Abstract

A device for optical switches and logic gates is proposed in two-dimensional photonic crystals based on self-collimated beams. The main structure of the device is a line-defect-induced 3 dB splitter. Operating principle, as revealed by both theoretical calculation and finite-difference time-domain simulation, is based on the interference of reflected and transmitted self-collimated beams. This device is potentially applicable for photonic integrated circuits.

© 2007 Optical Society of America

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References

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  1. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
    [CrossRef]
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
    [CrossRef]
  6. J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
    [CrossRef]
  7. X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
  8. S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).
  9. M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).
  10. C. Chen, A. Sharkawy, D. M. Pustai, S. Shi, and D. W. Prather, "Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides," Opt. Express 11, 3153-3159 (2003).
    [CrossRef] [PubMed]
  11. B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
    [CrossRef]
  12. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
    [CrossRef]
  13. M. F. Yanki, S. Fan, M. Soljačić, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2508 (2003).
    [CrossRef]
  14. N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
    [CrossRef]
  15. Z.-H. Zhu, W.-M. Ye, J.-R. Ji, X.-D. Yuan, and C. Zen, "High-contrast light-by-light switching and AND gate based on nonlinear photonic crystals," Opt. Express 14, 1783-1788 (2006).
    [CrossRef] [PubMed]
  16. R. S. Chu and T. Tamir, "Group velocity in space-time periodic media," Electron. Lett. 7, 410-412 (1971).
    [CrossRef]
  17. Z. Y. Ou and L. Mandel, "Derivation of reciprocity relations for a beam splitter from energy balance," Am. J. Phys. 57, 66-67 (1989).
    [CrossRef]
  18. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, 1998), chap. 3.1.

2007 (2)

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

2006 (2)

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Z.-H. Zhu, W.-M. Ye, J.-R. Ji, X.-D. Yuan, and C. Zen, "High-contrast light-by-light switching and AND gate based on nonlinear photonic crystals," Opt. Express 14, 1783-1788 (2006).
[CrossRef] [PubMed]

2005 (2)

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

2003 (4)

2002 (1)

J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

1989 (1)

Z. Y. Ou and L. Mandel, "Derivation of reciprocity relations for a beam splitter from energy balance," Am. J. Phys. 57, 66-67 (1989).
[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]

1971 (1)

R. S. Chu and T. Tamir, "Group velocity in space-time periodic media," Electron. Lett. 7, 410-412 (1971).
[CrossRef]

Bona, G.-L.

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Chen, C.

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

C. Chen, A. Sharkawy, D. M. Pustai, S. Shi, and D. W. Prather, "Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides," Opt. Express 11, 3153-3159 (2003).
[CrossRef] [PubMed]

Chen, X.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

Chu, R. S.

R. S. Chu and T. Tamir, "Group velocity in space-time periodic media," Electron. Lett. 7, 410-412 (1971).
[CrossRef]

Fan, S.

Harbers, R.

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Ji, J.-R.

Jiang, X.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

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]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Kee, C.-S.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

Kim, J.-E.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

Kim, M.-W.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

Kim, T.-T.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Lee, S.-G.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

Loncar, M.

J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
[CrossRef]

Mahrt, R. F.

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Mandel, L.

Z. Y. Ou and L. Mandel, "Derivation of reciprocity relations for a beam splitter from energy balance," Am. J. Phys. 57, 66-67 (1989).
[CrossRef]

Miao, B.

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Moll, N.

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Oh, S. S.

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

Ou, Z. Y.

Z. Y. Ou and L. Mandel, "Derivation of reciprocity relations for a beam splitter from energy balance," Am. J. Phys. 57, 66-67 (1989).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
[CrossRef]

Park, H. Y.

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

Prather, D. W.

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

C. Chen, A. Sharkawy, D. M. Pustai, S. Shi, and D. W. Prather, "Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides," Opt. Express 11, 3153-3159 (2003).
[CrossRef] [PubMed]

Pustai, D. M.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Scherer, A.

J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Sharkawy, A.

Shi, S.

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

C. Chen, A. Sharkawy, D. M. Pustai, S. Shi, and D. W. Prather, "Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides," Opt. Express 11, 3153-3159 (2003).
[CrossRef] [PubMed]

Soljacic, M.

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Tamir, T.

R. S. Chu and T. Tamir, "Group velocity in space-time periodic media," Electron. Lett. 7, 410-412 (1971).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
[CrossRef]

Witzens, J.

J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yanki, M. F.

Yao, P.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

Ye, W.-M.

Yu, X.

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Yuan, X.-D.

Zen, C.

Zhang, J.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

Zhao, D.

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

Zhu, Z.-H.

Am. J. Phys. (1)

Z. Y. Ou and L. Mandel, "Derivation of reciprocity relations for a beam splitter from energy balance," Am. J. Phys. 57, 66-67 (1989).
[CrossRef]

Appl. Phys. Lett. (6)

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Line-defect-induced bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 87, 1811061-3 (2005).

M.-W. Kim, S.-G. Lee, T.-T. Kim, J.-E. Kim, H. Y. Park, and C.-S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett. 90, 1131211-3 (2007).

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, "Photonic crystal Mach-Zehnder interferometer based on self-collimation," Appl. Phys. Lett. 90, 231114-1 (2007).
[CrossRef]

N. Moll, R. Harbers, R. F. Mahrt, and G.-L. Bona, "Integrated all-optical switch in a cross-waveguide geometry," Appl. Phys. Lett. 88, 1711041-3 (2006).
[CrossRef]

Electron. Lett. (1)

R. S. Chu and T. Tamir, "Group velocity in space-time periodic media," Electron. Lett. 7, 410-412 (1971).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Witzens, M. Lončar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Top. Quantum Electron. 8, 1246-1257 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. Miao, C. Chen, S. Shi, and D. W. Prather, "A high-efficiency in-plane splitting coupler for planar photonic crystal self-collimation devices," IEEE Photon. Technol. Lett. 17, 61-63 (2005).
[CrossRef]

Nature (London) (1)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature (London),  426, 404 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B,  58, R10096-R10099 (1998).
[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 (1)

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, 1998), chap. 3.1.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the proposed optical switches and logic gates. The defect region (green area, the reducing Si rods) and the surrounding region (cyan area, the host rods) corresponds to an optically thinner medium (low refractive index, nL) and an optically denser medium (high refractive index, nH), respectively.

Fig. 2.
Fig. 2.

(a). Band diagram of the PC structure for E -polarized mode. The inset shows the PC structure, which consists of square lattice of Si rods in air. The frequency 0.194(a/λ) is marked by the orange line. (b) Equifrequency contours of the first band.

Fig. 3.
Fig. 3.

Simulated steady-state field distribution of the E -polarized mode at 0.194(a/λ) when incident beams propagate along the Γ-M direction. (a) and (b) for the case that the incident beam is only launched into face I1 and I2, respectively.

Fig. 4.
Fig. 4.

(a). Schematic diagram of the switch. Two beams with different phases are incident on the input faces I1 and I2. (b) and (c) Simulated steady-state field distribution of the E -polarized mode at 0.194(a/λ) when incident beams propagate along the Γ-M direction. The phase difference φ12 of the two incident beams particularly sets as π/2 and -π/2, respectively.

Fig. 5.
Fig. 5.

(a). The normalized intensity spectra of faces O1 (green line) and O2 (violet line) for Fig. 3(a). The red line represents the total output efficiency. (b) The normalized intensity and extinction ratio spectra for Fig. 4(b).

Tables (1)

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Table 1. The total device functions.

Equations (4)

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t 2 + r 2 = 1
T I 1 = E 1 · te i φ = uE e i ( φ 1 φ ) 2 R I 1 = E 1 · re i ( φ + π 2 ) = uE e i ( φ 1 φ π 2 ) 2 T I 2 = E 2 · te i φ = uE e i ( φ 2 φ ) 2 R I 2 = E 2 · re i ( φ + π 2 ) = uE e i ( φ 2 φ π 2 ) 2 }
O 1 = R I 1 + T I 2 = uE e i ( φ 1 φ π 2 ) 2 + uEe i ( φ 2 φ ) 2 = 2 uE cos ( φ 1 φ 2 2 + π 4 ) e i ( φ 1 + φ 2 2 φ π 4 ) O 2 = R I 2 + T I 1 = uE e i ( φ 2 φ π 2 ) 2 + uEe i ( φ 1 φ ) 2 = 2 uE cos ( φ 1 φ 2 2 + π 4 ) e i ( φ 1 + φ 2 2 φ π 4 ) }
I O 1 = O 1 2 = 2 uE 2 cos 2 ( φ 1 φ 2 2 + π 4 ) = uE 2 [ 1 + sin ( φ 1 φ 2 ) ] I O 2 = O 2 2 = 2 uE 2 cos 2 ( φ 1 φ 2 2 + π 4 ) = uE 2 [ 1 sin ( φ 1 φ 2 ) ] }

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