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.

© 2000 Optical Society of America

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References

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    [Crossref]
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1999 (4)

1998 (1)

1997 (1)

1995 (3)

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

1989 (1)

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

Abushagur, M. A. G.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

Bergey, J. S.

Collins, J. P.

Deguzman, P.

Deguzman, P. C.

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 and David B. Chenault, Editors, Proceedings of SPIE, 3754, 169–177, (1999).

Goldberg, D. E.

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

Gram, E.

Johnson, E. G.

Jones, M.

Jones, M. W.

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 and David B. Chenault, Editors, Proceedings of SPIE, 3754, 169–177, (1999).

Krishnakumar, K.

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

Mait, J. N.

Meier, J.

Meier, J. T.

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 and David B. Chenault, Editors, Proceedings of SPIE, 3754, 169–177, (1999).

Mirotznik, M. S.

Moharam, M. G.

Nordin, G.

Nordin, G. P.

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 and David B. Chenault, Editors, Proceedings of SPIE, 3754, 169–177, (1999).

Pommet, D. A.

Prather, D. W.

Prather, W.

Shi, S.

Smith, G. S.

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

Taflove, A.

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

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

J. Opt. Soc. Am. A (7)

Opt. Eng. (1)

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodectors,” Opt. Eng.,  38, 870–878 (1999).
[Crossref]

Opt. Lett. (1)

SPIE (1)

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

Other (4)

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 and David B. Chenault, Editors, Proceedings of SPIE, 3754, 169–177, (1999).

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

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

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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