A rigorous unidirectional method for designing finite aperture diffractive optical elements

Jianhua Jiang; Gregory P. Nordin

doi:10.1364/OE.7.000237

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.

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References

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Publication

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 and 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, and 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).

1999 (4)

D. W. Prather, S. Shi, and J. S. Bergey, “Field stitching algorithm for the analysis of electrically large diffractive optical elements,” Opt. Lett. 24, 273–275 (1999).
[Crossref]

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

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]

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]

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.

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]

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.

D. W. Prather, S. Shi, and J. S. Bergey, “Field stitching algorithm for the analysis of electrically large diffractive optical elements,” Opt. Lett. 24, 273–275 (1999).
[Crossref]

Collins, J. P.

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]

Deguzman, P.

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]

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.

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]

Johnson, E. G.

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]

Jones, M.

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]

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.

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]

J. N. Mait., “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A, 12, 2145–2158 (1995).
[Crossref]

Meier, J.

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]

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.

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]

Moharam, M. G.

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]

Nordin, G.

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]

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.

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]

Prather, D. W.

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

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

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]

Prather, W.

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]

Shi, S.

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]

D. W. Prather, S. Shi, and J. S. Bergey, “Field stitching algorithm for the analysis of electrically large diffractive optical elements,” Opt. Lett. 24, 273–275 (1999).
[Crossref]

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)

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]

J. N. Mait., “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A, 12, 2145–2158 (1995).
[Crossref]

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. 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]

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]

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)

D. W. Prather, S. Shi, and J. S. Bergey, “Field stitching algorithm for the analysis of electrically large diffractive optical elements,” Opt. Lett. 24, 273–275 (1999).
[Crossref]

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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Fig. 1. Schematic diagram of the 2-D FDTD geometry showing TE polarization definition

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Fig. 2. Design geometry for the numerical design examples

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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.

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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.

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Fig. 5. Optimized wide-angle 1-to-3 beamfanner with 50um peak separartions (a) Optimized DOE profile and (b) its field distribution

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Equations (2)

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f = \sum_{i = 1}^{L} ∣ {∣ E (x_{i}) ∣}^{2} - {∣ E_{analy} (x_{i}) ∣}^{2} ∣,

f = \sum_{i = 1}^{L} ∣ E (x_{i}) ∣ \cdot [\exp (- \frac{{(x_{i} - 12.5)}^{2}}{2 σ^{2}}) + \exp (- \frac{{(x_{i} + 12.5)}^{2}}{2 σ^{2}}) - 5 (1 - rect (\frac{x_{i}}{40}))]

Abstract

References

1999 (4)

1998 (1)

1997 (1)

1995 (3)

1994 (1)

1989 (1)

Abushagur, M. A. G.

Berenger, J. P.

Bergey, J. S.

Collins, J. P.

Deguzman, P.

Deguzman, P. C.

Goldberg, D. E.

Gram, E.

Johnson, E. G.

Jones, M.

Jones, M. W.

Krishnakumar, K.

Mait, J. N.

Meier, J.

Meier, J. T.

Mirotznik, M. S.

Moharam, M. G.

Nordin, G.

Nordin, G. P.

Pommet, D. A.

Prather, D. W.

Prather, W.

Shi, S.

Smith, G. S.

Taflove, A.

J. Comput. Phys. (1)

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

Opt. Eng. (1)

Opt. Lett. (1)

SPIE (1)

Other (4)

Cited By

Figures (5)

Equations (2)

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