Abstract

A comprehensive analysis of an optically tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented. We demonstrate that, under certain circumstances, if one modifies the band structure of the crystal through the Kerr effect induced by a pump beam, the refraction angle of the transmitted signal beam can be tuned over tens of degrees. Two complementary geometries are considered, namely, air holes in a dielectric background and dielectric rods surrounded by air, and in both cases the TE and TM polarizations are studied. We also show that, because of the slow light effect, in both cases the optical power required to tune the refracted angle is dramatically reduced if the frequency of the pump beam is close to a photonic bandgap edge.

© 2004 Optical Society of America

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2004 (1)

N. C. Panoiu, M. Bahl, and R. M. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Exp. 12, 1605–1610 (2004), http://www.opticsexpress.org.
[CrossRef]

2003 (7)

M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003).
[CrossRef] [PubMed]

A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, “Electro-optic control of the superprism effect in photonic crystals,” Appl. Phys. Lett. 82, 3176–3178 (2003).
[CrossRef]

N. C. Panoiu, M. Bahl, and R. M. Osgood, “Optically tunable superprism effect in nonlinear photonic crystals,” Opt. Lett. 28, 2503–2505 (2003).
[CrossRef] [PubMed]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef] [PubMed]

M. Bahl, N. C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects,” Phys. Rev. E 67, 056604 (2003).
[CrossRef]

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

2002 (4)

W. Park and C. J. Summers, “Extraordinary refraction and dispersion in two-dimensional photonic crystal slabs,” Opt. Lett. 27, 1397–1399 (2002).
[CrossRef]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38, 915–918 (2002).
[CrossRef]

K. B. Chung and S. W. Hong, “Wavelength demultiplexers based on the superprism phenomena in photonic crystals,” Appl. Phys. Lett. 81, 1549–1551 (2002).
[CrossRef]

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
[CrossRef]

2001 (2)

V. Lousse and J. P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
[CrossRef]

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature (London) 414, 289–293 (2001).
[CrossRef]

2000 (6)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

P. Halevi and F. R. Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85, 1875–1878 (2000).
[CrossRef] [PubMed]

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]

M. J. Steel, M. Levy, and R. M. Osgood, “High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects,” IEEE Photonics Technol. Lett. 12, 1171–1173 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, “Large magnetooptical Kerr rotation with high reflectivity from photonic bandgap structures with defects,” J. Lightwave Technol. 18, 1289–1296 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, “Photonic bandgaps with defects and the enhancement of Faraday rotation,” J. Lightwave Technol. 18, 1297–1308 (2000).
[CrossRef]

1999 (5)

O. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[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]

K. Bush and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[CrossRef]

1998 (6)

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]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of crosstalk in waveguide intersections,” Opt. Lett. 23, 1855–1857 (1998).
[CrossRef]

B. D’Urso, O. Painter, J. O’Brian, T. Tombrello, A. Yariv, and A. Scherer, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities,” J. Opt. Soc. Am. B 15, 1155–1159 (1998).
[CrossRef]

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

1996 (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771–1773 (1996).
[CrossRef] [PubMed]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

1990 (3)

K. M. Ho, K. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1880 (1990).
[CrossRef] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
[CrossRef] [PubMed]

1989 (1)

E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case,” Phys. Rev. Lett. 63, 1950–1953 (1989).
[CrossRef] [PubMed]

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]

Albert, J. P.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Baba, T.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
[CrossRef]

Bahl, M.

N. C. Panoiu, M. Bahl, and R. M. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Exp. 12, 1605–1610 (2004), http://www.opticsexpress.org.
[CrossRef]

M. Bahl, N. C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects,” Phys. Rev. E 67, 056604 (2003).
[CrossRef]

N. C. Panoiu, M. Bahl, and R. M. Osgood, “Optically tunable superprism effect in nonlinear photonic crystals,” Opt. Lett. 28, 2503–2505 (2003).
[CrossRef] [PubMed]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Bo, X. Z.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature (London) 414, 289–293 (2001).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Briot, O.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Bristow, A. D.

A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Bush, K.

K. Bush and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Cassagne, D.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Centeno, E.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Chan, K. T.

K. M. Ho, K. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chen, Y.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Chow, E.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Chung, K. B.

K. B. Chung and S. W. Hong, “Wavelength demultiplexers based on the superprism phenomena in photonic crystals,” Appl. Phys. Lett. 81, 1549–1551 (2002).
[CrossRef]

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]

Coquillat, D.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

D’Urso, B.

d’Yerville, M.

D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Fan, S.

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
[CrossRef]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of crosstalk in waveguide intersections,” Opt. Lett. 23, 1855–1857 (1998).
[CrossRef]

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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
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M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003).
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P. Halevi and F. R. Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85, 1875–1878 (2000).
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S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of crosstalk in waveguide intersections,” Opt. Lett. 23, 1855–1857 (1998).
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S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
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S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
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A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
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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).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, “Electro-optic control of the superprism effect in photonic crystals,” Appl. Phys. Lett. 82, 3176–3178 (2003).
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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).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
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Levy, M.

Lin, S. Y.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
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Malkova, N.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, “Electro-optic control of the superprism effect in photonic crystals,” Appl. Phys. Lett. 82, 3176–3178 (2003).
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L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, “Superprism phenomena in planar photonic crystals,” IEEE J. Quantum Electron. 38, 915–918 (2002).
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R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
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A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998).
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A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
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P. Halevi and F. R. Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85, 1875–1878 (2000).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
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Panoiu, N. C.

N. C. Panoiu, M. Bahl, and R. M. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Exp. 12, 1605–1610 (2004), http://www.opticsexpress.org.
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M. Bahl, N. C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects,” Phys. Rev. E 67, 056604 (2003).
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N. C. Panoiu, M. Bahl, and R. M. Osgood, “Optically tunable superprism effect in nonlinear photonic crystals,” Opt. Lett. 28, 2503–2505 (2003).
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R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
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D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

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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).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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[CrossRef]

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K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[CrossRef]

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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
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Soukoulis, C. M.

K. M. Ho, K. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
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Straub, M.

M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003).
[CrossRef] [PubMed]

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Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature (London) 414, 289–293 (2001).
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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
[CrossRef]

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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]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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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).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
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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).
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D. Peyrade, J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, Y. Chen, L. M. Ferlazzo, S. Ruffenach, O. Briot, M. d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert, “Equifrequency surfaces in GaN/sapphire photonic crystals,” Photonics Spectra 17, 423–425 (2003).

Ventura, M.

M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003).
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V. Lousse and J. P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
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[CrossRef]

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Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature (London) 414, 289–293 (2001).
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A. D. Bristow, J. P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides,” Appl. Phys. Lett. 83, 851–853 (2003).
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RSoft Design Group, http://www.rsoftdesign.com.

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Figures (10)

Fig. 1
Fig. 1

Schematic design of a device based on the optically controlled superprism effect in a nonlinear PC.

Fig. 2
Fig. 2

(a) PBS of the TE modes for an air-hole hexagonal PC at P=0. (b) The band corresponding to the signal frequency ωs=0.672 calculated for P=0 (solid curve) and P/a=20 W/µm2. In the latter case, the pump frequency is ωp=0.15 (dashed–dotted curve) and ωp=0.21 (dotted curve).

Fig. 3
Fig. 3

Equifrequency dispersion curves at ωs=0.672, calculated for P=0 (solid lines) and P0 (dashed lines). The dotted line and the dashed–dotted circle represent the input facet of the PC and the dispersion curve of the air modes, respectively.

Fig. 4
Fig. 4

Refraction angle θr versus the intensity P/a. The continuous curve shows θr versus the intensity P/a for the case in which only the signal beam is present (see text for details).

Fig. 5
Fig. 5

Refraction angle θr versus the pump intensity P/a for different incident angles θi in the case in which only the signal beam with ωs=0.672 is present.

Fig. 6
Fig. 6

(a) PBS of the TM modes for an air-hole hexagonal PC at P=0. (b) The band corresponding to the signal frequency ωs=0.211 calculated for P=0 (solid curve) and P/a=15 W/µm2. In the latter case, the pump frequency is ωp=0.1 (dashed–dotted curve) and ωp=0.2 (dotted curve).

Fig. 7
Fig. 7

Equifrequency dispersion curves at (a) ω=0.211 and (b) ω=0.381 calculated for P=0 (solid lines) and P0 (dashed lines). The vertical lines correspond to a beam incident from air at (a) θi=50° and (b) θi=9°. The dotted line and the dashed–dotted circle represent the input facet of the PC and the dispersion curve of the air modes, respectively.

Fig. 8
Fig. 8

Refraction angle θr versus the intensity P/a. The continuous curve shows θr versus the intensity P/a for the case in which only the signal beam is present. At θr=90, total reflection occurs (see text for details).

Fig. 9
Fig. 9

(a) PBS of the TM modes for an hexagonal lattice of dielectric rods surrounded by air at P=0. (b) The band corresponding to the signal frequency ωs=0.23 calculated for P=0 (solid curve) and P/a=15 W/µm2. In the latter case, the pump frequency is ωp=0.1 (dashed–dotted curve) and ωp=0.215 (dotted curve).

Fig. 10
Fig. 10

Refraction angle θr versus the intensity P/a. The continuous curve shows θr versus the intensity P/a for the case in which only the signal beam is present.

Equations (7)

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

×[-1(r)×H(r)]=(ω2/c2)H(r),
-1(r)=GG-1 exp(iG·r),
Hk(r)=Gλ=1,2hGλ exp(iG·r)eˆGλ,
Gλ=1,2MGλ,GλhGλ=(ω2/c2)hGλ.
MGλ,Gλ=G-G-1[(k+G)×eˆGλ] × [(k+G)×eˆGλ].
h·kM·h=2ω(k)c2kω(k),
P=0(r)|Ek(r)|2vg(k)a/2

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