Abstract

In this paper, finite-aperture diffractive optical element with its critical dimension smaller than illumination wavelength is modeled and optimized using an integrated method. This method employs rigorous analysis model based on Finite Difference Time Domain (FDTD), and simulated annealing (SA) global search algorithm. Numerical results reveal that the diffraction efficiency of the 8-step microlens quickly climbs to its global optimum along with the optimization process, which manifests its global search ability. The design algorithm and implementation are discussed in details. Considering its time consuming efficiency and global search ability, our method provides valuable reference value in practical multistep microlens design.

© 2014 Optical Society of America

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    [CrossRef]
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2013 (1)

2010 (2)

2007 (2)

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

J. Vaillant, A. Crocherie, F. Hirigoyen, A. Cadien, J. Pond, “Uniform illumination and rigorous electromagnetic simulations applied to CMOS image sensors,” Opt. Express 15(9), 5494–5503 (2007).
[CrossRef] [PubMed]

2005 (1)

Y. Liu, H. Liu, “Rigorous vector analysis of diffractive microlens by using the finite-difference time-domain method,” Proc. SPIE 7506, 7506141–7506148 (2005).

2004 (1)

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

2003 (1)

2001 (1)

2000 (3)

1999 (2)

D. W. Prather, 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(5), 1131 (1999).
[CrossRef]

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
[CrossRef]

1998 (1)

1997 (2)

1996 (1)

M. B. Stern, “Binary optics: A VLSI-based microoptics technology,” Microelectron. Eng. 32(1–4), 369–388 (1996).
[CrossRef]

1995 (1)

1994 (2)

D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11(6), 1827–1834 (1994).
[CrossRef]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Bendickson, J. M.

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Bryngdahl, O.

Bu, J.

Cadien, A.

Chen, S.

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

Crocherie, A.

Dial, O.

Ding, Y.

Dong, B.-Z.

Du, C. L.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Gao, X.

Gaylord, T. K.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Glytsis, E. N.

Grann, E. B.

Gu, B.-Y.

He, M.

Hirigoyen, F.

Hu, B.

Ishikawa, K. L.

Jiang, J.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Kong, L.

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

Li, X.

Lian, K.

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

Liu, H.

Y. Liu, H. Liu, “Analysis of a diffractive microlens using the finite-difference time-domain method,” J. Micro-Nanolith. MEM 9(3), 033004 (2010).
[CrossRef]

Y. Liu, H. Liu, “Rigorous vector analysis of diffractive microlens by using the finite-difference time-domain method,” Proc. SPIE 7506, 7506141–7506148 (2005).

Liu, J.

Liu, Y.

Y. Liu, H. Liu, “Analysis of a diffractive microlens using the finite-difference time-domain method,” J. Micro-Nanolith. MEM 9(3), 033004 (2010).
[CrossRef]

Y. Liu, H. Liu, “Rigorous vector analysis of diffractive microlens by using the finite-difference time-domain method,” Proc. SPIE 7506, 7506141–7506148 (2005).

Ma, X. Z.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Mait, J. N.

Mirotznik, M. S.

Moharam, M. G.

Ngo, N.

Nordin, G.

Pommet, D. A.

Pond, J.

Prather, D. W.

Qiu, C. K.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Scherer, A.

Schmitz, M.

Shao, J.

Shi, S.

Shirakawa, T.

Stern, M. B.

M. B. Stern, “Binary optics: A VLSI-based microoptics technology,” Microelectron. Eng. 32(1–4), 369–388 (1996).
[CrossRef]

Suzuki, S.

Takahashi, H.

Tang, J.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Tao, S.

Tian, H.

Tian, Z. W.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Vaillant, J.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Yamada, Y.

Yang, G.-Z.

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Yi, X.

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

Yuan, X. C.

Zhai, H.

Zhang, L.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Zhuang, J. L.

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

Adv. Mater. (1)

L. Zhang, X. Z. Ma, J. L. Zhuang, C. K. Qiu, C. L. Du, J. Tang, Z. W. Tian, “Microfabrication of a Diffractive Microlens Array on n-GaAs by an Efficient Electrochemical Method,” Adv. Mater. 19(22), 3912–3918 (2007).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

J. Comput. Phys. (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Micro-Nanolith. MEM (1)

Y. Liu, H. Liu, “Analysis of a diffractive microlens using the finite-difference time-domain method,” J. Micro-Nanolith. MEM 9(3), 033004 (2010).
[CrossRef]

J. Micromech. Microeng. (1)

L. Kong, X. Yi, K. Lian, S. Chen, “Design and optical performance research of multi-phase diffractive microlens arrays,” J. Micromech. Microeng. 14(8), 1135–1139 (2004).
[CrossRef]

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

Microelectron. Eng. (1)

M. B. Stern, “Binary optics: A VLSI-based microoptics technology,” Microelectron. Eng. 32(1–4), 369–388 (1996).
[CrossRef]

Opt. Eng. (2)

D. W. Prather, “Design and application of subwavelength diffractive lenses for integration with infrared photodetectors,” Opt. Eng. 38(5), 870–878 (1999).
[CrossRef]

D. W. Prather, S. Shi, “Combined scalar-vector method for the analysis of diffractive optical elements,” Opt. Eng. 39(7), 1850–1857 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (1)

Y. Liu, H. Liu, “Rigorous vector analysis of diffractive microlens by using the finite-difference time-domain method,” Proc. SPIE 7506, 7506141–7506148 (2005).

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier optics, Third Edition, (Roberts and Company Publishers, Colorado, 2005, third edition).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, MA, 2005, third edition).

T.-F. Huang, S.-H. Hua, K.-C. Hu, and C.-w. Su, “LED chip having micro-lens structure,” (Google Patents, 2012).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the microlen integration with photodetectors and 2D Yee's grid.

Fig. 2
Fig. 2

Flowchart representation of simulated annealing optimization algorithm.

Fig. 3
Fig. 3

Efficiency and annealing temperature evolution of microlens vs. loop cycle.

Fig. 4
Fig. 4

Field distribution of conventional scalar designed structure (a) and vector based optimization structure (b).

Fig. 5
Fig. 5

Point spread function at the focal plane of initial and optimized structure.

Fig. 6
Fig. 6

Cross section profile of initial and optimized microles structure.

Equations (2)

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dE= f n f n1

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