Free Access
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
Page(s) 143 - 155
Published online 28 January 2013
  1. Y. Akahane, T. Asano, B. Song, S. Noda. High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature, 425 (2003), 944–947. [CrossRef] [PubMed]
  2. S. Albeverio, R. Hryniv, Ya. Mykytyuk. Inverse spectral problems for coupled oscillating systems : reconstruction from three spectra. Methods Funct. Anal. Topology, 13 (2007), No. 1, 110–123. [MathSciNet]
  3. S. Burger, J. Pomplun, F. Schmidt, L. Zschiedrich. Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap. Proc. SPIE Vol. 7933 (2011), 79330T (Physics and Simulation of Optoelectronic Devices XIX).
  4. S. Cox, E. Zuazua. The rate at which energy decays in a string damped at one end. Indiana Univ. Math. J., 44 (1995), No. 2, 545–573. [MathSciNet]
  5. P. Heider, D. Berebichez, R.V. Kohn, M.I. Weinstein. Optimization of scattering resonances. Struct. Multidisc. Optim., 36 (2008), 443–456. [CrossRef]
  6. G.M. Gubreev, V.N. Pivovarchik. Spectral analysis of the Regge problem with parameters. Funktsional. Anal. i Prilozhen., 31 (1997), No. 1, 70–74 (Russian); Engl. transl. : Funct. Anal. Appl., 31 (1997), No. 1, 54–57. [CrossRef]
  7. I.S. Kac, M.G. Krein. On the spectral functions of the string. Supplement II in Atkinson, F. Discrete and continuous boundary problems. Mir, Moscow, 1968. Engl. transl. : Amer. Math. Soc. Transl., Ser. 2, 103 (1974), 19–102.
  8. C.-Y. Kao, F. Santosa. Maximization of the quality factor of an optical resonator. Wave Motion, 45 (2008), 412–427. [CrossRef]
  9. I.M. Karabash. Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures. To appear in Asymptotic Analysis (see also the preprint of the paper arXiv :1103.4117v5 [math.SP]).
  10. I.M. Karabash. Optimization of quasi-normal eigenvalues for Krein-Nudelman strings. Integral Equations and Operator Theory, DOI : 10.1007/s00020-012-2014-4
  11. T. Kato. Perturbation theory for linear operators. Springer-Verlag, Berlin-Heidelberg-New York, 1980.
  12. M.V. Keldysh. On the characteristic values and characteristic functions of certain classes of non-self-adjoint equations. Doklady Akad. Nauk SSSR, 77 (1951), 11–14 (Russian). [MathSciNet]
  13. M.G. Krein. On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability. Prikl. Mat. Meh., 15 (1951), 323–348 (Russian); English transl. : Amer. Math. Soc. Transl.(2), 1 (1955), 163–187.
  14. M.G. Krein, A.A. Nudelman. On direct and inverse problems for the boundary dissipation frequencies of a nonuniform string. Dokl. Akad. Nauk SSSR, 247 (1979), No. 5, 1046–1049 (Russian). Engl. transl. : Soviet Math. Dokl., 20 (1979), No. 4, 838–841.
  15. L.D. Landau, E.M. Lifshitz. Electrodynamics of continuous media. Pergamon, 1984.
  16. P.T. Leung, S.Y. Liu, S.S. Tong, K. Young. Time-independent perturbation theory for quasinormal modes in leaky optical cavities. Phys. Rev. A, 49 (1994), 3068–3073. [CrossRef] [PubMed]
  17. J. Moro, J.V. Burke, M.L. Overton. On the Lidskii-Vishik-Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure. SIAM J. Matrix Anal. Appl., 18 (1997), No. 4, 793–817. [CrossRef] [MathSciNet]
  18. M. Notomi, E. Kuramochi, H. Taniyama. Ultrahigh-Q nanocavity with 1d photonic gap. Opt. Express, 16 (2008), 11095. [CrossRef] [PubMed]
  19. V.N. Pivovarchik, Inverse problem for a smooth string with damping at one end. J. Operator Theory, 38 (1997), No. 2, 243–263. [MathSciNet]
  20. V. Pivovarchik, C. van der Mee. The inverse generalized Regge problem. Inverse Problems, 17 (2001), No. 6, 1831–1845. [CrossRef]
  21. M. Reed, B. Simon. Methods of modern mathematical physics. IV. Analysis of operators. Academic Press, New York-London, 1978.
  22. G. Rempe. One atom in an optical cavity : spatial resolution beyond the standard diffraction limit. Appl. Phys. B, 60 (1995), 233–237. [CrossRef]
  23. M.A. Shubov. Spectral operators generated by damped hyperbolic equations. Integral Equations Operator Theory, 28 (1997), No. 3, 358–372. [CrossRef] [MathSciNet]
  24. K. Ujihara. Quantum theory of a one-dimensional optical cavity with output coupling. Field quantization. Phys. Rev. A, 12 (1975), 148–158. [CrossRef]
  25. K.J. Vahala. Optical microcavities. Nature, 424 (2003), 839–846. [CrossRef] [PubMed]
  26. Y. Yamamoto, F. Tassone, H. Cao. Semiconductor cavity quantum electrodynamics. Springer, New York, 2000.

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