Free Access
Issue
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
Page(s) 143 - 155
DOI https://doi.org/10.1051/mmnp/20138110
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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  5. P. Heider, D. Berebichez, R.V. Kohn, M.I. Weinstein. Optimization of scattering resonances. Struct. Multidisc. Optim., 36 (2008), 443–456. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  8. C.-Y. Kao, F. Santosa. Maximization of the quality factor of an optical resonator. Wave Motion, 45 (2008), 412–427. [CrossRef] [Google Scholar]
  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]). [Google Scholar]
  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 [Google Scholar]
  11. T. Kato. Perturbation theory for linear operators. Springer-Verlag, Berlin-Heidelberg-New York, 1980. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  15. L.D. Landau, E.M. Lifshitz. Electrodynamics of continuous media. Pergamon, 1984. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  18. M. Notomi, E. Kuramochi, H. Taniyama. Ultrahigh-Q nanocavity with 1d photonic gap. Opt. Express, 16 (2008), 11095. [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  20. V. Pivovarchik, C. van der Mee. The inverse generalized Regge problem. Inverse Problems, 17 (2001), No. 6, 1831–1845. [CrossRef] [Google Scholar]
  21. M. Reed, B. Simon. Methods of modern mathematical physics. IV. Analysis of operators. Academic Press, New York-London, 1978. [Google Scholar]
  22. G. Rempe. One atom in an optical cavity : spatial resolution beyond the standard diffraction limit. Appl. Phys. B, 60 (1995), 233–237. [CrossRef] [Google Scholar]
  23. M.A. Shubov. Spectral operators generated by damped hyperbolic equations. Integral Equations Operator Theory, 28 (1997), No. 3, 358–372. [CrossRef] [MathSciNet] [Google Scholar]
  24. K. Ujihara. Quantum theory of a one-dimensional optical cavity with output coupling. Field quantization. Phys. Rev. A, 12 (1975), 148–158. [CrossRef] [Google Scholar]
  25. K.J. Vahala. Optical microcavities. Nature, 424 (2003), 839–846. [Google Scholar]
  26. Y. Yamamoto, F. Tassone, H. Cao. Semiconductor cavity quantum electrodynamics. Springer, New York, 2000. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.