OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 5 — May. 1, 1999
  • pp: 1124–1130

Pseudospectral method for the analysis of diffractive optical elements

P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, and L. Lading  »View Author Affiliations


JOSA A, Vol. 16, Issue 5, pp. 1124-1130 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001124


View Full Text Article

Enhanced HTML    Acrobat PDF (342 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A pseudospectral method for the analysis of diffractive optical elements is presented. This method is a full-vectorial direct solution of the time-domain Maxwell equations based on a spectral approximation of the spatial derivatives employed within a multidomain framework. The method exhibits little numerical dispersion, and only a few points per wavelength are needed to accurately resolve the propagation of the optical field over long distances. A comparison with the analytic solution for a thin-film waveguide is performed, and examples of analyses of grating couplers are given to demonstrate the feasibility of the method.

© 1999 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory

History
Original Manuscript: August 4, 1998
Revised Manuscript: November 30, 1998
Manuscript Accepted: December 2, 1998
Published: May 1, 1999

Citation
P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, and L. Lading, "Pseudospectral method for the analysis of diffractive optical elements," J. Opt. Soc. Am. A 16, 1124-1130 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-5-1124


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992). [CrossRef] [PubMed]
  2. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985). [CrossRef]
  3. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997). [CrossRef]
  4. M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite element-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1321 (1996). [CrossRef]
  5. D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997). [CrossRef]
  6. M. Schmitz, O. Bryngdahl, “Rigorous concept for the design of diffractive microlenses with high numerical apertures,” J. Opt. Soc. Am. A 14, 901–906 (1997). [CrossRef]
  7. M. Mirotznik, J. N. Mait, D. W. Prather, W. A. Beck, “Three-dimensional vector-based analysis of subwavelength diffractive optical elements using the finite-difference time-domain (FDTD) method,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 91–93.
  8. S. Ura, T. Suhara, H. Nishihara, “Aberration characterizations of a focusing grating coupler in an integrated-optic disk pickup device,” Appl. Opt. 26, 4777–4782 (1987). [CrossRef] [PubMed]
  9. J. J. M. Braat, M. O. E. Laurijs, “Geometrical optics design and aberration analysis of a focusing grating coupler,” Opt. Eng. 33, 1037–1043 (1994). [CrossRef]
  10. P.-P. Borsboom, H. J. Frankena, “Field analysis of two-dimensional focusing grating couplers,” J. Opt. Soc. Am. A 12, 1142–1146 (1995). [CrossRef]
  11. R. W. Ziolkowski, “The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations,” IEEE Trans. Antennas Propag. 45, 375–391 (1997). [CrossRef]
  12. B. Yang, D. Gottlieb, J. S. Hesthaven, “Spectral simulation of electromagnetic wave scattering,” J. Comput. Phys. 134, 216–230 (1997). [CrossRef]
  13. A. Taflove, Computational Electrodynamics—The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).
  14. J. S. Hesthaven, P. G. Dinesen, J.-P. Lynov, “Parallel pseudospectral time-domain modeling of diffractive optical elements,” submitted to J. Comput. Vision.
  15. M. H. Carpenter, C. A. Kennedy, “Fourth order 2N-storage Runge–Kutta scheme,” (NASA, Washington, D.C., 1994).
  16. D. Funaro, Polynomial Approximation of Differential Equations, Vol. 8 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1992).
  17. W. J. Gordon, C. A. Hall, “Transfinite element methods: blending-function interpolation over arbitrary curved element domains,” Numer. Math. 21, 109–129 (1973). [CrossRef]
  18. J. S. Hesthaven, “A stable penalty method for the compressible Navier–Stokes equations. III. Multi-dimensional domain decomposition schemes,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 62–93 (1999). [CrossRef]
  19. B. Yang, D. Gottlieb, J. S. Hesthaven, “On the use of PML ABC’s in spectral time-domain simulations of electromagnetic scattering,” in Proceedings of the 13th Annual Review of Progress in Applied Computational Electromagnetics (ACES ’97), E. C. Michielssen, ed. (Applied Computational Electromagnetics Society, Monterey, Calif., 1997), Vol. 2, pp. 926–933.
  20. S. A. Schelknuoff, “Some equivalence theorems of electromagnetics and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936). [CrossRef]
  21. S. Ramo, J. R. Whinnery, T. van Duzer, Fields and Waves in Communications Electronics, 3rd ed. (Wiley, New York, 1993).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited