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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

Higher order aberration correction      3
Hilbert space      278 290
Hill operator      230 253
Hodge decomposition      182 194 197
Holographic lithography      30
Holomorphic framework      73
Honeycomb structure      245
Hybrid finite element-boundary element methods      61
Hypoelliptic operator      226
Image quality      10
Imbeddings      193
Impurities in PBG materials      248
Impurity eigenvalue      250
Impurity spectra      258
Incidence vector      40
Incident beam of finite width      63
Incident wave      55
Inf-sup condition      52
Infinite eigenvalue problem      117
Infinitely degenerate eigenvalues      245
Integer programming      62
Integral equation approach      45
Integral equations      72 90
Integrated optical circuits      273
Integrated optical guide      276
Interface least-squares finite element      52
Interface problem      201
Interior problem      312
Inverse diffraction problem      55
Inverse problem      30 37 54 274
Inverse rule      123
Irreducible      225
Irreducible Brillouin zone      240
Isobathic procedure      10
Isobathic process      5
Isotropic      179
Isotropic gratings      112
Joint analyticity      73
Jointly analytic      79
Jump conditions      45
Kato's perturbation theory      286
Kernel      221
Kinoforms      1
Kirchhoff approximation      62
L-periodic Sobolev space      43
Lagrange elements      316
Laplace operator      211
Laplace — Beltrami operator      230
Laplace's equation      98
Large, sparse matrix equation      50
Laser writing      4
Laurent's multiplication rule      121
Laurent's rule      116
Lax — Milgram lemma      45 47 195 197 293
Leaky modes      274
Least-squares finite element methods      51
Least-squares functional      53
Least-squares minimization problem      53
Lebesgue's theorem      303
Left-circularly and right-circularly polarized plane waves      185
Legendre functions      77
LIGA techniques      17
Linear defect      254
Linear self-adjoint operators      275
Linear systems theory      10
Liouville — Green transform      216
Liouville-type theorems      232
Lipman — Schwinger equation      309
Liquid crystals      180
Local propagation velocity      276
Localized defect      249 250
Localized perturbation      252
Localized waves      258
Locally Lipschitz      286
Low dielectric filling fractions      233
Low-frequency asymptotics      180
Low-order diffractive gratings      2 30
Low-order methods      72
Low-pass spectral filter      18
Lower threshold      288
Luminance      11
Magnetic field vectors      39
Magnetic permeability      39 276
Magnitude of the ratio P/X      89
Manufacturing constraints      62
Mask alignment error      8
Material tensors      209
Matrix eigenvalue problem      111
Maxwell's equations      2 6 113 142 208 274 276
Maxwell's time-dependent curl equations      144
Mean value      294
Mellin transform      244
MEMS technology      16
Metallic gratings      112
Method of integral equations      183
Method of moments      90
Method of moments (MoM)      143
Method of separation of variables      42
Micro-electrical-mechanical structures (MEMS)      51
Microelectromechanical systems (MEMS)      13
Microstrip grating      201
Microwave devices      180
Microwave structures      37
Min-max principle      284 285 298 299 302 322
Minimum feature size      2 5
Minimum Fresnel zone      7
Modal method      111
Modes      273
Modulation      11
Modulation transfer function (MTF)      10
Moharam — Gaylord method      111
Multigrid methods      52
Multimode      14
Narrow strip gratings      201
Nedelec's finite elements      183 200
Neumann series      73
Non-Hermitian matrix      50
Nonconforming method      317
Nonconformity      319
Nonellipticity      212
Nonexistence      284 302
Nonexistence of bound states      216
Nonlinear devices      63
Nonlinear effects      258
Nonlinear media      31
Nonlinear optical crystal      63
Nonlinear susceptibility      63
Nonlinear thin optical coatings      64
Nonperiodic bounded inhomogeneous medium      47
Nonresonant      64
Nonsquare geometries      236
Normal form      116
Normal trace      310
Numerical dispersion      153
Open waveguide      273 274
Optical data storage      13
optical fiber      273 276
Optical path difference      6
Optical path length      6
Optical power      6
Optical waveguides      273
Optimal design      30
Optimal design of nonlinear films      64
Optimal design problem      54 57 59
Optimal error estimate      201
Optoelectronics      2
Orthogonal decomposition      279 306
Orthogonal projector      211
ORTHOMIN      50
oscillations      89

Oscillatory minimizing sequences      60
Pade approximant      84 85
Pade approximation      96
Pade problem      84
Paley — Wiener theorem      220 252
Parameterization      79
Parameterized eigenvalue problem      274
Pattern transfer      5
PBG waveguides      258
Perfect conductor      75
Perfectly conducting bounded obstacle      90
Perfectly conducting obstacle      91
Perfectly matched layer      154
Perimeter-to-wavelength ratio      91
Periodic (elliptic) differential operators      216
Periodic gratings      73 111
Periodic Pauli operators      232
Periodic potential      253
Periodic radiation condition      187
periodic structure      55 182
periodicity      216
Permeability      144
Permittivity      144
Permittivity function e(x)      115
Perturbation theory      71
Phase contour      4
Phase function      6
Phase incident wavefront      2
Phase mask lithography      30
Phase modulation      2
Phase retardation      4
Phase-coherent surface-relief gratings      1
photolithography      5
Photonic band gap (PBG)      207
Photonic crystal      32 207
Piecewise regularity      276
Planar waveguide      22 276 306
Plancherel theorem      220
Plane wave (Fourier expansion) methods      255
Plane wave spectrum (PWS) technique      161
Plane wave spectrum method      160
Plane waves      159
PML ABCs      156
PML matching condition      157
PML method      157
PMMA      17
Poincare's inequality      195 293 296
Point source      10
Point spectrum      216
Point spread function      10
Polar coordinates      77 79 292
Polarization effects      12
Polarization sensitivity      27
Poles of a meromorphic function      274
Power monitor      15
Precision micromachining      4
Preconditioner      50
Principle of conservation of energy      77
Printing      13
Prohibited frequencies      207
Propagating modes      58 255
Propagating reflected mode      58
Propagating transmitted modes      58
Pseudodifferential operator      238
Pump field intensity      63
Quadrature error      319
quantum mechanics      31
Quasi momentum      217 223
Quasi-periodic      7
Quasi-periodic solutions      40
Quasi-uniform mesh      48
Quasiperiodic solutions      55
Radar cross section      90
Radiating ones      274
Radiation condition      40 42
Random impurities      255
Rayleigh expansion      39 72 113
Rayleigh hypothesis      73 76
Rayleigh points      23
Rayleigh — Sommerfeld diffraction      169
Rayleigh's approach      76
RayTracing      6 97
Reactive ion etching      27
Real Bloch variety      224
Reciprocal      179
Reciprocal lattice      218
Reciprocity      313
Rectangular coordinate system      145
Rectangular crossed gratings      128
Rectangular gratings      128
Recursive formulas      79 81
Reducible      225
Reduction method      115
Reference medium      298
Refractive element      2
Refractive index      6
Relaxation method      59
Relaxed formulation      59
Rellich's theorem      284
Replication methods      5
Resolvent set      321
Resonance      21 22 42 63
Resonance phenomenon      242
Resonance regime      72
Resonances      189
Resonant cavity      30
Resonant frequencies      201
Resonant waveguide gratings      4
Resonant wavelength      24
Resummation techniques      72
Rib waveguide      273
Ridge waveguide      297
Right-handedness      179
Rigorous coupled-wave approach      112
Scalar diffraction theory      141
Scaling property      214
Scanning electron microscope (SEM)      17
Scattered field      55
Schauder's lemma      64
Schroedinger operator      214
Schroedinger-type      211
Second harmonic field      64
Second harmonic generation      31
Second-order Mur ABC      156
Second-order nonlinear susceptibility tensor      63
Self-adjoint      315 321
Self-adjoint operator      210 253 281 298
Self-adjointness      280
Semi-infinite formulation of the BEM      171
Semi-infinite symmetric BEM (SSBEM)      170
sensors      13
Separation of variables      77
Shape interpolation basis functions      167
Silver — Mueller radiation condition      181 189
Simple reference medium      275
Simulated annealing      61
Simulated quenching algorithms      61
Simultaneous coordinate overrelaxation      256
Single point diamond      8
Singular continuous      226
Singular frequencies      47
Singular sequence      282 321
Singularities      73
Singularities of analytic continuation      244
Sinusoidal dielectric grating      90
Sinusoidal grating      83
Sinusoidal profile      83
Skew-symmetrical fields      306
Slab waveguide      274
Slanted volume gratings      112

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