Application of Genetic Algorithm for Optimization Photonic Crystals

Alireza Rezaee

Abstract


In this paper, great attention has been paid to photonic crystals due to their potential applications in ultra compact photonic integrated circuits. The goal of this work is applying a genetic algorithm to search for photonic crystals with large band gaps. The algorithm adopted in this work is based on introducing single-pixel perturbations to an initial seed with small relative band gap. Each filling pattern of the grids is translated into a matrix of binary elements. By applying innovative crossover and mutation operators, the number of generations needed to achieve the fittest photonic crystal structure is considerably reduced. Besides, the required time to get optimal structure is significantly decreased. This is due to decreasing both the time needed to evaluate a band structure of each chromosome and generation number.  Because of this efficient method, the required computation time of the fitness function is significantly decreased. The paper presents two optimized photonic crystal structures with almost 21% relative band gap.


Keywords


genetic, crystal, optimization, photonic.

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References


J. D. Joannopoulos, R. D. Meade, and N. J. Winn, Photonic Crystals: Molding the Flow of Light Princeton, NJ, Sept. 1995.

K. Busch, S. Lolkes, R. B. Wehrspohn, and H. Foll, Photonic Crystals: advances in design, fabrication, and characterization, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2004.

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B, vol. 60, pp. 5751–5758, 1999.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic crystal slabs,” Phys. Rev. B, vol. 62, pp. 8212–8222, 2000.

M. Imdada, S. Noda, A. Chutinan, M. Mochizuk, and T. Tanaka, “Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide,” J. of Lightwave Tech., vol. 20, pp. 873-878, 2002.

H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. of Selected Topics in Quantum Electronics, vol. 8, pp. 891-908, 2002.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, ‘‘Novel applications of photonic bandgap materials: Low-loss bends and high-Q cavities,’’ J. Appl. Phys. vol. 75, pp. 4753–4755, 1994.

Z. Li, B. Gu, and G. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett., vol. 81, pp. 2574-2577, 1998.

C. S. Kee, J. E. Kim, and H. Y. Park, “ Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air,” Phys. Rev. E., vol. 56, pp. 6291-6293, 1997.

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett., vol. 77, pp. 2949-2952, 1996.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Appl. Phys. Lett., vol. 61, pp. 495-497, 1992.

Z. Li, J. Wang, and B. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B., vol. 58, pp. 3721-3729, 1998.

C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B., vol. 56, pp. 7313-7320, 1997.

M. Mitchell, An introduction to genetic algorithms, MIT Press, 1996.

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., vol. 68, pp. 035109, 2003.

C. Chen, A. Sharkawy, S. Shi, and D. W. Prather, “Band gap optimization of 2-dimensional photonic crystals,” Proc. of SPIE, vol.5360, pp. 69-76, 2004.

Z. Ye, L. Shen, and S. He, “Design for 2D anisotropic photonic crystal with large absolute band gaps by using a genetic algorithm,” Phys. Rev. B., vol. 37, pp. 417-419, 2004.




DOI: http://dx.doi.org/10.22385/jctecs.v11i0.161