2021-11-03
Theory of Gaussian Beam Diffraction by a Transmission Dielectric Grating
By
Progress In Electromagnetics Research B, Vol. 93, 195-213, 2021
Abstract
An advanced 2D mode theory of plane electromagnetic wave diffraction by a transmission dielectric grating (rectangular relief or planar sinusoidal one) is considered. On the bases of this theory, a new model of diffraction of a spatially inhomogeneous light field (a Gaussian beam) by a transmission grating with arbitrary thickness is developed. It provides the opportunity to compute the transverse spatial structure of radiation diffraction orders and to estimate character of their distortions in comparison with the initial Gaussian beam structure. It is shown that such distortions appear under abrupt variations of intensity of all orders and can be caused by transformation of a certain diffraction order from the radiation regime of propagation into the waveguide regime and inversely (Wood's anomalies), and also it can be induced by a set of additional reflections on the boundaries of a thick substrate.
Citation
Vladimir Serdyuk, "Theory of Gaussian Beam Diffraction by a Transmission Dielectric Grating," Progress In Electromagnetics Research B, Vol. 93, 195-213, 2021.
doi:10.2528/PIERB21090105
References

1. Elachi, C., "Waves in active and passive periodic structures: A review," Proc. IEEE, Vol. 64, No. 12, 1666-1698, 1976.
doi:10.1109/PROC.1976.10409        Google Scholar

2. Gaylord, T. K. and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE, Vol. 73, No. 5, 894-937, 1985.
doi:10.1109/PROC.1985.13220        Google Scholar

3. Petit, R., Electromagnetic Theory of Gratings, Springer, 1980.
doi:10.1007/978-3-642-81500-3

4. Belyakov, V. A., Diffraction Optics of Complex-structured Periodic Media, Springer, 1992.
doi:10.1007/978-1-4612-4396-0

5. Rashid, I., H. Butt, A. K. Yetisen, B. Dlubak, J. E. Davies, P. Seneor, A. Vechhiola, F. Bouamrane, and S. Xavier, "Wavelength-selective diffraction from silica thin-film gratings," ACS Photonics, Vol. 4, No. 10, 2402-2409, 2017.
doi:10.1021/acsphotonics.7b00419        Google Scholar

6. Shi, J., V. Hsiao, and T. Huang, "Nanoporous polymeric transmission gratings for high-speed humidity sensing," Nanotechnology, Vol. 18, No. 46, 465501 (6pp), 2007.
doi:10.1088/0957-4484/18/46/465501        Google Scholar

7. Halir, R., D. Benedicovic, A. Ortega-Monux, and G. Mashanovich, "Subwavelength-grating metamaterial structures for silicon photonic devices," Proc. IEEE, Vol. 106, No. 12, 1-14, 2018.
doi:10.1109/JPROC.2018.2851614        Google Scholar

8. Wu, Sh.-D., T. K. Gaylord, E. N. Glytsis, and Y.-M. Wu, "Three-dimensional converging-diverging Gaussian beam diffraction by a volume grating," J. Opt. Soc. Amer. A, Vol. 22, No. 7, 1293-1304, 2005.
doi:10.1364/JOSAA.22.001293        Google Scholar

9. Ciapurin, I. V., L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. of SPIE, Vol. 5742, 183-194, 2005.
doi:10.1117/12.591215        Google Scholar

10. Harvey, J. E. and E. A. Nevis, "Angular grating anomalies: Effects of finite beam size on wide-angle diffraction phenomena," Applied Optics, Vol. 43, No. 31, 6783-6788, 1992.
doi:10.1364/AO.31.006783        Google Scholar

11. Serdyuk, V. M. and J. A. Titovitsky, "A simple analytic approximation for the refracted field at Gaussian beam incidence upon a boundary of absorbing medium," Journ. Electrom. Analysis Applic., Vol. 2, No. 11, 640-648, 2010.        Google Scholar

12. Serdyuk, V. M. and A. S. Rudnitsky, "Efficiency of Gaussian light beam transformation into a waveguide mode of a plane dielectric layer under frustrated total internal reflection," JOSA A, Vol. 36, No. 9, 1573-1582, 2019.
doi:10.1364/JOSAA.36.001573        Google Scholar

13. Hessel, A. and A. A. Oliner, "A new theory of Wood's anomalies on optical gratings," Applied Optics, Vol. 4, No. 10, 1275-1297, 1965.
doi:10.1364/AO.4.001275        Google Scholar

14. Russell, P., "Optical volume holography," Physics Reports, Vol. 71, No. 4, 209-312, 1981.
doi:10.1016/0370-1573(81)90196-4        Google Scholar

15. Lindquist, R. G., J. H. Kulick, G. P. Nordin, J. M. Jarem, S. T. Kowel, M. Friends, and T. Leslie, "High resolution liquid crystal phase grating formed by fringing fields from interdigitated electrodes," Opt. Lett., Vol. 19, No. 9, 67-72, 1994.
doi:10.1364/OL.19.000670        Google Scholar

16. Born, M. and E. Wolf, Principles of Optics, 7th Ed., Cambridge University Press, 1999.
doi:10.1017/CBO9781139644181

17. Sheng, P., R. S. Stepleman, and P. N. Sanda, "Exact eigenfunction for square-wave gratings: Application to diffraction and surface-plasmon calculations," Physical Review B, Vol. 26, No. 6, 2907-2916, 1982.
doi:10.1103/PhysRevB.26.2907        Google Scholar

18. Rudnitsky, A. S. and V. Serdyuk, "Diffraction of a plane electromagnetic wave by a slot in a conducting screen of finite thickness placed in front of a half-infinite dielectric," Progress In Electromagnetics Research, Vol. 86, 277-290, 2008.
doi:10.2528/PIER08092605        Google Scholar

19. Marcuse, D., Light Transmission Optics, Van Nostrand, 1972.

20. Faddeev, D. K. and V. N. Faddeeva, Computational Methods of Linear Algebra, W. H. Freeman & Co., 1964.

21. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, 9th Ed., National Bureau of Standards, 1964.

22. Serdyuk, V., "Method of additive regularization of field integrals in the problem of electromagnetic diffraction by a slot in a conducting screen, placed before a dielectric layer," Progress In Electromagnetics Research B, Vol. 83, 129-151, 2019.
doi:10.2528/PIERB18102906        Google Scholar