volume | PIER Journals

Abstract

Arbitrarily polarized plane-wave diffraction equations for semiinfinite periodic rectangular grooves (RG) in a perfectly conducting plane are approximately proposed. To obtain diffraction equations for semi-infinite periodic RG, we utilize an overlapping T-block method as proposed for the analyses of finite and infinite numbers of RG, and the subtraction technique with infinite periodic solutions. The proposed semi-infinite solutions are then applied to finite periodic RG with very large number of diffracting elements. For verification of our approach, we performed numerical computations for finite periodic RG and compared our solutions based on semi-infinite equations with previously published analytic solutions, thus obtaining favorable agreement and proving computational efficiency.

1. Bendickson, J. M., E. N. Glytsis, T. K. Gaylord, and D. L. Brundrett, "Guided-mode resonant subwavelength gratings: Effects of finite beams and finite gratings," J. Opt. Soc. Am. A, Vol. 18, No. 6, 1912-1928, 2001.
doi:10.1364/JOSAA.18.001912

2. Wu, S.-D. and E. N. Glytsis, "Finite-number-of-periods holo-graphic gratings with funite-width incident beams: Analysis using the ¯nite-di®erence frequency-domain method," J. Opt. Soc. Am. A, Vol. 19, No. 10, 2018-2029, 2002.
doi:10.1364/JOSAA.19.002018

3. Lin, A. and J. Phillips, "Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms," Sol. Energ. Mat. Sol. C, Vol. 92, No. 12, 1689-1696, 2008.
doi:10.1016/j.solmat.2008.07.021

4. Basha, M. A., S. K. Chaudhuri, S. Safavi-Naeini, and H. J. Eom, "Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane," J. Opt. Soc. Am. A, Vol. 24, No. 6, 1647-1655, 2007.
doi:10.1364/JOSAA.24.001647

5. Scharstein, R. W., J. M. Keen, and D. L. Faircloth, "Two-term Ritz-Galerkin solution for the low frequency scattering by a rectangular trough in a soft ground plane," IEEE Trans. Antennas Propagat., Vol. 56, No. 7, 1993-2001, 2008.
doi:10.1109/TAP.2008.924741

6. Cho, Y. H., "TE scattering from large number of grooves using Green's functions and Floquet modes," 2007 Korea-Japan Micro. Wave Conference (KJMW), 41-44, 2007.
doi:10.1109/KJMW.2007.4402235

7. Cho, Y. H., "Transverse magnetic plane-wave scattering equations for in¯nite and semi-in¯nite rectangular grooves in a conducting plane," IET Proc. --- Microw. Antennas Propag., Vol. 2, No. 7, 704-710, 2008.
doi:10.1049/iet-map:20070251

8. Linton, C. M. and P. A. Martin, "Semi-infinite arrays of isotropic point scatters. A unified approach," SIAM J. Appl. Math., Vol. 64, No. 3, 1035-1056, 2004.
doi:10.1137/S0036139903427891

9. Linton, C. M., R. Porter, and I. Thompson, "Scattering by a semi-infinite periodic array and the excitation of surface waves," SIAM J. Appl. Math., Vol. 67, No. 5, 1233-1258, 2007.
doi:10.1137/060672662

10. Citrin, D. S., Y. Wang, and Z. Zhou, "Far-field optical coupling to semi-infinite metal-nanoparticle chains," J. Opt. Soc. Am. B, Vol. 25, No. 6, 937-944, 2008.
doi:10.1364/JOSAB.25.000937

11. Wasylkiwskyj, W., "Mutual coupling effects in semi-infinite arrays," IEEE Trans. Antennas Propagat., Vol. 21, No. 3, 277-285, 1973.
doi:10.1109/TAP.1973.1140507

12. Fallahi, A. and C. Hafner, "Analysis of semi-infinite periodic structures using a domain reduction technique," J. Opt. Soc. Am. A, Vol. 27, No. 1, 40-49, 2010.
doi:10.1364/JOSAA.27.000040

13. Hills, N. L. and S. N. Karp, "Semi-infinite diffraction gratings --- I," Comm. Pure Appl. Math., Vol. 18, No. 1-2, 203-233, 1965.
doi:10.1002/cpa.3160180119

14. Zheng, J.-P. and K. Kobayashi, "Diffraction by a semi-in¯nite parallel-plate waveguide with sinusoidal wall corrugation: Combined perturbation and Wiener-Hopf analysis," Progress In Electromagnetics Research B, Vol. 13, 75-110, 2009.
doi:10.2528/PIERB08120704

15. Skinner, J. P. and P. J. Collins, "A one-sided version of the Poisson sum formula for semi-infinite array Green's functions," IEEE Trans. Antennas Propagat., Vol. 45, No. 4, 601-607, Apr. 1997.
doi:10.1109/8.564085

16. Capolino, F., M. Albani, S. Maci, and L. B. Felsen, "Frequency-domain Green's function for a planar periodic semi-infinite phased array --- Part I: Truncated Floquet wave formulation," IEEE Trans. Antennas Propagat., Vol. 48, No. 1, 67-74, Jan. 2000.
doi:10.1109/8.827387

17. Polemi, A., A. Toccafondi, and S. Maci, "High-frequency Green's function for a semi-infinite array of electric dipoles on a grounded slab --- Part I: Formulation," IEEE Trans. Antennas Propagat., Vol. 49, No. 12, 1667-1677.
doi:10.1109/8.982445

Prof. Yong Heui Cho