**(25)** * << * >> * Russian * English * Content * All Issues

**Pages: **24-28.

**Abstract:**

The paper considers an iterative algorithm for solving the Fredholm integral equation of the second kind based on the application of the fast Fourier transform algorithm for the convolution integral calculation. The algorithm is applied to the analysis of diffraction of an electromagnetic wave with TE-polarization (for example, a non-paraxial Gaussian beam) by cylindrical dielectric micro-objects with the transverse size comparable to the wavelength. The results of numerical simulation and the results of its comparison with an analytical calculation are presented.

**Keywords**:

diffraction electromagnetic wave, dielectric object, Fredholm integral equation, Fourier transform, integral calculation, TE-polarization, Gaussian beam.

**Citation**:

Kotlyar VV, Nalimov AG, Skidanov RV. Method for rapidly calculating the diffraction of electromagnetic waves by cylindrical dielectric objects. Computer Optics 2003; 25: 24-28.

References:

- Taflove A. Computation electromagnetics: The finite-difference time-domain method. Boston: Artech House; 1995.
- Prather DW, Shi S. Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements. J Opt Soc Am A 1999; 16(5): 1131-1142.
- Golovashkin DL, Soifer VA. Analysis of propagation of electromagnetic radiation through a diffraction lens [In Russian]. Avtometriya 1999; 6: 119-121.
- Gruzdev V, Gruzdeva A. Finite-difference timedomain modeling of laser beam propagation and scattering in dielectric materials. Proc SPIE 2001; 4436: 27-38.
- Davies JB. Finite elements analysis of waveguides and cavities – a review. IEEE Trans Magn 1993; 29: 1508-1583.
- Mirotznik M, Prather D, Mait J. A hybrid finite element-boundary element method for the analysis of diffractive elements. J Mod Opt 1996; 43(7): 1309-1321.
- Kotlyar VV, Nesterenko DV. A finite elements method on the problem of light diffraction by micro-optics. Optical Memory and Neural Networks 2000; 9(3): 209-219.
- Dong B, Lin J, Gu B, Yang G. Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution. J Opt Soc Am A 2001; 8(7): 1465-1470.
- Ilyinsky AS, Kravtsov VV, Sveshnikov AG. Mathematical models of electrodynamics [In Russian]. Moscow: Vyshaya Shkola" Publisher; 1991.
- Kotlyar VV, Lichmanov MA. Analysis of light diffraction by micro-optics using finite elements method. Optical Memory and Neural Networks 2001; 10(4): 257-265.
- Neganov VA, Raevskii SB, Yarovoi GP. Linear macroscopic electrodynamics [In Russian]. Moscow: "Radio i Svyaz" Publisher; 2000; 1.
- Vasilenko GI, Taratorin AM. Restoration of images [In Russian]. Moscow: "Radio i Svyaz" Publisher; 1986.
- Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series. Volume 2: Special functions. Amsterdam: Gordon and Breach Science Publishers; 1986.
- Vaganov RB, Katsenelenbaum BZ. Fundamentals of the theory of diffraction [In Russian]. Moscow: "Nauka" Publisher; 1982: 272.
- Petersson LE, Smith GS. Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane. J Opt Soc Am A 2002; 19(11): 2265-2280.

© 2009, IPSI RAS151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20