Abstract
Eigenmodes propagating in cylindrical dielectric gratings (CDGs) are studied. Solution of the boundary value problem on propagation of electromagnetic waves in CDGs is reduced to solution of a system of two integrodifferential equations (IDEs) of the second kind. The singular components of the kernels of the IDEs entering the system are separated and analytically transformed. The collocation and Galerkin methods are applied to solve the first and second IDEs, respectively.
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References
A. Hamakawa, T. Kato, G. Sasaki, and M. Higehara, Proc. 22 European Conf. on Optical Communication, ECOC’96, Oslo, Norway, 1996 (Telenor, Kjeller, 1996), p. MoC.3.6.
P. M. Tomczak, E. M. Pawlik, and K. M. Abramski, Proc. 2 Int. Conf. on Transparent Optical Networks, ICTON, Gdansk, Poland, 2000 (IEEE, Piscataway, 2000), p. 165.
C. R. Giles, J. Stone, L. W. Stulz, et al., Technol. Dig. Optic. Amplifiers and Their Applications 13, 148 (1991).
J.-M. P. Delavaux, C. R. Giles, S. W. Granlund, and C. D. Chen, Optic. Fiber Technol 2, 351 (1996).
C. R. Giles and A. McCormick, Proc. Topical Meeting on Optical Amplifiers and Their Applications, OAA’95, Davos, Switzerland, 1995 (Opt. Soc. Amer., Washington, 1995), p. Th. D1-2.
C. R. Giles and S. Jiang, IEEE Photon. Technol. Lett. 9, 523 (1997).
C. R. Giles, V. Mizrahi, and T. Erdogan, IEEE Photon. Technol. Lett. 7, 126 (1995).
A. D. Kersey, Optic. Fiber Technol. 2, 291 (1996).
G. Meltz, Proc. SPIE. Distributed and Multiplexed Sensors VI SPIE-2838, 2 (1996).
A. D. Kersey, M. A. Davis, T. A. Berkoff, et al., Proc. SPIE. Fiber Optic and Laser Sensors XIV SPIE-2839, 40 (1996).
Ames Research Center. Security System Based on Bragg Gratings in an Optic. Fiber, http://www.nasatech. com/Briefs/Mar00/ARC12092.html.
Ning-Ning Feng, Gui-Rong Zhou, Chenglin Xu, Wei-Ping Huang, J. Lightwave Technol. 20, 1976 (2002).
G. I. Churyumov and I. S. Maksymov, Proc. Int. Conf. on Mathematical Methods in Electromagnetic Theory, MMET, Kiev, 2002 (IEEE, Piscataway, 2002), p. 201.
M. Koshiba and Y. Tsuji, J. Lightwave Technol. 20, 463 (2002).
A. K. Ghatak, I. C. Goyal, and R. K. Varshney, J. Lightwave Technol. 16, 697 (1998).
A. M. Lerer and A. A. Yachmenov, Radiotekh. Elektron. (Moscow) 49, 445 (2004) [J. Commun. Technol. Electron. 49, 411 (2004)].
L. A. Vainshtein, The Diffraction Theory and the Factorization Method (Sovetskoe Radio, Moscow, 1966) [in Russian].
A. M. Lerer, Radiotekh. Elektron. (Moscow) 36, 1923 (1991).
E. I. Nefedov and A. N. Sivov, Electromagnetics of Periodic Structures (Nauka, Moscow, 1977) [in Russian].
E. P. Kurushin and E. I. Nefedov, Electromagnetics of Anisotropic Waveguiding Structures (Nauka, Moscow, 1983) [in Russian].
T. Zinenko, A. Nosich, and Y. Okuno, IEEE Trans. Antennas Propag. 46, 1498 (1998).
E. N. Vasil’ev, A. V. Polynkin, and V. V. Solodukhov, Izv. Vyssh. Uchebn. Zaved., Radioelektronika 26 (2), 72 (1983).
S. Voriskina and A. Nosish, Radiofiz. Radioastron. 2, 333 (1997).
G. A. Kalinchenko, A. G. Kyurkchan, A. M. Lerer, et al., Radiotekh. Elektron. (Moscow) 46, 1087 (2001) [J. Commun. Technol. Electron. 46, 1005 (2001)].
A. M. Lerer, Izv. Vyssh. Uchebn. Zaved., Radioelektronika 33 (5), 56 (1990).
G. A. Kalinchenko and A. M. Lerer, Radiotekh. Elektron. (Moscow) 48, 1330 (2003) [J. Commun. Technol. Electron. 48, 1221 (2003)].
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Original Russian Text © A.M. Lerer, V.V. Makhno, A.A. Yachmenov, 2006, published in Radiotekhnika i Elektronika, 2006, Vol. 51, No. 1, pp. 46–53.
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Lerer, A.M., Makhno, V.V. & Yachmenov, A.A. Propagation of eigenmodes in cylindrical dielectric gratings simulated using the impedance boundary conditions. J. Commun. Technol. Electron. 51, 40–47 (2006). https://doi.org/10.1134/S1064226906010050
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DOI: https://doi.org/10.1134/S1064226906010050