## Form-birefringence limits of Fourier-expansion methods in grating theory

JOSA A, Vol. 13, Issue 5, pp. 1013-1018 (1996)

http://dx.doi.org/10.1364/JOSAA.13.001013

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### Abstract

Standard formulations of rigorous Fourier-expansion analysis methods of lamellar gratings reduce, irrespective of the state of polarization, to the TE result of the lowest-order theory of form birefringence when only the zeroth-order terms are retained in the field and permittivity expansions. A reformulation is presented that reduces to the correct form-birefringence result also in the TM case. Expressions are given for the effective relative permittivities *∊*_{eff} of a subwavelength-period grating with an arbitrary relative-permittivity profile *∊** _{r}*(

*x*): the lowest-order approximation for

*∊*

_{eff}is given by the zeroth-order Fourier coefficient of

*∊*

*(*

_{r}*x*) in TE polarization and of 1/

*∊*

*(*

_{r}*x*) in TM polarization.

© 1996 Optical Society of America

**History**

Original Manuscript: July 14, 1995

Revised Manuscript: October 23, 1995

Manuscript Accepted: October 30, 1995

Published: May 1, 1996

**Citation**

Jari Turunen, "Form-birefringence limits of Fourier-expansion methods in grating theory," J. Opt. Soc. Am. A **13**, 1013-1018 (1996)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-5-1013

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### References

- M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. A 72, 1385–1392 (1982). [CrossRef]
- T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985). [CrossRef]
- M. G. Moharam, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
- C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc. Am. 56, 1502–1509 (1966). [CrossRef]
- S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975). [CrossRef]
- K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978). [CrossRef]
- L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981). [CrossRef]
- R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar gratings,” J. Opt. Soc. Am. A 12, 1043–1056 (1995). [CrossRef]
- M. Nevière, P. Vincent, “Differential theory of gratings: answer to an objection on its validity for TM polarization,” J. Opt. Soc. Am. A 5, 1522–1524 (1988). [CrossRef]
- M. Nevière, E. Popov, “Analysis of dielectric gratings of arbitrary profiles and thicknesses: comment,” J. Opt. Soc. Am. A 9, 2095–2096 (1992). [CrossRef]
- L. Li, C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184–1189 (1993). [CrossRef]
- D. H. Raguin, G. M. Morris, “Analysis of antireflection structured surfaces with continuous one-dimensional profiles,” Appl. Opt. 32, 2582–2598 (1993). [CrossRef] [PubMed]
- M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 705–708 and 61–66.
- G. Campbell, R. K. Kostuk, “Effective-medium theory of sinusoidally modulated volume holograms,” J. Opt. Soc. Am. A 12, 1113–1117 (1995). [CrossRef]
- P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980). [CrossRef]
- M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983). [CrossRef]
- The choice of the reference plane z= hin the terms exp[−iγ(z− h)] that appear in Eqs. (9) and (10) ensures that the physical nature of evanescent waves will be properly accounted for in the solution of the boundary value problem: the amplitudes of evanescent waves are appreciable only in the vicinity of the particular boundary, either z= 0 or z= h, at which they are generated. Therefore the numerical stability problems resulting from growing exponentials9,10 are eliminated.
- S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

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