Abstract

We present a concept of graded photonic crystals used to enhance the control of light propagation. Gradual modifications of the lattice periodicity make it possible to bend the light at the micrometer scale. This effect is tailored by parametric studies of the isofrequency curves. As a demonstration, we propose a two-dimensional graded photonic crystal that could provide frequency-selective tunable bending.

© 2005 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).
  2. J. P. Dowling has compiled a bibliography at http://phys.lsu.edu/~jdowling/pbgbib.html.
  3. M. Augustin, H. J. Fuchs, D. Sechelle, E. B. Kley, S. Nolte, and A. Tünnermann, Opt. Express 11, 3284 (2003).
    [CrossRef] [PubMed]
  4. S. Fan, H. Haus, P. R. Villeneuve, and J. D. Joannopoulos, Opt. Express 3, 4 (1998).
    [CrossRef] [PubMed]
  5. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
    [CrossRef]
  6. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
    [CrossRef]
  7. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
    [CrossRef]
  8. B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
    [CrossRef]
  9. A. L. Cabuz, E. Centeno, and D. Cassagne, Appl. Phys. Lett. 84, 2031 (2004).
    [CrossRef]
  10. T. Ochiai and J. Sanchez-Dehesa, Phys. Rev. B 64, 245113 (2001).
    [CrossRef]
  11. L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. Ph. Lalanne and A. Talneau, French patent 0115057 (November 21, 2001).
  19. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  21. M. Notomi, Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  22. X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
    [CrossRef]
  23. E. Centeno and D. Felbacq, J. Opt. Soc. Am. A 17, 320 (2000).
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    [CrossRef]
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    [CrossRef] [PubMed]

2005 (1)

X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
[CrossRef]

2004 (5)

2003 (2)

2002 (4)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

A. Talneau, Ph. Lalanne, M. Agio, and C. M. Soukoulis, Opt. Lett. 27, 1522 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

2001 (3)

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

T. Ochiai and J. Sanchez-Dehesa, Phys. Rev. B 64, 245113 (2001).
[CrossRef]

2000 (3)

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

1998 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

S. Fan, H. Haus, P. R. Villeneuve, and J. D. Joannopoulos, Opt. Express 3, 4 (1998).
[CrossRef] [PubMed]

1994 (1)

Agio, M.

Augustin, M.

Baba, T.

Baerh-Jones, T.

J. Witzens, M. Hochberg, T. Baerh-Jones, and A. Scherer, Phys. Rev. E 69, 46609 (2004).
[CrossRef]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Cabuz, A. L.

A. L. Cabuz, E. Centeno, and D. Cassagne, Appl. Phys. Lett. 84, 2031 (2004).
[CrossRef]

Cassagne, D.

A. L. Cabuz, E. Centeno, and D. Cassagne, Appl. Phys. Lett. 84, 2031 (2004).
[CrossRef]

Cassan, E.

Centeno, E.

A. L. Cabuz, E. Centeno, and D. Cassagne, Appl. Phys. Lett. 84, 2031 (2004).
[CrossRef]

E. Centeno and D. Felbacq, J. Opt. Soc. Am. A 17, 320 (2000).
[CrossRef]

Chigrin, D. N.

Chutinan, A.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

Dowling, J. P.

J. P. Dowling has compiled a bibliography at http://phys.lsu.edu/~jdowling/pbgbib.html.

Echizen, M.

Enoch, S.

Fan, S.

Fedeli, J. M.

Felbacq, D.

Fuchs, H. J.

Gralak, B.

Haus, H.

Hochberg, M.

J. Witzens, M. Hochberg, T. Baerh-Jones, and A. Scherer, Phys. Rev. E 69, 46609 (2004).
[CrossRef]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Imada, M.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

Joannopoulos, J. D.

C. Luo, M. Soljacic, and J. D. Joannopoulos, Opt. Lett. 29, 745 (2004).
[CrossRef] [PubMed]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

S. Fan, H. Haus, P. R. Villeneuve, and J. D. Joannopoulos, Opt. Express 3, 4 (1998).
[CrossRef] [PubMed]

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

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kempa, K.

X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
[CrossRef]

Kley, E. B.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Krauss, T. F.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Lalanne, Ph.

A. Talneau, Ph. Lalanne, M. Agio, and C. M. Soukoulis, Opt. Lett. 27, 1522 (2002).
[CrossRef]

Ph. Lalanne and A. Talneau, French patent 0115057 (November 21, 2001).

Laval, S.

Lidoriskis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Luo, C.

C. Luo, M. Soljacic, and J. D. Joannopoulos, Opt. Lett. 29, 745 (2004).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Lupu, A.

Lyan, P.

Matsumoto, T.

Maystre, D.

Mazilu, M.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Meade, R.

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

Melhaoui, L. El.

Mochizuki, M.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

Noda, S.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

Nolte, S.

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Ochiai, T.

T. Ochiai and J. Sanchez-Dehesa, Phys. Rev. B 64, 245113 (2001).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Ren, Z. F.

X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
[CrossRef]

Sanchez-Dehesa, J.

T. Ochiai and J. Sanchez-Dehesa, Phys. Rev. B 64, 245113 (2001).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Scherer, A.

J. Witzens, M. Hochberg, T. Baerh-Jones, and A. Scherer, Phys. Rev. E 69, 46609 (2004).
[CrossRef]

Sechelle, D.

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Soljacic, M.

Sotomayor Torres, C. M.

Soukoulis, C. M.

Talneau, A.

A. Talneau, Ph. Lalanne, M. Agio, and C. M. Soukoulis, Opt. Lett. 27, 1522 (2002).
[CrossRef]

Ph. Lalanne and A. Talneau, French patent 0115057 (November 21, 2001).

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Tayeb, G.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Tünnermann, A.

Villeneuve, P. R.

Wang, X.

X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
[CrossRef]

Winn, J.

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

Witzens, J.

J. Witzens, M. Hochberg, T. Baerh-Jones, and A. Scherer, Phys. Rev. E 69, 46609 (2004).
[CrossRef]

Wu, L.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

Appl. Phys. Lett. (4)

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, Appl. Phys. Lett. 79, 2690 (2001).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

A. L. Cabuz, E. Centeno, and D. Cassagne, Appl. Phys. Lett. 84, 2031 (2004).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, Appl. Phys. Lett. 86, 61105 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, IEEE J. Quantum Electron. 38, 915 (2002).
[CrossRef]

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

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. B (4)

T. Ochiai and J. Sanchez-Dehesa, Phys. Rev. B 64, 245113 (2001).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Phys. Rev. E (2)

J. Witzens, M. Hochberg, T. Baerh-Jones, and A. Scherer, Phys. Rev. E 69, 46609 (2004).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidoriskis, and J. D. Joannopoulos, Phys. Rev. E 66, 66608 (2002).
[CrossRef]

Other (3)

Ph. Lalanne and A. Talneau, French patent 0115057 (November 21, 2001).

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

J. P. Dowling has compiled a bibliography at http://phys.lsu.edu/~jdowling/pbgbib.html.

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Figures (3)

Fig. 1
Fig. 1

IF curves for the wavelength 1550 nm and for three aspect ratios. The solid curve corresponds to a square lattice ( ρ = 1.00 ) ; the dotted and the dashed curves are obtained for ρ = 1.04 and ρ = 1.08 , respectively. The vertical line is the construction line corresponding to an incident angle of 11°, and the arrows indicate the light propagation directions.

Fig. 2
Fig. 2

Design of the graded photonic crystal. GPC2 is constituted by n b x columns and by n b y layers. The number of the corresponding layer and column defines the air hole positions inside GPC2.

Fig. 3
Fig. 3

Map of the modulus of the Poynting vector. The Gaussian beam is curved inside the GPC. The arrows indicate the position of the center of the incident and transmitted beams. (a) For λ = 1550 nm ; the lateral shift is about 22 μ m . (b) For the shorter wavelength λ = 1530 nm , the shift decreases to 18 μ m .

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