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Bao G., Cowsar L., Masters W. — Mathematical Modeling in Optical Science

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Название: Mathematical Modeling in Optical Science

Авторы: Bao G., Cowsar L., Masters W.

Аннотация:

This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.

Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2001

Количество страниц: 333

Добавлена в каталог: 10.04.2010

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Предметный указатель

$H(\rm{curl, \Omega})$       192
$H(\rm{div, \Omega})$       192
$H(\rm{rot; {R}^{2}})$       279
${div}_{\beta}u$       279
${H}_{\rho}(\rm{rot, {R}^{2}})$       289
${L}^{2}$ -based Sobolev space      43 192
${P}_{1}$ -Lagrange finite-element approximation      200
${rot}_{\beta}$       278
${\bigtriangledown}_{\beta\varphi}$       279
(quasi) characterization      289
Aberrations      10
Abscissae of the discontinuities      122
Absence of embedded impurity eigen-values      258
Absolutely continuous      226
Absolutely convergent      116
Absorbers      201
Absorbing boundary condition (ABC)      41 154
Acoustical closed waveguides      306
Acoustically soft      96
Admissible class      59
Admissible curves      59
Almost localize      243
Analytic continuation      72 80 84
Analytically      73
Anderson localization      255 258
Angle of incidence      55
Anisotropic gratings      112
Anisotropic lamellar gratings      131
Antenna arrays      37
Antennas      180
Antirefiective (AR) conditions      24
Artificial index modulation      4
Artificial nonlinearity      309
Aspheric aberration correction      3
Asymptotic behavior      237
Asymptotic behavior of the spectrum      248
Asymptotic matching techniques      63
Axial symmetry      148
Banach theorem      321
Band functions      217 219 222
Band gap      32
Band gap structures      180 201
Beltrami fields      185
BEM      162 167
BEM for perfectly conducting DOEs      169
Bessel functions      98 311
Bethe — Sommerfeld conjecture      230
Bilinear form      280 314
Binary optical elements      4
Binary optical structures      10 61
Binary optics      1
Biperiodic surfaces      92
Birman — Schwinger method      251
Bisinusoidal gratings      92
BKK method      111
Bohren transform      187 188
Born approximation      181
Bound states      245
Boundary element      61
Boundary element method (BEM)      31 143 183
Boundary integral formulation for perfect conductors      169
Boundary integral methods (BIMs)      143 162
Boundary perturbation methods      72
Boundary pseudodifferential operators      190
Boundary variations      73
Bounded cylindrical obstacle      90
Bounded obstacles      82
Branch point singularities      73
Brillouin zone      218 223 256
Cartesian coordinates      79 155
Cauchy — Schwarz inequality      199
Cauchy's principal value of integration      166
Cavities      96
Cavity mirrors      29
Central difference method      149
Central finite-difference approximation      144
Characteristic length      89
Characterizations of uniqueness      56
Chiral gratings      180
Chiral medium      179
Chiral object      179
Chirality admittance      179
Chirality parameter      186
chromatic aberration      2 3
Circular step-index fiber      274
Circularly birefringent      179
Cladding      275
Closed waveguides      274
Coherent multiple scattering      207
Cohomologies      212
Cokernel      221
Compact admissible set      60
Compact imbedding result      182
Compact perturbations      281
Compact resolvent      274 281 315
Compactness      291
Compactness lemma      194
Comparison principle      288 302
Complementary jumps      122
Complete band gap      207
Complex Bloch variety      224
Complex pseudodifferential      244
Concurrent discontinuities      122
Conductivity      144
Conformal transformation      86
Conforming triangulation      316
Conical diffraction      44
Conical mountings      112
Connected structures      242
Constant coefficient partial differential operator      216
Constitutive relations      209
Continuation of multiple eigenvalues      98
Continuous dependence      48
Contraction mapping argument      64
Convergence analysis      49
Convolution operators      216
Corrugated surfaces      72
Coupling FEM/BEM variational formulations      183
Covariant Cauchy — Riemann derivative operator      228
Critical values      288
Crossed gratings      112
Crystalline materials      37
Curl operator      212
Curvilinear tetrahedra      200
Cut-off function      303
Cutoff property      18
Cylindrical coordinates      146
Dammann gratings      3
Data communications      13
Dense subspace      321
Determinant of infinite order      116
Diamond turning      4
Dielectric coefficient      39
Dielectric permittivity e      276
Dielectric-air coupling      245
Differential formalisms      72
Diffraction      37 111
Diffraction efficiencies      7 15 128
Diffraction efficiency of the rath order      7
Diffraction gratings      1 37 63 71 92
Diffraction problem      51
Diffraction theory      10
Diffractive optical element (DOE)      1 12 141
Diffractive optics      1—3 37
Diffractive optics technology      5
Diffractive orders      7 10
Diffractive orders, negative      7
Diffractive orders, positive      7
Diffractive orders, reflective      7
Diffractive orders, transmissive      7

Diffusion equation      31
Direct problem      30
Direct-write electron beam lithography      4 27
Dirichlet Laplacian      248
Dirichlet problem      238
Dirichlet — to — Neumann (D-N) operator      190 238 309
Discrete spectrum      284 321
Discretization of the continuous problem      49
Dispersion curves      275 318
Dispersion relations      217 219 222 240 245 274 278 306
Distinct eigenvalues      98
Distributed Bragg reflector (DBR)      29
Divergence-free condition      316
Divergence-type problem      215
Domain of analyticity      86
Domain of validity      73
Drude — Born — Fedorov constitutive equations      179 184
dry etching      4
Dry-plasma etch procedures      5
Dual lattice      218
E-formulation      278
Edge-emitting lasers      13
Edge-type elements      309
Effective dielectric constant      25
Effective refractive index      26
Effective-medium theory      31
Efficiency      39
Eigenfunctions      111
Eigenvalue branches      217
Eigenvalue problem      96 310
Eikonal equation      6
Elastic waveguides      306
Electric      39
Electromagnetic gratings      306
Electromagnetic waves      111
Elliptic complex      212
Embedded eigenvalue      253 307
Embedding      313
Engquist — Majda wave equation      154
Enhanced convergence      88
Essential spectrum      249 281 282 298 306 307 321
Euler's number      166
Evanescent      249
Evanescent modes      39
Exact penalty method      309
Existence      287
Existence and size of gaps      258
Existence and uniqueness      194 197
Existence of spectral gaps      229 230
Existence of the point spectrum      217
Exponential localization estimates      226
Far-field eigenfunction expansions      80
Faraday's law      150
Fast Fourier transform (FFT)      51 161
FDTD approach      32 97
Fermi surface      224 227 254
Fiber coupler      15
Finite aperture      31
Finite differences      72
Finite element approximations      37
Finite element method      31 48 255
Finite elements      72 275 316
Finite Laurent's rule      122
Finite periodic structures      63
Finite-difference method (FDM)      143
Finite-difference time-domain method (FDTD)      31 143 255
Finite-dimensional subspaces      48
Finite-element method (FEM)      143 183
Finite-element subspaces      200
Finiteness of the number of gaps      258
First Hankel function      77
First spherical Hankel functions      77
First-order diffraction efficiency      120
Fixed point eigenvalue problem      314
Fixed-point equations      309
Fixed-point iteration      64
Flattened bands      258
Floquet condition      218 252
Floquet modes      182
Floquet theory      216
Floquet transform      217 220 252
Floquet — Bloch eigenmodes      234 242
Floquet — Bloch solution      225
Floquet — Bloch theorem      20 40
Floquet — Bloch transform      226
Floquet — Fourier series      114
Focal length      6
Fourier expansion method      111
Fourier factorization      119 122
Fourier factorization theory      127
Fourier modal method (FMM)      111 112
Fourier modes      147
Fourier series      111 114
Fourier series coefficients      81
Fourier series expansion      41 99 147 292
Fourier transform      209 216 298
Fraunhofer approximation      2 7
Fredholm alternative      45
Fredholm theory      45
Frequency domain techniques      143
Fresnel lens      2
Fresnel phase lenses      1
Fresnel zone      2 4 6
Fundamental cell      40
Fundamental domain      218
Fundamental guided mode      306
Galerkin-type methods      257
Gaussian beams      159 171
Gelfand transform      217
Generalized gradient      258
Generalized Helmholtz decomposition      313
generic algorithm      62
Geometric dimensions      19
Geometric perturbations      71
Geometrical optics      6 10 37
Geometrical wavefront      6
Gibbs — Wilbraham phenomenon      126
Global uniqueness result      56
gmres      50
Grating efficiencies      78
Grating enhanced second harmonic generation      63
Grating period      12
Grating profile      58
Gratings      90 182
Gratings with high aspect ratio      30
Grayscale lithography      4
Green's function      98 161
Green's second identity      163
Guided modes      274 277 297
Guided waves      277
Guided-mode grating resonance      23
Guiding condition      274
H-formulation      278 304
Hankel functions      166
Hard acoustic media      63
Hardy's inequality      290
Harmonic conversion efficiency      63
Harmonic plane wave      277
Hausdorff distance      57 234
Head-mounted display (HMD)      11
Head-up displays      1
Helices      179
Helmholtz equation      44 75 80
Helmholtz type      215
High dielectric contrast      232
High modulation rates      14
High-contrast PBG material      248
High-contrast periodic medium      248
High-order boundary perturbation theory      97
High-resolution pattern generation techniques      4

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