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