mode
95(4)
7.3 TM-Polarised Mode of a Porous Slab Waveguide
99(4)
7.3.1 Effective Refractive Index and Losses of the Fundamental TM Mode
99(1)
7.3.2 Single-Mode Propagation Criterion, TM Modes
100(1)
7.3.3 Dispersion of the Fundamental TM Mode
101(2)
8 Circular Fibres Made of Isotropic Materials
103(34)
8.1 Circular Symmetric Solutions of Maxwell's Equations for an Infinite Uniform Dielectric
104(3)
8.2 Transfer Matrix Method
107(3)
8.3 Fundamental Mode of a Step-Index Fibre
110(5)
8.3.1 Low Refractive-Index Contrast (Weakly Guiding Approximation)
111(3)
8.3.2 Fundamental Mode Dispersion Relation in the Long-Wavelength Limit (Any Refractive-Index Contrast)
114(1)
8.4 Higher-Order Modes and their Dispersion Relations Near Cutoff Frequencies
115(7)
8.4.1 Method 1
116(1)
8.4.2 Method 2
117(5)
8.5 Dispersion of the Fundamental m = 1 Mode
122(1)
8.6 Losses of the Fundamental m = 1 Mode
123(2)
8.7 Modal Confinement and Modal Field Extent into the Cladding Region
125(12)
8.7.1 Short-Wavelength Limit (Strong Confinement)
126(1)
8.7.2 Long-Wavelength Limit (Weak Confinement), General Considerations
126(1)
8.7.3 Modal Extent into Cladding in the Weak Confinement Regime. Case of Modes with m > 1
126(4)
8.7.4 Modal Extent into Cladding of the Fundamental m = 1 Mode in the Long-Wavelength Limit
130(3)
8.7.5 Examples of Field Distributions for m = 1, and m = 3 Modes
133(2)
8.7.6 Angle-Integrated Longitudinal Flux in the Weak Confinement Regime
135(2)
9 Circular Fibres Made of Anisotropic Materials
137(18)
9.1 Circular Symmetric Solutions of Maxwell's Equations for an Infinite Anisotropic Dielectric
137(2)
9.2 Transfer Matrix Method to Compute Eigenmodes of a Circular Fibre Made of Anisotropic Dielectrics
139(2)
9.3 Fundamental Mode of a Step-Index Fibre
141(5)
9.3.1 Low Refractive-Index Contrast, Low Anisotropy
141(3)
9.3.2 Long Wavelength Regime
144(2)
9.4 Linearly Polarised Modes of a Circular Fibre
146(9)
9.4.1 Fields of the Fundamental m = 1 Mode of a Circular Fibre in the Long-Wavelength Regime
150(5)
10 Metamaterials in the Form of a Periodic Lattice of Inclusions
155(12)
10.1 Effective Dielectric Tensor of Periodic Metamaterials in the Long-Wavelength Limit
156(8)
10.1.1 Effective Medium Theory for a Square Lattice of Circular Rods
158(3)
10.1.2 Effective Medium Approximation for a Square Lattice of Square Inclusions
161(3)
10.2 Bloch Wave Solutions in the Periodic Arrays of Arbitrary-Shaped Inclusions, Details of the Planewave Expansion Method
164(3)
11 Circular Fibres Made of All-Dielectric Metamaterials
167(18)
11.1 Porous-Core Fibres, Application in Low-Loss Guidance of THz Waves
167(8)
11.2 Multifilament Core Fibres, Designing Large Mode Area, Single-Mode Fibres
175(7)
11.3 Water-Core Fibres in THz, Guiding with Extremely Lossy Materials
182(3)
12 Modes at the Interface between Two Materials
185(24)
12.1 Surface Modes Propagating at the Interface between Two Positive Refractive Index Materials
185(3)
12.2 Geometrical Solution for the Bound Surface Modes
188(3)
12.3 Modes at the Interface between a Lossless Dielectric and an Ideal Metal, Excitation of an Ideal Surface Plasmon
191(3)
12.4 Modes at the Interface between a Lossless Dielectric and a Lossy Material (Metal or Dielectric)
194(10)
12.4.1 Modes at the Interface between One Lossless Dielectric and One Lossy Dielectric
194(2)
12.4.2 Modes at the Interface between a Lossless Dielectric and an Imperfect Metal. Frequency Region in the Vicinity of a Plasma Frequency (UV--Visible)
196(7)
12.4.3 Modes at the Interface between a Lossless Dielectric and an Imperfect Metal. Far-Infrared (THz) Spectral Range
203(1)
12.5 Material Parameters and Practical Examples of Surface Plasmons
204(5)
13 Modes of a Metal Slab Waveguide
209(24)
13.1 Modes of a Metal Slab Waveguide Surrounded by Two Identical Dielectric Claddings
210(11)
13.1.1 Weakly Coupled Surface Plasmons Guided by Thick and Lossless Metal Slab
211(4)
13.1.2 Long-Range Plasmon (Even Supermode) Guided by Thin and Lossless Metal Slab
215(4)
13.1.3 Odd Supermode Guided by Thin and Lossy Metal Slab
219(2)
13.2 Long-Range Plasmon Guided by Thin and Lossy Metal Slab
221(5)
13.2.1 Long-Range Plasmon Guided by Thin and Lossy Metal Slab. Visible--Mid-IR Spectral Range
221(1)
13.2.2 Long-Range Plasmon Guided by Thin and Lossy Metal Slab. Far-IR--(THz) Spectral Range
222(4)
13.3 Modes of a Metal Slab Surrounded by Two Distinct Lossless Claddings. Leaky Plasmonic Modes
226(7)
13.3.1 Radiation Losses of a Leaky Supermode Guided by a Nonsymmetric Slab Waveguide
228(5)
14 Modes of a Metal Slot Waveguide
233(14)
14.1 Odd-Mode Dispersion Relation Near the Light Line of the Core Material neff ~ no. Visible--Mid-IR Spectral Range
235(3)
14.2 Odd-Mode Dispersion Relation near the Mode Cutoff neff ~
0. Visible--Mid-IR Spectral Range
238(2)
14.3 Fundamental Mode of a Metal Slot Waveguide. Visible--Mid-IR Spectral Range
240(3)
14.4 Fundamental Mode Dispersion Relation at Low Frequencies ω →
0. Far-IR Spectral Range
243(4)
15 Planar Metal/Dielectric Metamaterials
247(6)
15.1 Extended Waves in the Infinite Metal/Dielectric Periodic Multilayers (Long-Wavelength Limit)
247(3)
15.2 Extending Metamaterial Approximation to Shorter Wavelengths
250(3)
16 Examples of Applications of Metal/Dielectric Metamaterials
253(28)
16.1 Optically Transparent Conductive Layers, Case of εII > 0, εT > 0
253(3)
16.2 Perfect Polarisation Splitter, Case of εII > 0, εT < 0
256(4)
16.3 Surface States at the Interface between Lossless Dielectric and Metal/Dielectric Metamaterials
260(2)
16.4 Surface Plasmons in a Two-Material System εi = εd
262(9)
16.4.1 Surface Plasmon at the Interface with Metamaterial 1
262(4)
16.4.2 Surface Plasmon at the Interface with Metamaterial 2
266(2)
16.4.3 Surface Plasmon at the Interface with Metamaterial 3
268(3)
16.5 Practical Application of Surface Plasmons Supported by Metamaterials 1, 2, 3
271(10)
16.5.1 Sensing of Changes in the Analyte Refractive Index Using Surface Plasmons
271(4)
16.5.2 Field Enhancement at the Metallic Surface
275(6)
17 Modes of Metallic Wires, Guidance in the UV--near-IR, Mid-IR and Far-IR Spectral Ranges
281(20)
17.1 Guidance by the Metallic Wires with Diameters Smaller than the Metal Skin Depth
281(4)
17.2 Guidance by the Metallic Wires with Diameters Much Larger than the Metal Skin Depth
285(1)
17.3 Wire Plasmons in the Visible--Near-IR Spectral Range
286(5)
17.3.1 Cutoff Frequencies of the Wire Plasmons in the Visible--Near-IR
291(1)
17.4 Wire Plasmons in the Mid-IR--Far-IR Spectral Range
291(10)
17.4.1 m = 1 Wire Plasmon in the Mid-IR Range
291(2)
17.4.2 m = 0 Wire Plasmon in the Mid-IR Spectral Range
293(2)
17.4.3 m = 1 Wire Plasmon in the Far-IR Spectral Range
295(2)
17.4.4 m = 0 Wire Plasmon in the Far-IR Spectral Range
297(4)
18 Semianalytical Methods of Solving Nonlinear Equations of Two Variables
301(6)
18.1 Polynomial Solution of a Nonlinear Equation in the Vicinity of a Known Particular Solution
301(1)
18.2 Method of Consecutive Functional Iterations
302(2)
18.3 Method of Asymptotics
304(3)
References 307(4)
Index 311
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.
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