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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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  5. L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B68, no. 035109 (2003).
    [Crossref]
  6. Stefan Preble, Michal Lipson, and Hod Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86, 061111–061113 (2005).
    [Crossref]
  7. M. Burger, S. J. Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. Andreas H°akansson and José Sánchez-Dehesa, “Comment on ‘Optimization of photonic crystal structures’, J. Opt. Soc. Am. A 21, 2223–2232 (2004),” arXiv.org, cond-mat/0504581 (2005)
    [Crossref]
  25. E. Cantú-Paz and 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).
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    [Crossref]

2005 (1)

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

2004 (8)

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

I. Gheorma, S. Haas, and A. Levi, “Aperiodic nano-photonic design,” J. of Appl. Phys. 95, 1420–1426 (2004).
[Crossref]

P. Borel, A. Harpoth, L. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004).
[Crossref] [PubMed]

Jasmin Smajic, Christian Hafner, and Daniel Erni, “Optimization of photonic crystal structures,” J. Opt. Soc. Am. A 21, 2223–2232 (2004).
[Crossref]

Davy Pissoort, Bart Denecher, Peter Bienstman, Fank Olyslager, and Danil De Zutter, “Comparative study of three methods for the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).
[Crossref]

Andreas H°akansson and José Sánchez-Dehesa, “Comment on ‘Optimization of photonic crystal structures’, J. Opt. Soc. Am. A 21, 2223–2232 (2004),” arXiv.org, cond-mat/0504581 (2005)
[Crossref]

L. Sanchis, A. H°akansson, 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]

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]

2003 (3)

E. Cantú-Paz and 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).

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]

P. Bienstman, S. Assefa, S.G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into PhC slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[Crossref]

2002 (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]

2001 (1)

2000 (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]

1999 (1)

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

1998 (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]

1987 (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]

Assefa, S.

Bienstman, P.

Bienstman, Peter

Blasco, J.

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]

Borel, P.

Boscolo, S.

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]

Bravo-Abad, J.

L. Sanchis, A. H°akansson, 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]

Burger, M.

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

Cantú-Paz, E.

E. Cantú-Paz and 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).

Chutinan, A.

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]

Denecher, Bart

Erni, Daniel

Forchel, A.

Frandsen, L.

Garca, A.

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]

Geremia, J.

J. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E66, no. 066606 (2002).
[Crossref]

Gheorma, I.

I. Gheorma, S. Haas, and A. Levi, “Aperiodic nano-photonic design,” J. of Appl. Phys. 95, 1420–1426 (2004).
[Crossref]

Goldberg, D. E.

E. Cantú-Paz and 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).

Goldberg, D.E.

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

H°akansson, A.

L. Sanchis, A. H°akansson, 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]

H°akansson, Andreas

Haas, S.

I. Gheorma, S. Haas, and A. Levi, “Aperiodic nano-photonic design,” J. of Appl. Phys. 95, 1420–1426 (2004).
[Crossref]

Hafner, Christian

Håkansson, A.

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

Happ, T.D.

Harpoth, A.

He, S.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B68, no. 035109 (2003).
[Crossref]

Holland, J.H.

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

Imada, M.

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]

Ishimaru, A.

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

Jensen, J. S.

Joannopoulos, J. D.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Johnson, S.G.

Kamp, M.

Kawakami, S

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

Kawashima, T.

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

Kim, C.K.

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]

Kolodziejski, L. A.

Kosaka, H.

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

Kristensen, M.

Lee, Y.S.

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]

Levi, A.

I. Gheorma, S. Haas, and A. Levi, “Aperiodic nano-photonic design,” J. of Appl. Phys. 95, 1420–1426 (2004).
[Crossref]

Lipson, Hod

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

Lipson, Michal

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

Lopez-Zanón, D.

L. Sanchis, A. H°akansson, 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]

Mabuchi, H.

J. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E66, no. 066606 (2002).
[Crossref]

Mart, J.

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]

Martnez, A.

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]

Meade, R. D.

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

Midrio, M.

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]

Moon, B.R.

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]

Noda, S.

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]

Notomi, M.

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

Olyslager, Fank

Olyslager, Frank

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]

Osher, S. J.

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

Petrich, G. S.

Pissoort, Davy

Davy Pissoort, Bart Denecher, Peter Bienstman, Fank Olyslager, and Danil De Zutter, “Comparative study of three methods for the simulation of two-dimensional photonic crystals,” J. Opt. Soc. Am. A 21, 2186–2195 (2004).
[Crossref]

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]

Preble, Stefan

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

Sánchez-Dehesa, J.

L. Sanchis, A. H°akansson, 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]

Sánchez-Dehesa, José

Sanchis, L.

L. Sanchis, A. H°akansson, 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]

Sanchis, P.

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]

Sato, T.

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

Shen, L.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B68, no. 035109 (2003).
[Crossref]

Shi, P.

Sigmund, O.

Smajic, Jasmin

Tamamura, T.

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

Tomita, A.

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

Williams, J.

J. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E66, no. 066606 (2002).
[Crossref]

Winn, J. N.

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

Yablonovitch, E.

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

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Ye, Z.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B68, no. 035109 (2003).
[Crossref]

Zutter, Danil De

Appl. Phys. Lett. (3)

L. Sanchis, A. H°akansson, 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 S Kawakami, “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]

Genetic and Evolutionary Computation - GECCO 2003, PT I, Proceedings lecture notes in Computer Science (1)

E. Cantú-Paz and 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 Letters (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]

IEICE Trans. Electron. (1)

M. Burger, 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. 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 (7)

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

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B68, no. 035109 (2003).
[Crossref]

J. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E66, no. 066606 (2002).
[Crossref]

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

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)

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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)

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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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