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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