Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction

doi:10.1364/OE.18.026274

Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction

Kofi Edee, Jean-Pierre Plumey, Gérard Granet, and Jérome Hazart »View Author Affiliations

Optics Express, Vol. 18, Issue 25, pp. 26274-26284 (2010)
http://dx.doi.org/10.1364/OE.18.026274

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Abstract

The perturbation method is combined with the Rigorous Coupled Wave Analysis (RCWA) to enhance its computational speed. In the original RCWA, a grating is approximated by a stack of lamellar gratings and the number of eigenvalue systems to be solved is equal to the number of subgratings. The perturbation method allows to derive the eigensolutions in many layers from the computed eigensolutions of a reference layer provided that the optical and geometrical parameters of these layers differ only slightly. A trapezoidal grating is considered to evaluate the performance of the method.

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: September 14, 2010
Revised Manuscript: October 26, 2010
Manuscript Accepted: October 26, 2010
Published: December 1, 2010

Citation
Kofi Edee, Jean-Pierre Plumey, Gérard Granet, and Jérome Hazart, "Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction," Opt. Express 18, 26274-26284 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-26274

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References

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microw. Theory Tech. MTT-23, 123-133 (1975). [CrossRef]
M. G. Moharam, and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. A 72, 1385-1392 (1982). [CrossRef]
I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta (Lond.) 28, 413-428 (1981).
I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The finitely conducting lamellar diffraction grating," Opt. Acta (Lond.) 28, 1087-1102 (1981).
K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am. 68, 1206-1210 (1978). [CrossRef]
Ph. Lalanne, and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM-polarization," J. Opt. Soc. Am. A 13, 779-784 (1996). [CrossRef]
G. Granet, and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]
L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Am. A 10, 2581-2591 (1993). [CrossRef]
J. Y. Suratteau, M. Cadilhac, and R. Petit, "Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds," J. Opt. (Paris) 14, 273-288 (1983).
D. M. Pai, and K. A. Awada, "Analysis of dielectric gratings of arbitrary profiles and thicknesses," J. Opt. Soc. Am. A 8, 755-762 (1991). [CrossRef]
N. Chateau, and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994). [CrossRef]
N. P. van der Aa, and R. M. M. Mattheij, "Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA," J. Opt. Soc. Am. A 24, 2692-2700 (2007). [CrossRef]
E. Popov, M. Nevière, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings," J. Opt. Soc. Am. A 19, 33-42 (2002). [CrossRef]
J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. (Paris) 11, 235-241 (1980).
L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt. 38, 304-313 (1999). [CrossRef]
T. Vallius, "Comparing the Fourier modal method with the C method: analysis of conducting multilevel gratings in TM polarization," J. Opt. Soc. Am. A 19, 1555-1562 (2002). [CrossRef]
G. Granet, J. Chandezon, J.-P. Plumey, and K. Raniriharinosy, "Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings," J. Opt. Soc. Am. A 18, 2102-2108 (2001). [CrossRef]
L. D. Landau, and E. M. Lifschitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed. Ed. Pergamon, New York, (1977).
C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique quantique, T2, Ed. Hermann, Paris, (1994). [PubMed]

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[1] S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microw. Theory Tech. MTT-23, 123-133 (1975). [CrossRef]

[2] M. G. Moharam, and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. A 72, 1385-1392 (1982). [CrossRef]

[3] I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta (Lond.) 28, 413-428 (1981).

[4] I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The finitely conducting lamellar diffraction grating," Opt. Acta (Lond.) 28, 1087-1102 (1981).

[5] K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am. 68, 1206-1210 (1978). [CrossRef]

[6] Ph. Lalanne, and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM-polarization," J. Opt. Soc. Am. A 13, 779-784 (1996). [CrossRef]

[7] G. Granet, and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]

[8] L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]

[9] L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Am. A 10, 2581-2591 (1993). [CrossRef]

[10] J. Y. Suratteau, M. Cadilhac, and R. Petit, "Sur la détermination numérique des efficacités de certains réseaux diélectriques profonds," J. Opt. (Paris) 14, 273-288 (1983).

[11] D. M. Pai, and K. A. Awada, "Analysis of dielectric gratings of arbitrary profiles and thicknesses," J. Opt. Soc. Am. A 8, 755-762 (1991). [CrossRef]

[12] N. Chateau, and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994). [CrossRef]

[13] N. P. van der Aa, and R. M. M. Mattheij, "Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA," J. Opt. Soc. Am. A 24, 2692-2700 (2007). [CrossRef]

[14] E. Popov, M. Nevière, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings," J. Opt. Soc. Am. A 19, 33-42 (2002). [CrossRef]

[15] J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. (Paris) 11, 235-241 (1980).

[16] L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt. 38, 304-313 (1999). [CrossRef]

[17] T. Vallius, "Comparing the Fourier modal method with the C method: analysis of conducting multilevel gratings in TM polarization," J. Opt. Soc. Am. A 19, 1555-1562 (2002). [CrossRef]

[18] G. Granet, J. Chandezon, J.-P. Plumey, and K. Raniriharinosy, "Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings," J. Opt. Soc. Am. A 18, 2102-2108 (2001). [CrossRef]

[19] L. D. Landau, and E. M. Lifschitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed. Ed. Pergamon, New York, (1977).

[20] C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique quantique, T2, Ed. Hermann, Paris, (1994). [PubMed]

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Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction