Abstract

We have developed a rigorous unidirectional method for designing finite-aperture diffractive optical elements (DOE’s) that employs a micro-genetic algorithm (µGA) for global optimization in conjunction with a 2-D Finite-Difference Time-Domain (FDTD) method for rigorous electromagnetic computation. The theory and implementation of this µGA-FDTD design method for normally incident TE illumination are briefly discussed. Design examples are presented, including a micro-lens, a 1-to-2 beam-fanner and a 1-to-3 beam-fanner.

© Optical Society of America

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References

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  1. G.Nordin, J. Meier, P. Deguzman and M. Jones, "Micropolazier array for infrared imaging polarimetry," J. Opt. Soc. Am. A, 16, 1168-1174 (1999).
    [CrossRef]
  2. G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. W. Jones, "Diffractive Optical Element for Stokes Vector Measurement With a Focal Plane Array," in Polarization: Measurement, Analysis, and Remote Sensing II, Dennis H. Goldstein, David B. Chenault, Editors, Proceedings of SPIE, 3754, 169-177, (1999).
  3. D. W. Prather, "Design and application of subwavelength diffractive lenses for integration with infrared photodectors," Opt. Eng., 38, 870-878 (1999).
    [CrossRef]
  4. D. A. Pommet,M. G. Moharam, and E. Gram, "Limits of scalar diffarction theory for diffractive phase elements," J. Opt. Soc. Am. A, 11, 1827-1834 (1995).
    [CrossRef]
  5. W. Prather, J. N. Mait, M. S. Mirotznik and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A, 15, 1599-1607 (1998).
    [CrossRef]
  6. D. W. Prather, M. S. Mirotznik and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A, 14, 34-43 (1997).
    [CrossRef]
  7. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).
  8. K. Krishnakumar, "Micro-genetic algorithm for stationary and non-stationary function optimization," SPIE 1196, 289-296 (1989).
  9. J. N. Mait., "Understanding diffractive optic design in the scalar domain," J. Opt. Soc. Am. A, 12, 2145-2158 (1995).
    [CrossRef]
  10. D. W. Prather, S. Shi, J. S. Bergey, "Field stitching algorithm for the analysis of electrically large diffractive optical elements," Opt. Lett. 24, 273-275 (1999).
    [CrossRef]
  11. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  12. D. W. Prather and S. Shi, "Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements," J. Opt. Soc. Am. A, 16, 1131-1142 (1999).
    [CrossRef]
  13. G. S. Smith, An Introduction to Classical Electromagnetic Radiation, (Cambridge Univ. Press, Cambridge, Mass., 1997).
  14. E. G. Johnson and M. A. G. Abushagur, Microgenetic-algorithm optimization methods applied to dielectric gratings," J. Opt. Soc. Am. A, 12, 1152-1160 (1995).
    [CrossRef]
  15. D. E. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning, (Addision-Wesley, Reading, Mass., 1989).

Other (15)

G.Nordin, J. Meier, P. Deguzman and M. Jones, "Micropolazier array for infrared imaging polarimetry," J. Opt. Soc. Am. A, 16, 1168-1174 (1999).
[CrossRef]

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. W. Jones, "Diffractive Optical Element for Stokes Vector Measurement With a Focal Plane Array," in Polarization: Measurement, Analysis, and Remote Sensing II, Dennis H. Goldstein, David B. Chenault, Editors, Proceedings of SPIE, 3754, 169-177, (1999).

D. W. Prather, "Design and application of subwavelength diffractive lenses for integration with infrared photodectors," Opt. Eng., 38, 870-878 (1999).
[CrossRef]

D. A. Pommet,M. G. Moharam, and E. Gram, "Limits of scalar diffarction theory for diffractive phase elements," J. Opt. Soc. Am. A, 11, 1827-1834 (1995).
[CrossRef]

W. Prather, J. N. Mait, M. S. Mirotznik and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A, 15, 1599-1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A, 14, 34-43 (1997).
[CrossRef]

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).

K. Krishnakumar, "Micro-genetic algorithm for stationary and non-stationary function optimization," SPIE 1196, 289-296 (1989).

J. N. Mait., "Understanding diffractive optic design in the scalar domain," J. Opt. Soc. Am. A, 12, 2145-2158 (1995).
[CrossRef]

D. W. Prather, S. Shi, J. S. Bergey, "Field stitching algorithm for the analysis of electrically large diffractive optical elements," Opt. Lett. 24, 273-275 (1999).
[CrossRef]

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

D. W. Prather and S. Shi, "Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements," J. Opt. Soc. Am. A, 16, 1131-1142 (1999).
[CrossRef]

G. S. Smith, An Introduction to Classical Electromagnetic Radiation, (Cambridge Univ. Press, Cambridge, Mass., 1997).

E. G. Johnson and M. A. G. Abushagur, Microgenetic-algorithm optimization methods applied to dielectric gratings," J. Opt. Soc. Am. A, 12, 1152-1160 (1995).
[CrossRef]

D. E. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning, (Addision-Wesley, Reading, Mass., 1989).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the 2-D FDTD geometry showing TE polarization definition

Fig. 2.
Fig. 2.

Design geometry for the numerical design examples

Fig. 3.
Fig. 3.

Microlens test case for µGA-FDTD Design tool with field distribution of analytical profile as target function (a) µGA convergence curve, (b) field distributions of both analytical and optimized profiles, and (c) the analytical and optimized microlens profiles.

Fig. 4.
Fig. 4.

Two µGA-FDTD optimized DOE profiles for 1-to-2 beamfanner with 25µm peak separation (a) Optimized DOE profiles and (b) their corresponding field distribution.

Fig. 5.
Fig. 5.

Optimized wide-angle 1-to-3 beamfanner with 50um peak separartions (a) Optimized DOE profile and (b) its field distribution

Equations (2)

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f = i = 1 L E ( x i ) 2 E analy ( x i ) 2 ,
f = i = 1 L E ( x i ) · [ exp ( ( x i 12.5 ) 2 2 σ 2 ) + exp ( ( x i + 12.5 ) 2 2 σ 2 ) 5 ( 1 rect ( x i 40 ) ) ]

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