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Green's Function Integral Equation Methods in Nano-Optics [Kõva köide]

(Aalborg University, Northern Jutland, Denmark)
  • Formaat: Hardback, 418 pages, kõrgus x laius: 234x156 mm, kaal: 739 g, 14 Tables, black and white; 205 Illustrations, black and white
  • Ilmumisaeg: 28-Jan-2019
  • Kirjastus: CRC Press Inc
  • ISBN-10: 0815365969
  • ISBN-13: 9780815365969
Teised raamatud teemal:
Green's Function Integral Equation Methods in Nano-OpticsSuurem pilt
  • Formaat: Hardback, 418 pages, kõrgus x laius: 234x156 mm, kaal: 739 g, 14 Tables, black and white; 205 Illustrations, black and white
  • Ilmumisaeg: 28-Jan-2019
  • Kirjastus: CRC Press Inc
  • ISBN-10: 0815365969
  • ISBN-13: 9780815365969
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780815365969.html
Märksõnad:
This book gives a comprehensive introduction to Greens function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Greens function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Greens function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions.

Each presented method is accompanied by examples from nano-optics, including: resonant metal nano-particles placed in a homogeneous medium or on a surface or waveguide; a microstructured gradient-index-lens; the Purcell effect for an emitter in a photonic crystal; the excitation of surface plasmon polaritons by second-harmonic generation in a polymer fiber placed on a thin metal film; and anti-reflective, broadband absorbing or resonant surface microstructures. Each presented method is also accompanied by guidelines for software implementation and exercises.

Features











Comprehensive introduction to Greens function integral equation methods for scattering problems in the field of nano-optics





Detailed explanation of how to discretize and solve integral equations using simple and higher-order finite-element approaches





Solution strategies for large structures





Guidelines for software implementation and exercises





Broad selection of examples of scattering problems in nano-optics
Preface ix
Chapter 1 Introduction 1(8)
1.1 Overview of methods and scattering problems
1(2)
1.2 Optics versus microwaves
3(1)
1.3 Examples of nano-optics
4(2)
1.4 Notation, abbreviations and symbols
6(3)
Chapter 2 Theoretical foundation 9(30)
2.1 Maxwell's equations
9(5)
2.1.1 Boundary conditions
11(1)
2.1.2 Wave equations
11(1)
2.1.3 Poynting vector
12(2)
2.2 Planar layered structures
14(8)
2.2.1 Fresnel reflection and transmission
15(3)
2.2.2 Planar waveguides and guided modes
18(4)
2.3 Scattering theory
22(15)
2.3.1 Scatterer in homogeneous material (2D)
23(3)
2.3.2 Scatterer on a layered structure (2D)
26(6)
2.3.3 Scatterer in homogeneous media (3D)
32(2)
2.3.4 Scatterer on a layered structure (3D)
34(3)
2.4 Exercises
37(2)
Chapter 3 One-dimensional scattering problems 39(10)
3.1 Green's function integral equations
39(2)
3.2 Numerical approach
41(1)
3.3 Example of a simple barrier
42(1)
3.4 Iterative FFT-based approach for large structures
43(2)
3.5 Guidelines for software implementation
45(1)
3.6 Exercises
46(3)
Chapter 4 Surface integral equation method for 2D scattering problems 49(156)
4.1 Scatterer in a homogeneous medium
50(43)
4.1.1 Green's function integral equations
50(4)
4.1.2 Finite-element-based discretization approaches
54(6)
4.1.3 Pulse expansion and point-matching
60(5)
4.1.4 Linear-field expansion and point-matching
65(2)
4.1.5 Higher-order polynomial field expansion and point matching
67(8)
4.1.6 Fourier expansion methods
75(2)
4.1.7 Calculating electric and magnetic field distributions
77(2)
4.1.8 Examples of metal nanostrip resonators
79(11)
4.1.9 Guidelines for software implementation
90(2)
4.1.10 Exercises
92(1)
4.2 Scatterer on or near planar surfaces
93(64)
4.2.1 Green's function for a layered reference struc- ture with planar surfaces
94(11)
4.2.2 GFSIEM for a layered reference structure
105(2)
4.2.3 Calculation of fields using the angular spectrum representation
107(9)
4.2.4 Example: Gold nanostrip on a dielectric substrate
116(7)
4.2.5 Example: Silver nanostrip above a silver surface
123(6)
4.2.6 Example: Single groove in metal
129(4)
4.2.7 Example: Silver nanostrip on a thin-film- silicon-on-silver waveguide
133(10)
4.2.8 Example: Microstructured gradient-index lens for THz photoconductive antennas
143(11)
4.2.9 Guidelines for software implementation
154(2)
4.2.10 Exercises
156(1)
4.3 Periodic structures
157(48)
4.3.1 Bloch waves
158(1)
4.3.2 Green's function for periodic structures
158(2)
4.3.3 GFSIEM for periodic structures
160(3)
4.3.4 Derivatives of periodic Green's function and tabulation
163(2)
4.3.5 Calculating the fields
165(2)
4.3.6 Calculating reflection and transmission
167(2)
4.3.7 Multilayer periodic structures
169(5)
4.3.8 Transfer-matrix method for large structures
174(9)
4.3.9 Example: Photonic crystal
183(5)
4.3.10 Example: Anti-reflective groove array in a dielectric
188(6)
4.3.11 Example: Broadband-absorber ultra-sharp groove array in a metal
194(7)
4.3.12 Guidelines for software implementation
201(1)
4.3.13 Exercises
202(3)
Chapter 5 Area integral equation method for 2D scattering problems 205(60)
5.1 Green's function integral equations
206(3)
5.1.1 s polarization
206(1)
5.1.2 p polarization
207(2)
5.2 Discretization with square-shaped elements
209(2)
5.3 Discretization with triangular elements
211(3)
5.4 Scatterer in a homogeneous medium
214(14)
5.4.1 s polarization
214(8)
5.4.2 p polarization
222(6)
5.5 Scatterer on or near planar surfaces
228(6)
5.5.1 s polarization
228(1)
5.5.2 p polarization
229(5)
5.6 Periodic surface microstructures
234(7)
5.6.1 s polarization
235(3)
5.6.2 p polarization
238(3)
5.7 Fast iterative W1-based approach for large structures
241(3)
5.8 Example: Purcell factor of emitter in a photonic crystal
244(8)
5.9 Example: Excitation of surface plasmon polaritons by second harmonic generation in a single organic nanofiber
252(9)
5.10 Guidelines for software implementation
261(1)
5.11 Exercises
261(4)
Chapter 6 Volume integral equation method for 3D scattering problems 265(40)
6.1 Green's function integral equation
265(1)
6.2 Scatterer in a homogeneous medium
266(9)
6.2.1 Discretization with cubic volume elements
268(5)
6.2.2 Discrete dipole approximation (DDA)
273(2)
6.3 Scatterer on or near planar surfaces
275(18)
6.3.1 Green's tensor for layered reference structures
275(7)
6.3.2 Far-field Green's tensor
282(5)
6.3.3 Green's tensor in Cartesian vector form
287(1)
6.3.4 Optical cross sections
288(1)
6.3.5 Example: Scattering by a nanostrip on a thin metal film
289(4)
6.4 Periodic surface microstructures
293(10)
6.4.1 Green's tensor for periodic structures
294(4)
6.4.2 Calculating reflection and transmission
298(1)
6.4.3 Example: 2D periodic antireflective surface microstructure
299(4)
6.5 Guidelines for software implementation
303(1)
6.6 Exercises
303(2)
Chapter 7 Volume integral equation method for cylindrically symmetric structures 305(36)
7.1 Expansion of homogeneous-medium dyadic Green's tensor in cylindrical harmonics
306(7)
7.1.1 Eigenfunctions
306(2)
7.1.2 Orthogonality relations and normalization
308(1)
7.1.3 Constructing the direct Green's tensor
309(4)
7.2 Green's tensor for a layered structure
313(3)
7.2.1 Indirect Green's tensor: Cylindrical harmonics
314(1)
7.2.2 Transmitted Green's tensor: Cylindrical harmonics
315(1)
7.3 Out-of-plane far-field approximations of the cylindrical Green's tensor elements
316(5)
7.3.1 Far-field direct Green's tensor
319(1)
7.3.2 Far-field indirect Green's tensor
320(1)
7.3.3 Far-field transmitted Green's tensor
321(1)
7.4 Guided-mode far-field approximations of the cylindrical Green's tensor elements
321(3)
7.5 Optical cross sections
324(1)
7.6 Numerical approach: ring elements with rectangular cross section
325(2)
7.7 Example: Nanocylinder on a layered structure
327(5)
7.7.1 Cylindrical scatterer on a dielectric substrate
328(2)
7.7.2 Cylindrical scatterer on a thin-film silicon-on- silver waveguide
330(2)
7.8 Example: Microstructured gradient-index lens
332(7)
7.8.1 Dipole reference field
333(2)
7.8.2 Calculation of emitted power
335(1)
7.8.3 Emission patterns and emitted powers
336(3)
7.9 Guidelines for software implementation
339(1)
7.10 Exercises
340(1)
Chapter 8 Surface integral equation method for the quasi-static limit 341(18)
8.1 Green's function integral equations
341(3)
8.2 Numerical approach: Pulse expansion
344(3)
8.3 Finite-element-approach: Linear expansion
347(6)
8.4 Finite-element-approach: Quadratic expansion
353(2)
8.5 Examples of absorption cross sections of 3D silver nanoparticles
355(1)
8.6 Guidelines for software implementation
356(1)
8.7 Exercises
357(2)
Chapter 9 Surface integral equation method for 3D scattering problems 359(22)
9.1 Surface integral equations
359(6)
9.2 Calculating optical cross sections
365(1)
9.3 Numerical approach: General structure
366(3)
9.4 Numerical approach: Cylindrically symmetric structure
369(6)
9.5 Example: Metal nano-disc resonators
375(3)
9.6 Guidelines for software implementation
378(1)
9.7 Exercises
379(2)
Appendix A Residue theorem 381(2)
Appendix B Conjugate gradient algorithm 383(2)
Appendix C Bessel functions 385(2)
Appendix D Analytic scattering from a circular cylinder 387(4)
Appendix E Analytic scattering from a spherical particle 391(4)
Appendix F Calculating guided modes of planar waveguides 395(8)
F.1 Exercises
401(2)
Appendix G Plane-wave-expansion theory 403(4)
G.1 Exercises
406(1)
References 407(8)
Index 415
Dr. Thomas Søndergaard is currently an Associate Professor in Nano Optics, Aalborg University, Denmark. His areas of expertise include numerical methods for theoretical analysis of electromagnetic fields in micro- and nanostructures. Plasmonics: waveguiding, optical antennas, resonators and sensors based on a type of electromagnetic surface wave at metal-dielectric interfaces known as Surface Plasmon Polaritons. Photonic crystals: wavelength-scale periodic structures in which light with certain wavelengths cannot propagate, similar to electrons with certain energies not being able to progagate in semiconductors, and how this can be exploited for e.g. designing optical waveguides and cavities. Greens function integral equation methods. Dr. Sondergaard has been awarded The Danish Independent Research Councils' Young Researcher's Award (2006) and The Danish Optical Society Award (2008). He is a board member of the Danish Optical Society and reviewer of 15-20 papers per year for such journals as Physical Review B, Physical Review Letters, Applied Physics Letters, Optics Express, IEEE Journal of Quantum Electronics, IEEE Journal of Lightwave Technology, Optics Communications, Physica status solidi (b), Nature Photonics, Optics Letters, and Journal of the Optical Society of America A/B. Dr. Sondergaard has also been published 84 papers in peerreviewed journals and holds three patents.