Genetic optimization of photonic bandgap structures

doi:10.1364/OE.15.008218

Optics Express

Editor: C. Martijn de Sterke
Vol. 15, Iss. 13 — Jun. 25, 2007
pp: 8218–8230

Genetic optimization of photonic bandgap structures

Joel Goh, Ilya Fushman, Dirk Englund, and Jelena Vučković »View Author Affiliations

Optics Express, Vol. 15, Issue 13, pp. 8218-8230 (2007)
http://dx.doi.org/10.1364/OE.15.008218

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Abstract
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Abstract

We investigate the use of a Genetic Algorithm (GA) to design a set of photonic crystals (PCs) in one and two dimensions. Our flexible design methodology allows us to optimize PC structures for specific objectives. In this paper, we report the results of several such GA-based PC optimizations. We show that the GA performs well even in very complex design spaces, and therefore has great potential as a robust design tool in a range of PC applications.

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(140.3410) Lasers and laser optics : Laser resonators
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5750) Optical devices : Resonators
(230.6080) Optical devices : Sources

ToC Category:
Photonic Crystals

History
Original Manuscript: March 9, 2007
Revised Manuscript: May 8, 2007
Manuscript Accepted: May 10, 2007
Published: June 18, 2007

Citation
Joel Goh, Ilya Fushman, Dirk Englund, and Jelena Vučković, "Genetic optimization of photonic bandgap structures," Opt. Express 15, 8218-8230 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8218

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References

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y., Yamamoto, and J. Vučković, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95 (2005). [CrossRef] [PubMed]
M. Boroditsky, R. Vrijen, T. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, "Control of spontaneous emission in photonic crystals," Proceedings of SPIE - The International Society for Optical Engineering 3621, 190-197 (1999).
H. Altug and J. Vučković, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86 (2005). [CrossRef]
Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005). [CrossRef] [PubMed]
H. Altug and J. Vučković, "Photonic crystal nanocavity array laser," Opt. Express 13, 8819 - 8828 (2005). [CrossRef] [PubMed]
B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005). [CrossRef]
J. Vučković, M. Lon¡car, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65 (2001).
D. Englund, I. Fushman, and J. Vučković, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005). [CrossRef] [PubMed]
D.A.B. Miller Y. Jiao, S. Fan, "Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator," Opt. Lett. 30, 141-143 (2005). [CrossRef] [PubMed]
S. Preble, H. Lipson, and M. Lipson, "Two-dimensional photonic crystals designed by evolutionary algorithms," Appl. Phys. Lett. 86 (2005). [CrossRef]
R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, "Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization," Appl. Phys. Lett. 86 (2005). [CrossRef]
J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, Univ. of Michigan Press (1975). [PubMed]
D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley (1989).
L. Davis, Genetic Algorithms and Simulated Annealing, Morgan Kaufmann (1987).
L. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68 (2003). [CrossRef]
E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, "Photonic crystal fiber design by means of a genetic algorithm," Opt. Express 12, 1990-1995 (2004). [CrossRef] [PubMed]
S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003). [CrossRef] [PubMed]
P. Lalanne, S. Mias, and J. Hugonin, "Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities," Opt. Express 12, 458-467 (2004). [CrossRef] [PubMed]
A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, John Wiley and Sons Inc (2002).
L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons Inc (1995).
J. Vučkovićc, M. Pelton, A. Scherer, and Y. Yamamoto, "Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics," Phys. Rev. A 66 (2002).
R. Brent, Algorithms for Minimization Without Derivatives. Prentice-Hall (1973).

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[1] S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]

[2] E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]

[3] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y., Yamamoto, and J. Vučković, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95 (2005). [CrossRef] [PubMed]

[4] M. Boroditsky, R. Vrijen, T. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, "Control of spontaneous emission in photonic crystals," Proceedings of SPIE - The International Society for Optical Engineering 3621, 190-197 (1999).

[5] H. Altug and J. Vučković, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86 (2005). [CrossRef]

[6] Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005). [CrossRef] [PubMed]

[7] H. Altug and J. Vučković, "Photonic crystal nanocavity array laser," Opt. Express 13, 8819 - 8828 (2005). [CrossRef] [PubMed]

[8] B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005). [CrossRef]

[9] J. Vučković, M. Lon¡car, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65 (2001).

[10] D. Englund, I. Fushman, and J. Vučković, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005). [CrossRef] [PubMed]

[11] D.A.B. Miller Y. Jiao, S. Fan, "Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator," Opt. Lett. 30, 141-143 (2005). [CrossRef] [PubMed]

[12] S. Preble, H. Lipson, and M. Lipson, "Two-dimensional photonic crystals designed by evolutionary algorithms," Appl. Phys. Lett. 86 (2005). [CrossRef]

[13] R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, "Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization," Appl. Phys. Lett. 86 (2005). [CrossRef]

[14] J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, Univ. of Michigan Press (1975). [PubMed]

[15] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley (1989).

[16] L. Davis, Genetic Algorithms and Simulated Annealing, Morgan Kaufmann (1987).

[17] L. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68 (2003). [CrossRef]

[18] E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, "Photonic crystal fiber design by means of a genetic algorithm," Opt. Express 12, 1990-1995 (2004). [CrossRef] [PubMed]

[19] S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]

[20] Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003). [CrossRef] [PubMed]

[21] P. Lalanne, S. Mias, and J. Hugonin, "Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities," Opt. Express 12, 458-467 (2004). [CrossRef] [PubMed]

[22] A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, John Wiley and Sons Inc (2002).

[23] L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons Inc (1995).

[24] J. Vučkovićc, M. Pelton, A. Scherer, and Y. Yamamoto, "Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics," Phys. Rev. A 66 (2002).

[25] R. Brent, Algorithms for Minimization Without Derivatives. Prentice-Hall (1973).

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Genetic optimization of photonic bandgap structures