Abstract

A two-dimensional photonic crystal diplexer integrated with a waveguide coupler is proposed. The design is computer generated through an inverse design process, limited within an area measuring 5µm×5µm. The best working device was designed for the optical communication wavelengths, 1.50µm and 1.55µm, i.e. a channel spacing of 50 nm. The device exhibits crosstalks suppressed below 40dB and coupling efficiencies close to 80%, for both channels.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (3)

L. Sanchis, A. Håkansson, D. Lopez-Zanón, J. Bravo-Abad and J. Sánchez-Dehesa, �??Integrated optical devices design by genetic algorithm,�?? Appl. Phys. Lett. 84, 4460�??4462 (2004).
[CrossRef]

Stefan Preble, Michal Lipson and Hod Lipson, �??Two-dimensional photonic crystals designed by evolutionary algorithms,�?? Appl. Phys. Lett. 86, 061111-061113 (2005).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and Kawakami S, �??Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,�?? Appl. Phys. Lett. 74, 1370�??1372 (1999).
[CrossRef]

Electron. Lett. (1)

P. Sanchis, J. Mart, A. Garca, A. Martnez and J. Blasco, �??High efficiency coupling technique for planar photonic crystal waveguides,�?? Electron. Lett. 38, 961�??962 (2002).
[CrossRef]

GECCO (1)

E. Cantú-Paz, D. E. Goldberg, �??Are multiple runs of genetic algorithms better than one?,�?? Genetic and Evolutionary Computation - GECCO 2003, PT I, Proceedings lecture notes in Computer Science 2723, 801�??812 (2003).

IEEE Antennas and Wireless Propagation (1)

Davy Pissoort and Frank Olyslager, �??Termination of periodic waveguides by PMLs in time-harmonic integral equation-like techniques,�?? IEEE Antennas and Wireless Propagation Letters 2, 281�??284 (2003).
[CrossRef]

IEEE J. Sel. Area Comm. (1)

A. Håkansson and José Sánchez-Dehesa, �??Inverse design of photonic crystal devices,�?? IEEE J. Sel. Area Comm. (2005) (to be published).
[CrossRef]

IEICE Trans. Electron. (1)

Burger M., S. J. Osher, and E. Yablonovitch, �??Inverse problem techniques for the design of photonic crystals,�?? IEICE Trans. Electron. E87C, 258�??265 (2004).

J. Lightwave Tech. (1)

S. Boscolo and M. Midrio, �??Three-dimensional multiple-scattering technique for the analysis of photonic-crystal slabs,�?? J. Lightwave Tech. 22, 2778�??2786 (2004).
[CrossRef]

J. of Appl. Phys. (1)

I. Gheorma, S. Haas, and A. Levi, �??Aperiodic nano-photonic design,�?? J. of Appl. Phys. 95, 1420-1426 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Journal of Intelligent Manufacturing (1)

B.R. Moon, Y.S. Lee and C.K. Kim, �??GEORG: VLSI circuit partitioner with a new genetic algorithm framework,�?? Journal of Intelligent Manufacturing 9, 401-412 (1998).
[CrossRef]

Nature (London) (1)

S. Noda, A. Chutinan and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature (London) 407, 608�??610 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

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, no. 035109 (2003).
[CrossRef]

Phys. Rev. E (1)

J. Geremia, J. Williams, and H. Mabuchi, �??Inverse-problem approach to designing photonic crystals for cavity QED experiments,�?? Phys. Rev. E 66, no. 066606 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Other (4)

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals, (Princeton Press, Princeton, New Jersey, 1995).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, (Prentice Hall, New Jersey, 1991).

D.E. Goldberg, Genetic Algorithms in Search, Optimization and Learning, (Addison Wesley, Reading , MA, 1989).

J.H. Holland, Adaptation in natural and Artificial Systems, (The University of Michigan Press, Ann Arbor, 1975).

Supplementary Material (1)

» Media 1: MOV (1401 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

GA representation of a PhC structure. a) The black dots correspond to the PhC structure. b) The repetition of the lattice is marked out with squares, representing the lattice sites. c) A two dimensional representation of the virtual genome. Each lattice site is filled with a binary digit, where “0” and “1” represents the presence or absence of a cylinder, respectively. d) The color scale represents the geographical linkage with respect to the central allele. Blue (red) corresponds to high (low) geographical linkage.

Fig. 2.
Fig. 2.

The fitness as a function of the coupling efficiency and the crosstalk. The nonlinear scaleing of the crosstalk parameter is implemented as Eq. (2) with α=5.

Fig. 3.
Fig. 3.

The first crystal structure optimization set-up. The blue dots marks the cylinders implemented with absorption for semi-infinite WG simulation. The green dots correspond to the PhC-WG and are fixed throughout the optimization process. Cluster-1 and Cluster-2, identified by the black and red dots/circles are the lattice sites represented by the virtual genome in the GA. The optimized structure is identified by the dots (alleles=1), the circles correspond to absent lattice sites (alleles=0). The scale used is normalized to the lattice parameter a.

Fig. 4.
Fig. 4.

The second crystal structure optimization set-up. The blue dots marks the cylinders implemented with absorption for semi-infinite WG simulation. The green dots correspond to the PhC-WG and are fixed throughout the optimization process. Cluster-1, identified by the black dots/circles are the lattice sites represented by the virtual genome in the GA. The optimized structure is identified by the dots (alleles=1), the circles correspond to absent lattice sites (alleles=0). The scale used is normalized to the lattice parameter a.

Fig. 5.
Fig. 5.

The amplitude of the electric field for (left) a 0/λ1=0.31 and (right) a 0/λ 1=0.30, where red (blue) corresponds to a large (small) amplitude. The scale used is normalized to the lattice parameter a. [Media 1]

Fig. 6.
Fig. 6.

Normalized intensity spectra of the DEMUX-WGC device in Fig. 4. The blue line corresponds to port 1 (the top wave guide), the red line to port 2 (the bottom wave guide) and the black line show the loss due to reflection. The power is normalized to the total incident power through the input port.

Tables (1)

Tables Icon

Table 1. The crosstalk attenuation and coupling efficiency for the proposed device.

Equations (6)

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{ CE λ 1 = E 1 n 1 XT λ 1 = 20 log ( E 1 n 2 E 1 n 1 )
{ CE λ 2 = E 2 n 2 XT λ 2 = 20 log ( E 2 n 1 E 2 n 2 )
( XT ) sc = 1 1 ( XT α ) 2 + 1
f = ( XT λ 1 ) sc × CE λ 1 + ( XT λ 2 ) sc × CE λ 2
x n re = 10 a sin ( n 2 arcsin 1 10 )
x n im = 10 a [ 1 cos ( n 2 arcsin 1 10 ) ]

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