## Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

JOSA A, Vol. 20, Issue 5, pp. 827-835 (2003)

http://dx.doi.org/10.1364/JOSAA.20.000827

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### Abstract

A rigorous modal theory for the diffraction of Gaussian beams from <i>N</i> equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the <i>N</i> slits. The classical grating equation is tested for incident Gaussian beams under several conditions.

© 2003 Optical Society of America

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(050.1960) Diffraction and gratings : Diffraction theory

**Citation**

J. Sumaya-Martinez, O. Mata-Mendez, and F. Chavez-Rivas, "Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization," J. Opt. Soc. Am. A **20**, 827-835 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-827

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### References

- E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
- C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–99 (1954).
- K. Hongo, “Diffraction of an electromagnetic plane wave by a thick slit,” IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
- T. Otsuki, “Diffraction by two parallel slits in a plane,” J. Math. Phys. 19, 911–915 (1978).
- T. Otsuki, “Reexamination of diffraction problem of a slit by a method of Fourier orthogonal functions transformation,” J. Phys. Soc. Jpn. 41, 2046–2051 (1976).
- B. K. Sachdeva and R. A. Hurd, “Diffraction by multiple slits at the interface between two different media,” Can. J. Phys. 53, 1013–1021 (1975).
- A. S. Zil’bergleit, “Diffraction of electromagnetic waves by an ideal plate with an even number of symmetrically placed slits,” Sov. Phys. Tech. Phys. 20, 292–295 (1975).
- T. Otsuki, “Diffraction by multiple slits,” J. Opt. Soc. Am. A 7, 646–652 (1990).
- H. A. Kalhor, “Diffraction of electromagnetic waves by plane metallic gratings,” J. Opt. Soc. Am. 68, 1202–1205 (1978).
- J. J. Stamnes and H. A. Eide, “Exact and approximate solutions for focusing of two-dimensional waves. I. Theory,” J. Opt. Soc. Am. A 15, 1285–1291 (1998).
- M. Wirgin, “Influence de l’épaisseur de l’écran sur la diffraction par une fente,” C. R. Acad. Sci. Paris 270, 1457–1460 (1970).
- H. Henke and H. Fruchting, “Irradiation in a slotted half space and diffraction by a slit in a thick screen,” Nachrichtentech. 29, 401–405 (1976).
- J. L. Roumiguières, D. Maystre, R. Petit, and M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 402–405 (1973).
- F. L. Neerhoff and G. Mur, “Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media,” Appl. Sci. Res. 28, 73–88 (1973).
- K. Hongo, “A method of evaluating the near diffracted field,” IEEE Trans. Antennas Propag. AP-28, 409–412 (1980).
- D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).
- H. S. Tan, “On Kirchhoff’s theory in non-planar scalar diffraction,” Proc. Phys. Soc. Jpn. 91, 768–773 (1967).
- O. Mata-Mendez, “Diffraction and beam-diameter measurement of Gaussian beams at optical and microwave frequencies,” Opt. Lett. 16, 1629–1631 (1991).
- O. Mata-Mendez and F. Chavez-Rivas, “Diffraction of Gaussian and Hermite–Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537–545 (2001).
- O. Mata-Mendez, M. Cadilhac, and R. Petit, “Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen,” J. Opt. Soc. Am. 73, 328–331 (1983).
- O. Mata-Mendez and F. Chavez-Rivas, “Diffraction of Hermite–Gaussian beams by a slit,” J. Opt. Soc. Am. A 12, 2440–2445 (1995).
- G. A. Suedan and E. V. Jull, “Two-dimensional beam diffraction by a half-plane and wide slit,” IEEE Trans. Antennas Propag. AP-35, 1077–1082 (1987).
- R. A. Depine and D. C. Skigin, “Multilayer modal method for diffraction from dielectric inhomogeneous apertures,” J. Opt. Soc. Am. A 15, 675–683 (1998).
- D. C. Skigin and R. A. Depine, “Scattering by lossy inhomogeneous apertures in thick metallic screens”, J. Opt. Soc. Am. A 15, 2089–2096 (1998).
- O. Mata-Mendez and F. Chavez-Rivas, “New property in the diffraction of Hermite–Gaussian beams by a finite grating in the scalar diffraction regime: constant-intensity angles in the far field when the beam center is displaced through the grating,” J. Opt. Soc. Am. A 15, 2698–2704 (1998).
- T. Otsuki, “Diffraction by multiple slits,” J. Opt. Soc. Am. A 7, 646–652 (1990).
- B. Guizal and D. Felbacq, “Electromagnetic beam diffraction by a finite strip grating,” Opt. Commun. 165, 1–6 (1999).
- Em. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630–636 (1994).
- J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, “Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide,” IEICE Trans. Commun. E84–B, 95–99 (2001).
- J. S. Uppal, P. K. Gupta, and R. G. Harrison, “Aperiodic ruling for the measurement of Gaussian laser beam diameters,” Opt. Lett. 14, 683–685 (1989).

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