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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 10 — Oct. 1, 2001
  • pp: 2491–2501

Algorithm based on rigorous coupled-wave analysis for diffractive optical element design

Ni Y. Chang and Chung J. Kuo  »View Author Affiliations

JOSA A, Vol. 18, Issue 10, pp. 2491-2501 (2001)

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Diffractive optical element design is an important problem for many applications and is usually achieved by the Gerchberg–Saxton or the Yang–Gu algorithm. These algorithms are formulated on the basis of monochromatic wave propagation and the far-field assumption, because the Fourier transform is used to model the wave propagation. We propose an iterative algorithm (based on rigorous coupled-wave analysis) for the design of a diffractive optical element. Since rigorous coupled-wave analysis (instead of Fourier transformation) is used to calculate the light-field distribution behind the optical element, the diffractive optical element can thus be better designed. Simulation results are provided to verify the proposed algorithm for designing a converging lens. Compared with the well-known Gerchberg–Saxton and Yang–Gu algorithms, our method provides 7.8% and 10.8%, respectively, improvement in converging the light amplitude when a microlens is desired. In addition, the proposed algorithm provides a solution that is very close to the solution obtained by the simulated annealing method (within 1.89% error).

© 2001 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings

Original Manuscript: September 18, 2000
Revised Manuscript: February 28, 2001
Manuscript Accepted: November 28, 2000
Published: October 1, 2001

Ni Y. Chang and Chung J. Kuo, "Algorithm based on rigorous coupled-wave analysis for diffractive optical element design," J. Opt. Soc. Am. A 18, 2491-2501 (2001)

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Cambridge, UK, 1997).
  2. C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991). [CrossRef]
  3. L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995). [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994). [CrossRef]
  6. R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992). [CrossRef]
  7. W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996). [CrossRef]
  8. W. Dasher, P. Long, R. Stein, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of signal optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997). [CrossRef]
  9. G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge, Wellesley, Mass., 1986).
  10. R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).
  11. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).
  12. B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).
  13. B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986). [CrossRef] [PubMed]
  14. G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).
  15. L. Li, “Use of Fourier series in the analysis of discontinous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  16. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  17. S. T. Han, Y. L. Tsao, R. M. Walser, M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992). [CrossRef] [PubMed]
  18. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  19. M. G. Moharam, T. K. Gaylord, “Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings,” J. Opt. Soc. Am. 72, 187–190 (1982). [CrossRef]
  20. M. G. Moharam, T. K. Gaylord, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982). [CrossRef]
  21. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief grating,” J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  22. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983). [CrossRef]
  23. M. G. Moharam, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigor-ous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1996). [CrossRef]
  24. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase-only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990). [CrossRef] [PubMed]
  25. S. Kirkpartick, C. D. Gellatt, “Optimization by simulated annealing,” Science 220, 671–680 (1983). [CrossRef]
  26. N. Yoshikawa, T. Yatagai, “Phase optimization of a ki-noform by simulated annealing,” Appl. Opt. 33, 863–868 (1994). [CrossRef] [PubMed]
  27. E. Noponen, “Eigenmode method for electromagnetic syn-thesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994). [CrossRef]
  28. Please note that the DOE’s phase transmittance (before quantization) is different between the last two iterations of our algorithm and that the largest difference between the last two iterations is 2.87×10-3.However, our algorithm still converges, because the phases after quantization become identical.

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