Formulation of the radiation condition for modeling the cylindrical doe operation using a~finite difference solution of Maxwell's equations
Matematičeskoe modelirovanie, Tome 19 (2007) no. 3, pp. 3-14.

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We formulate the radiation condition with due regard for the reflected wave for modeling the radiation propagation through cylindrical diffractive optical elements using a finite difference solution of Maxwell's equations. Special emphasis is placed on the formulation of the boundary conditions and the arrangement of the absorbing layers in the computational domain. A comparison of the proposed radiation condition with the conventional condition is made. Advantages of the approach developed are discussed. The simulation results of operation of diffractive microlenses are reported.
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D. L. Golovashkin. Formulation of the radiation condition for modeling the cylindrical doe operation using a~finite difference solution of Maxwell's equations. Matematičeskoe modelirovanie, Tome 19 (2007) no. 3, pp. 3-14. http://geodesic.mathdoc.fr/item/MM_2007_19_3_a0/

[1] V. V. Panasyuk, M. P. Savruk, Z. T. Nazarchuk, Metod singulyarnykh integralnykh uravnenii v dvumernykh zadachakh difraktsii, Nauk. Dumka, Kiev, 1984 | MR

[2] E. N. Vasilev, “Algoritmizatsiya zadach difraktsii na osnove integralnykh uravnenii”, Sb. nauch.-metod. st. po prikl. elektrodinamike, no. 1, 1977, 94–128

[3] G. Kron, “Equivalent circuit of the field equations of Maxwell, I”, Proc. IRE, 32 (1944), 289–299 | DOI | MR | Zbl

[4] O. A. Taflove, S. Hagness, Computation Electrodynamics: The Finite-Difference Time-Domain Method, 2nd. ed., Arthech House Publishers, Boston, 2000 | MR | Zbl

[5] M. Mirotznik, D. Prather, J. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements”, J. Mod. Opt., 43:7 (1996), 1309–1321

[6] A. S. Ilinskii, V. V. Kravtsov, A. G. Sveshnikov, Matematicheskie modeli elektrodinamiki, Vysshaya shkola, M., 1991

[7] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media”, IEEE Trans. Antennas Propag., 14 (1966), 302–307 | DOI | Zbl

[8] D. L. Golovashkin, A. A. Degtyarev, “Algoritm vtorogo poryadka tochnosti po vremeni dlya resheniya uravnenii Maksvella”, Kompyuternaya optika, 1998, no. 18, 39–41

[9] G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations”, IEEE Trans. Electromagnetic Compatibility, 23 (1981), 377–382 | DOI

[10] J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves”, Journal of Computational Physics, 1994, no. 114, 185–200 | DOI | MR | Zbl

[11] A. Taflove, M. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations”, IEEE Transactions of Microwave Theory and Techniques, 23:8 (1975), 623–630 | DOI

[12] K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects”, IEEE Trans. Electromagnetic Compatibility, 24:4 (1982), 397–405 | DOI

[13] D. L. Golovashkin, “Difraktsii N-volny na dvumernoi idealno provodyaschei reshetke”, Matematicheskoe modelirovanie, 17:4 (2005), 53–61 | Zbl

[14] V. V. Nikolskii, T. I. Nikolskaya, Elektrodinamika i rasprostranenie radiovoln, Ucheb. posobie dlya vuzov, 3-e izd., pererab. i dop., Nauka, M., 1989

[15] D. L. Golovashkin, “Difraktsii H-volny na dvumernoi dielektricheskoi reshetke”, Matematicheskoe modelirovanie, 16:9 (2004), 83–91 | Zbl

[16] V. A. Soifer, Metody kompyuternoi optiki, Izdanie vtoroe, ispravlennoe, Fizmatlit, M., 2003 | Zbl

[17] Dzh. Golub, Ch. Van Loun, Matrichnye vychisleniya, Mir, M., 1999

[18] Dzheims M. Ortega, Vvedenie v parallelnye i vektornye metody resheniya lineinykh sistem, Mir, M., 1991 | MR

[19] R. B. Vaganov, B. Z. Katsenelenbaum, Osnovy teorii difraktsii, Nauka, M., 1982 | MR | Zbl

[20] E. I. Butikov, Optika, Uchebnoe posobie pererab. i dop., Nevskii Dialekt, BKhV-Peterburg, SPb., 2003