Abstract

We introduce a novel analysis technique for predicting thermo-optical sensitivities in photonic crystal (PC) circuits composed of either dielectric–semiconducting or metallic constituents. The proposed numerical analysis is based on a hybrid formalism of the scattering matrix technique combined with the adjoint network method. The proposed computational scheme can, with modest computational resources, predict with high accuracy, the effect of the temperature fluctuations to the light-wave propagation in PCs. Numerical simulations show that PC circuits based on metallic metamaterial platforms are significantly less sensitive to temperature variations than the usual dielectric or semiconducting PCs.

© 2006 Optical Society of America

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2005 (1)

2004 (1)

2003 (3)

B. T. Schwartz and R. Piestun, J. Opt. Soc. Am. B 20, 2448 (2003).
[CrossRef]

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

2000 (1)

P. Halevi and E. R. Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef] [PubMed]

1999 (2)

A. Chutinan and S. Noda, J. Opt. Soc. Am. B 16, 240 (1999).
[CrossRef]

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

1994 (1)

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16835 (1994).
[CrossRef]

1993 (1)

F. Alessandri, M. Mongiardo, and R. Sorrentino, IEEE Microw. Guid. Wave Lett. 3, 414 (1993).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

1972 (1)

J. W. Bandler and R. E. Seviora, IEEE Trans. Microwave Theory Tech. MTT-20, 138 (1972).
[CrossRef]

Abeles, F.

F. Abeles, Optical Properties of Solids (North-Holland, 1972).

Alessandri, F.

F. Alessandri, M. Mongiardo, and R. Sorrentino, IEEE Microw. Guid. Wave Lett. 3, 414 (1993).
[CrossRef]

Asatryan, A. A.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Bandler, J. W.

J. W. Bandler and R. E. Seviora, IEEE Trans. Microwave Theory Tech. MTT-20, 138 (1972).
[CrossRef]

Borel, P. I.

Botten, L. C.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Chutinan, A.

Fan, S.

Forchel, A.

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

Frandsen, L. H.

Halevi, P.

P. Halevi and E. R. Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef] [PubMed]

Harpoth, A.

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Jensen, J. S.

Jiao, Y.

Kamp, M.

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

Kanayama, T.

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

Klopf, F.

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

Kristensen, M.

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16835 (1994).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16835 (1994).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Mendieta, E. R.

P. Halevi and E. R. Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef] [PubMed]

Miller, D. A. B.

Mongiardo, M.

F. Alessandri, M. Mongiardo, and R. Sorrentino, IEEE Microw. Guid. Wave Lett. 3, 414 (1993).
[CrossRef]

Moroz, A.

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

Nicorovici, N. A.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Noda, S.

Piestun, R.

Pincemin, F.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16835 (1994).
[CrossRef]

Poborchii, V.

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

Reithmaier, J. P.

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

Robinson, P. A.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Schuller, C.

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

Schwartz, B. T.

Seviora, R. E.

J. W. Bandler and R. E. Seviora, IEEE Trans. Microwave Theory Tech. MTT-20, 138 (1972).
[CrossRef]

Shi, P.

Sigmund, O.

Sorrentino, R.

F. Alessandri, M. Mongiardo, and R. Sorrentino, IEEE Microw. Guid. Wave Lett. 3, 414 (1993).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Stekre, C. M.

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Taya, T.

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

V. Poborchii, T. Taya, T. Kanayama, and A. Moroz, Appl. Phys. Lett. 82, 508 (2003).
[CrossRef]

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, Appl. Phys. Lett. 82, 2767 (2003).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

F. Alessandri, M. Mongiardo, and R. Sorrentino, IEEE Microw. Guid. Wave Lett. 3, 414 (1993).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. W. Bandler and R. E. Seviora, IEEE Trans. Microwave Theory Tech. MTT-20, 138 (1972).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16835 (1994).
[CrossRef]

Phys. Rev. E (1)

R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. Stekre, Phys. Rev. E 60, 7614 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

P. Halevi and E. R. Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Other (1)

F. Abeles, Optical Properties of Solids (North-Holland, 1972).

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Figures (3)

Fig. 1
Fig. 1

Topology of a three-channel frequency-selective filter that uses planar photonic crystal waveguides composed of copper nanowires embedded in air.

Fig. 2
Fig. 2

Normalized transmission characteristics (TM polarization) for the system at T = 273 K for copper nanowires.

Fig. 3
Fig. 3

(a) Absolute thermal sensitivity as a function of temperature, and (b) normalized transmission characteristics for channel 1, for copper at various temperatures.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

[ I S 1 T 1 , 2 S 1 T 1 , N S 2 T 2 , 1 I S 2 T 2 , N S N T N , 1 S N T N , 2 q I ] [ B 1 B 2 B N ] = [ S 1 Q 1 S 2 Q 2 S N Q N ] ,
x f , subject to Z ̿ ( x ) B ¯ = V ¯ ,
x B ¯ = Z ̿ 1 ( x V ¯ x Z ̿ B ¯ ) .
x f = x e f + B ̂ T ( x V ¯ x Z ̿ B ¯ ) ,
Z ̿ T B ̂ = ( B ¯ f ) T .
ϵ m = 1 ϵ ω p 2 + ν c 2 ω 2 + ν c 2 + j ϵ ω p 2 + ν c 2 ω ν c ω 2 + ν c 2 ,
ν c ( ω , T ) = ν c 0 [ 1 + ( h ω 2 π k B T ) 2 ] ,
ϵ ( ω , T ) = ϵ d [ 1 ω p 2 ( T ) ω 2 ] , ω p 2 ( T ) = i 4 π n i e 2 m i ϵ d ,
n e ( T ) = 5.76 × 10 14 T 3 2 exp ( 0.13 k B T ) ,

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