Mathematical Surveys and Monographs
Volume: 235;
2018;
509 pp;
Hardcover
MSC: Primary 47; 31; 34; 35; 45; 30;
Print ISBN: 978-1-4704-4800-4
Product Code: SURV/235
List Price: $135.00
AMS Member Price: $108.00
MAA Member Price: $121.50
Electronic ISBN: 978-1-4704-4909-4
Product Code: SURV/235.E
List Price: $135.00
AMS Member Price: $108.00
MAA Member Price: $121.50
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Supplemental Materials
Mathematical and Computational Methods in Photonics and Phononics
Share this pageHabib Ammari; Brian Fitzpatrick; Hyeonbae Kang; Matias Ruiz; Sanghyeon Yu; Hai Zhang
The fields of photonics and phononics
encompass the fundamental science of light and sound propagation and
interactions in complex structures, as well as its technological
applications. This book reviews new and fundamental mathematical
tools, computational approaches, and inversion and optimal design
methods to address challenging problems in photonics and phononics.
An emphasis is placed on analyzing sub-wavelength resonators,
super-focusing and super-resolution of electromagnetic and acoustic
waves, photonic and phononic crystals, electromagnetic cloaking, and
electromagnetic and elastic metamaterials and metasurfaces. Throughout
this book, the authors demonstrate the power of layer potential
techniques for solving challenging problems in photonics and phononics
when they are combined with asymptotic analysis. This book might be of
interest to researchers and graduate students working in the fields of
applied and computational mathematics, partial differential equations,
electromagnetic theory, elasticity, integral equations, and inverse
and optimal design problems in photonics and phononics.
Readership
Graduate students and researchers interested in recent development in mathematical and computational advances in photonics and phononics (light and sound propagation on complex structures).
Table of Contents
Table of Contents
Mathematical and Computational Methods in Photonics and Phononics
- Cover Cover11
- Title page iii4
- Introduction 110
- Part 1 . Mathematical and Computational Tools 514
- Chapter 1. Generalized Argument Principle and Rouché’s Theorem 716
- Chapter 2. Layer Potentials 1928
- 2.1. Introduction 1928
- 2.2. Sobolev Spaces 1928
- 2.3. Layer Potentials for the Laplace Equation 2130
- 2.4. Neumann–Poincaré Operator 2332
- 2.5. Conductivity Problem in the Free Space 3847
- 2.6. Periodic and Quasi-Periodic Green’s Functions 5463
- 2.7. Shape Derivatives of Layer Potentials 6473
- 2.8. Layer Potentials for the Helmholtz Equation 6877
- 2.9. Laplace Eigenvalues 7685
- 2.10. Helmholtz-Kirchhoff Identity, Scattering Amplitude and Optical Theorem 8695
- 2.11. Scalar Wave Scattering by Small Particles 98107
- 2.12. Quasi-Periodic Layer Potentials for the Helmholtz Equation 105114
- 2.13. Computations of Periodic Green’s Functions 108117
- 2.14. Integral Representation of Solutions to the Full Maxwell Equations 120129
- 2.15. Integral Representation of Solutions to the Lamé System 141150
- 2.16. Quasi-Periodic Layer Potentials for the Lamé System 166175
- 2.17. Concluding Remarks 168177
- Chapter 3. Perturbations of Cavities and Resonators 169178
- Part 2 . Diffraction Gratings and Band-Gap Materials 193202
- Chapter 4. Diffraction Gratings 195204
- Chapter 5. Photonic Band Gaps 227236
- 5.1. Introduction 227236
- 5.2. Floquet Transform 228237
- 5.3. Structure of Spectra of Periodic Elliptic Operators 228237
- 5.4. Boundary Integral Formulation 229238
- 5.5. Sensitivity Analysis with Respect to the Index Ratio 239248
- 5.6. Photonic Band Gap Opening 248257
- 5.7. Sensitivity Analysis with Respect to Small Perturbations in the Geometry of the Holes 249258
- 5.8. Proof of the Representation Formula 250259
- 5.9. Characterization of the Eigenvalues of ̃Δ 252261
- 5.10. Maximizing Band Gaps in Photonic Crystals 252261
- 5.11. Photonic Cavities 254263
- 5.12. Concluding Remarks 255264
- Chapter 6. Phononic Band Gaps 257266
- Part 3 . Subwavelength Resonant Structures and Super-resolution 281290
- Chapter 7. Plasmonic Resonances for Nanoparticles 283292
- 7.1. Introduction 283292
- 7.2. Quasi-Static Plasmonic Resonances 284293
- 7.3. Effective Medium Theory for Suspensions of Plasmonic Nanoparticles 286295
- 7.4. Shift in Plasmonic Resonances Due to the Particle Size 290299
- 7.5. Plasmonic Resonance for a System of Spheres 299308
- 7.6. Quasi-Static Plasmonic Resonances for Domains with Corners 306315
- 7.7. Concluding Remarks 313322
- Chapter 8. Imaging of Small Particles 315324
- Chapter 9. Super-Resolution Imaging 325334
- Part 4 . Metamaterials 353362
- Part 5 . Sub-wavelength Phononics 413422
- Chapter 13. Helmholtz Resonator 415424
- Chapter 14. Minnaert Resonances for Bubbles 429438
- 14.1. Introduction 429438
- 14.2. Derivation of Minnaert Resonance Formula 430439
- 14.3. Effective Medium Theory for a System of Bubbles and Super-Resolution 438447
- 14.4. Sub-wavelength Phononic Bandgap Opening 453462
- 14.5. Double-Negative Refractive Index Phenomenon 461470
- 14.6. Numerical Illustrations 464473
- 14.7. Concluding Remarks 471480
- Appendix A. Spectrum of Self-Adjoint Operators 473482
- Appendix B. Optimal Control and Level Set Representation 477486
- Bibliography 481490
- Index 507516
- Back Cover Back Cover1522