Abstract
A method for representation of the algorithms for calculation of the spectra of plane waves with regard to the anisotropic properties of the medium and the presence of periodic spatial perturbations is proposed. The perturbations are assumed to have a limited spectrum and to be specified by a finite set of Fourier coefficients. General algorithms for calculation of the spectra of electromagnetic, elastic, and spin waves in the media with periodic irregularities are obtained. Some spectra of photonic waveguides are studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. V. Gulyaev and S. I. Nikitov, Nelineinyi Mir 1(2), 5 (2003).
L. Brillouin and M. Parodi, Wave Propagation in Periodic Structures (Dover, New York, 1953; Inostrannaya Literatura, Moscow, 1959).
I. M. Gel’fand, Lectures on Linear Algebra (Dobrosvet, Moscow, 2006) [in Russian].
J. P. Elliott and P. G. Dawber, Symmetry in Physics (Macmillan, London, 1979; Mir, Moscow, 1983).
R. A. Silin, Usp. Fiz. Nauk 176, 562 (2006).
J.-P. Dedieu and F. Tisseur, Linear Algebra Appl. 358, 71 (2003).
F. Tisseur and K. Meerbergen, SIAM Rev. 43(2), 235 (2001).
F. Tisseur, Linear Algebra Appl. 309, 339 (2000).
P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984; Mir, Moscow, 1987).
R. A. Silin and V. P. Sazonov, Slow-Wave Structures (Sovetskoe Radio, Moscow, 1966) [in Russian].
V. A. Vashkovskii and E. G. Lokk, Usp. Fiz. Nauk 176, 557 (2006).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Nauka, Moscow, 1982; Pergamon, New York, 1986).
M. S. Kushwaha, P. Halevi, and G. Martinez, Phys. Rev. B 49, 2313 (1994).
M. G. Evtikhov, Radiotekh. Elektron. (Moscow) 52, 923 (2007) [J. Commun. Technol. Electron. 52, 856 (2007)].
M. G. Evtikhov and S. A. Nikitov, Radiotekh. Elektron. (Moscow) 52, 927 (2007) [J. Commun. Technol. Electron. 52, 860 (2007)].
I. V. Lisenkov, S. A. Nikitov, R. S. Popov, and Chul Koo Kim, Radiotekh. Elektron. (Moscow) 52, 1122 (2007) [J. Commun. Technol. Electron. 52, 1037 (2007)].
A. I. Akhiezer, V. G. Bar’yakhtar, and S. V. Peletminskii, Spin Waves (Nauka, Moscow, 1967; North-Holland, Amsterdam, 1968).
D. H. Menzel, Fundamental Formulas of Physics (Prentice Hall, New York, 1955; Inostrannaya Literatura, Moscow, 1957).
N. I. Koshkin and M. G. Shirkevich, Handbook of Elementary Physics (Nauka, Moscow, 1972) [in Russian].
Additional information
Original Russian Text © M.G. Evtikhov, S.A. Nikitov, 2008, published in Radiotekhnika i Elektronika, 2008, Vol. 53, No. 3 pp. 261–275.
Rights and permissions
About this article
Cite this article
Evtikhov, M.G., Nikitov, S.A. Semigroup method for calculation of the spectra of photonic, phononic, and magnonic crystals. J. Commun. Technol. Electron. 53, 241–255 (2008). https://doi.org/10.1134/S1064226908030017
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064226908030017