202 INDEX
leading-order term, 41, 44, 47, 49, 50, 139,
140
level set method, 179, 180
Levenberg-Marquardt method, 65
local optimum, 183
low-frequency, 125
maximum principle, 14
min-max principle, 146, 171, 173
minimization problem, 63
modal measurements, 61, 63
Muller’s method, 131, 132, 134, 137, 158
multiple eigenvalue, 60
multiplicity, 9
Neumann function, 26, 27, 33, 92, 100
Newton’s method, 131
nonlinear eigenvalue technique, 134
nonlinearity, 77
normal point, 10
null multiplicity, 9
operator-valued function, 9, 10, 12
optimal design, 186
optimal geometry, 180
phononic band gap, 153
phononic crystal, 153, 179
photonic band gap, 133, 134
photonic crystal, 133, 134, 179, 186
photonic crystal fiber, 150
photonic crystal slab, 151
Plancherel theorem, 121
Poincar´ e’s min-max principle, 172, 173, 176
Poisson’s summation formula, 123, 126
polarization tensor, 50, 63, 109, 184
pole-pencil decomposition, 91, 92, 97, 101
projection, 88
quasi-momentum, 121, 126, 134, 154
quasi-periodic double-layer potential, 124,
127
quasi-periodic fundamental solution, 123,
125, 126
quasi-periodic layer potentials, 123, 126
quasi-periodic single-layer potential, 124,
127
radiation condition, 23, 30
rank, 9
reciprocal lattice, 123
reconstruction formula, 61, 68, 79, 116
regular point, 10
Rellich’s lemma, 24
representation formula, 32, 47, 135
residue theorem, 7, 141
resonator, 91
root function, 9
Rouch´ e’s theorem, 7
scaling property, 135
scattering pole, 100
Schr¨ odinger operator, 123
sensitivity analysis, 138, 146
shape deformation, 54, 115, 116
shape derivative, 58, 115, 179, 182, 183, 187
shape optimization, 179
single-layer potential, 20, 23, 29
slit, 91
slot, 91, 99
Sobolev spaces, 19
soft inclusion, 103
Sommerfeld-Kupradze radiation condition,
30
spatial representation, 123
spectral decomposition, 26, 33, 92
spectral representation, 123
splitting, 60
Steinberg’s theorem, 15, 91, 97, 136
structural design, 179
symmetry property, 110
tensor product, 115
theorem of Coifman, McIntosh, and Meyer,
57
topological derivative, 179, 182, 183
trace operator, 10, 13, 40
transmission problem, 31, 32, 108
transverse electric polarization, 186
transverse magnetic polarization, 186
unique continuation, 25
uniqueness, 24
vibration testing, 77
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