Green's Function Integral Equation Methods in Nano-Optics. ([2019])

• Record Type: Book
• Further Information: Note: Thomas M. Søndergaard.
• Authors: Søndergaard, Thomas M
• Contents: Chapter 1 Introduction ..........................................................................................1 1.1 Overview of methods and scattering problems...........................1 1.2 Optics versus microwaves...........................................................3 1.3 Examples of nano optics.............................................................4 1.4 Notation, abbreviations and symbols..........................................6 Chapter 2 Theoretical foundation .........................................................................9 2.1 Maxwells equations ....................................................................9 2.1.1 Boundary conditions ....................................................11 2.1.2 Wave equations ............................................................11 2.1.3 Poynting vector ............................................................12 2.2 Planar layered structures...........................................................14 2.2.1 Fresnel reflection and transmission..............................14 2.2.2 Planar waveguides and guided modes..........................18 2.3 Scattering theory.......................................................................22 2.3.1 Scatterer in homogeneous material (2D) .....................23 2.3.2 Scatterer on a layered structure (2D) ...........................26 2.3.3 Scatterer in homogeneous media (3D).........................32 2.3.4 Scatterer on a layered structure (3D) ...........................35 2.4 Exercises ...................................................................................37 Chapter 3 One-dimensional scattering problems................................................39 3.1 Greens function integral equations ...........................................39 3.2 Numerical approach..................................................................41 3.3 Example of a simple barrier......................................................42 3.4 Iterative FFT-based approach for large structures ....................43 3.5 Guide lines for software implementation .................................45 3.6 Exercises ...................................................................................46 Chapter 4 Surface integral equation method for 2D scattering problems...........49 4.1 Scatterer in a homogeneous medium........................................50 4.1.1 Greens function integral equations ..............................50 4.1.2 Finite-element-based discretization approaches ..........54 4.1.3 Pulse expansion and point-matching ...........................60 4.1.4 Linear-field expansion and point-matching .................65 4.1.5 Higher-order polynomial field expansion and point matching.......................................................................67 4.1.6 Fourier expansion methods ..........................................75 4.1.7 Calculating electric and magnetic field distributions...77 4.1.8 Examples of metal nanostrip resonators ......................79 4.1.9 Guidelines for software implementation......................90 4.1.10 Exercises ......................................................................92 4.2 Scatterer on or near planar surfaces..........................................93 4.2.1 Greens function for a layered reference structure with planar surfaces .....................................................94 4.2.2 GFSIEM for a layered reference structure.................105 4.2.3 Calculation of fields using the angular spectrum representation.............................................................107 4.2.4 Example: Gold nanostrip on a dielectric substrate ....116 4.2.5 Example: Silver nanostrip above a silver surface ......123 4.2.6 Example: Single groove in metal ...............................129 4.2.7 Example: Silver nanostrip on a thin-film-siliconon- silver waveguide ...................................................133 4.2.8 Example: Microstructured gradient-index lens for THz photoconductive antennas..................................143 4.2.9 Guidelines for software implementation....................154 4.2.10 Exercises ....................................................................156 4.3 Periodic structures ..................................................................158 4.3.1 Bloch waves ...............................................................159 4.3.2 Greens function for periodic structures......................159 4.3.3 GFSIEM for periodic structures.................................161 4.3.4 Derivatives of periodic Greens function and tabulation ..........................................................................164 4.3.5 Calculating the fields..................................................166 4.3.6 Calculating reflection and transmission .....................167 4.3.7 Multilayer periodic structures ....................................169 4.3.8 Transfer-matrix method for large structures ..............175 4.3.9 Example: Photonic crystal .........................................184 4.3.10 Example: Anti-reflective groove array in a dielectric 189 4.3.11 Example: broadband-absorber ultra-sharp groove array in a metal...........................................................195 4.3.12 Guidelines for software implementation....................202 4.3.13 Exercises ....................................................................203 Chapter 5 Area integral equation method for 2D scattering problems .............205 5.1 Greens function integral equations .........................................206 5.1.1 s polarization..............................................................206 5.1.2 p polarization .............................................................207 5.2 Discretization with square-shaped elements...........................209 5.3 Discretization with triangular elements ..................................211 5.4 Scatterer in a homogeneous medium......................................214 5.4.1 s-polarization..............................................................214 5.4.2 p-polarization.............................................................222 5.5 Scatterer on or near planar surfaces........................................229 5.5.1 s polarization..............................................................229 5.5.2 p polarization .............................................................229 5.6 Periodic surface microstructures.............................................234 5.6.1 s-polarization..............................................................235 5.6.2 p-polarization.............................................................238 5.7 Fast iterative FFT-based approach for large structures ...........241 5.8 Example: Purcell factor of emitter in a photonic crystal ........244 5.9 Example: Excitation of surface plasmon polaritons by second harmonic generation in a single organic nanofiber..........252 5.10 Guidelines for software implementation ................................261 5.11 Exercises .................................................................................262 Chapter 6 Volume integral equation method for 3D scattering problems.........265 6.1 Greens function integral equation...........................................265 6.2 Scatterer in a homogeneous medium......................................266 6.2.1 Discretization with cubic volume elements ...............268 6.2.2 Discrete dipole approximation (DDA).......................273 6.3 Scatterer on or near planar surfaces........................................275 6.3.1 Greens tensor for layered reference structures...........275 6.3.2 Far-field Greens tensor...............................................282 6.3.3 Greens tensor in cartesian vector form ......................287 6.3.4 Optical cross sections.................................................288 6.3.5 Example: Scattering by a nanostrip on a thin metal film .............................................................................289 6.4 Periodic
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 621.36; Micro-optics -- Mathematics; Green's functions; TECHNOLOGY & ENGINEERING / Mechanical; Electronic books
• Languages: English
• ISBNs: 9781351260183; 1351260189
• Related ISBNs: 9780815365969
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed February 4, 2019).; Note: Vendor-supplied metadata.
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