Abstract

We study the cascaded quadratic nonlinear interaction between a weak fundamental and an intense second-harmonic beam within a finite one-dimensional photonic crystal with a defect. We show that, in the neighborhood of the defect resonance, this quadratic interaction induces changes in the value of the effective index of refraction and in the effective group velocity of the fundamental wave as well. We show that the effective group velocity can actively be controlled by means of this cascaded interaction. In fact, the strongly reduced effective group velocity found at the resonance of the linear periodic structure is shown to be restored to a value close to its value in the homogeneous material. These effective group and phase velocity active changes were studied in two cascading cases. Both effects are present when the nonlinear interaction modifies the defect resonance.

© 2002 Optical Society of America

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]
  2. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  3. S. Trillo, S. Wabnitz, R. Chisari, and G. Cappellini, “Two-wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos,” Opt. Lett. 17, 637–639 (1992).
    [CrossRef] [PubMed]
  4. A. E. Kaplan, “Eigenmodes of χ(2) wave mixings: cross-induced second-order nonlinear refraction,” Opt. Lett. 18, 1223–1225 (1993).
    [CrossRef] [PubMed]
  5. P. St. J. Russell, “All-optical high gain transistor action using second-order nonlinearities,” Electron. Lett. 29, 1228–1229 (1993).
    [CrossRef]
  6. Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
    [CrossRef]
  7. C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
    [CrossRef]
  8. L. Lefort and A. Barthelemy, “Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching,” Opt. Commun. 119, 163–166 (1995).
    [CrossRef]
  9. C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
    [CrossRef]
  10. M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
    [CrossRef]
  11. L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).
  12. N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).
  13. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
    [CrossRef]
  14. K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two-and three-dimensional photonic crystals,” Opt. Express 4, 167–176 (1999).
    [CrossRef] [PubMed]
  15. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge lasers: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
    [CrossRef]
  16. K. Sakoda and K. Ohtaka, “Sum-frequency generation in atwo-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
    [CrossRef]
  17. K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
    [CrossRef]
  18. J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
    [CrossRef]
  19. L. Brillouin, Wave Propagation in Periodic Structures 2nd ed. (Dover, New York, 1953).
  20. L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
    [CrossRef]

2001 (2)

C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

2000 (1)

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

1999 (3)

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two-and three-dimensional photonic crystals,” Opt. Express 4, 167–176 (1999).
[CrossRef] [PubMed]

1998 (1)

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

1997 (1)

J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
[CrossRef]

1996 (3)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

K. Sakoda and K. Ohtaka, “Sum-frequency generation in atwo-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[CrossRef]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[CrossRef]

1995 (1)

L. Lefort and A. Barthelemy, “Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching,” Opt. Commun. 119, 163–166 (1995).
[CrossRef]

1994 (1)

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

1993 (2)

P. St. J. Russell, “All-optical high gain transistor action using second-order nonlinearities,” Electron. Lett. 29, 1228–1229 (1993).
[CrossRef]

A. E. Kaplan, “Eigenmodes of χ(2) wave mixings: cross-induced second-order nonlinear refraction,” Opt. Lett. 18, 1223–1225 (1993).
[CrossRef] [PubMed]

1992 (2)

1989 (1)

N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).

1967 (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Assanto, G.

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

Barthelemy, A.

L. Lefort and A. Barthelemy, “Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching,” Opt. Commun. 119, 163–166 (1995).
[CrossRef]

Behroozi, C.

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

Bertolotti, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

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

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

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

Brlashenkov, N. R.

N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).

Cappellini, G.

Centini, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

Chisari, R.

Cojocaru, C.

C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
[CrossRef]

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

Corbalán, R.

J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

DeSalvo, R.

Dowling, J. P.

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

Dutton, Z.

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

Fazio, E.

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

Gagarskii, S. V.

N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).

Hagan, D. J.

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Harris, S. E.

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

Hau, L. Vestergaard

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

Haus, J. W.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

Inochkin, M. V.

N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).

Kaplan, A. E.

Kim, Sungwon

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

Kobyakov, A.

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

Lederer, F.

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

Lefort, L.

L. Lefort and A. Barthelemy, “Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching,” Opt. Commun. 119, 163–166 (1995).
[CrossRef]

Martorell, J.

C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
[CrossRef]

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
[CrossRef]

Ohtaka, K.

K. Sakoda and K. Ohtaka, “Sum-frequency generation in atwo-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[CrossRef]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Russell, P. St. J.

P. St. J. Russell, “All-optical high gain transistor action using second-order nonlinearities,” Electron. Lett. 29, 1228–1229 (1993).
[CrossRef]

Sakoda, K.

K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two-and three-dimensional photonic crystals,” Opt. Express 4, 167–176 (1999).
[CrossRef] [PubMed]

K. Sakoda and K. Ohtaka, “Sum-frequency generation in atwo-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[CrossRef]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[CrossRef]

Scalora, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

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

Sheik-Bahae, M.

Sibilia, C.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Trillo, S.

Trull, J.

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

Van Stryland, E. W.

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Vanherzeele, H.

Vilaseca, R.

C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
[CrossRef]

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
[CrossRef]

Wabnitz, S.

Wang, Zuo

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

Appl. Phys. Lett. (2)

C. Cojocaru, R. Vilaseca, and J. Martorell, “Actively induced transmission via a quadratic nonlinear optical interaction in a potassium titanyl phosphate microcavity,” Appl. Phys. Lett. 79, 4479–4481 (2001).
[CrossRef]

C. Cojocaru, J. Martorell, R. Vilaseca, J. Trull, and E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
[CrossRef]

Electron. Lett. (1)

P. St. J. Russell, “All-optical high gain transistor action using second-order nonlinearities,” Electron. Lett. 29, 1228–1229 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

Sungwon Kim, Zuo Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
[CrossRef]

J. Appl. Phys. (1)

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

JETP Lett. (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Nature (1)

L. Vestergaard Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 595–598 (1999).
[CrossRef]

Opt. Commun. (3)

J. Martorell, R. Vilaseca, and R. Corbalán, “Pseudo-metal reflection at the interface between a linear and a nonlinear material,” Opt. Commun. 144, 65–69 (1997).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one-dimensional photonic band-gap structure,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

L. Lefort and A. Barthelemy, “Cross-phase modulation from second-harmonic to fundamental in cascaded second order processes; application to switching,” Opt. Commun. 119, 163–166 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Opt. Spectrosc. (1)

N. R. Brlashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second harmonic generation,” Opt. Spectrosc. 66, 1383–1386 (1989).

Phys. Rev. B (2)

K. Sakoda and K. Ohtaka, “Sum-frequency generation in atwo-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[CrossRef]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[CrossRef]

Phys. Rev. E (1)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63, 036610(1–5) (2001).
[CrossRef]

Other (1)

L. Brillouin, Wave Propagation in Periodic Structures 2nd ed. (Dover, New York, 1953).

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Figures (8)

Fig. 1
Fig. 1

Schematic scaled representation of a 1-D photonic crystal consisting of 20 periods of alternating layers of transparent dielectric materials. The indices of refraction of the layers are nh(ω)=1.93, nh(2ω)=1.94, nl(ω)=1.449, and nh(2ω)=1.46, and the corresponding thicknesses are lh=137.7 nm and ll=183.5 nm. The defect introduced into the middle of the structure is a nonlinear material with χ(2)=100 pm/V with n(ω)=1.449 and n(2ω)=1.46, and its thickness is L=2.2 µm.

Fig. 2
Fig. 2

Normalized averaged field intensity distribution within the defect of the photonic crystal plotted as a function of frequency in the linear case.

Fig. 3
Fig. 3

(a) Linear dispersion curve and (b) imaginary part of the wave vector for the 1-D truncated (solid curves) and the perfectly periodic (dashed curves) photonic crystals in the neighborhood of the resonant frequency ω0.

Fig. 4
Fig. 4

Normalized averaged intensity of the fundamental field within the defect plotted as a function of the frequency when χ(2)E(2ω0)=4.3×10-3 and the relative phase difference Δϕ is equal to Δϕ1=0.1π (short-dashed curve), Δϕ2=0.6π (solid curve), Δϕ3=π (long-dashed curve), and Δϕ4=1.6π (dotted–dashed curve). The dotted curve corresponds to the linear case.

Fig. 5
Fig. 5

(a) Reflectivity and (b) transmissivity of the fundamental beam plotted as functions of the frequency when the relative phase difference is Δϕ1 (short-dashed curve), Δϕ2 (solid curve), Δϕ3 (long-dashed curve) and Δϕ4 (dotted–dashed curve). For all these cases χ(2)E(2ω0)=4.3×10-3. The dotted curves correspond to the linear cases.

Fig. 6
Fig. 6

(a) Imaginary wave number and (b) real wave number for the fundamental beam when χ(2)E(2ω0)=4.3×10-3 and the relative phase difference is Δϕ1=0.1π (short-dashed curve) and Δϕ2=0.6π (solid curve). The dotted curve corresponds to the linear case.

Fig. 7
Fig. 7

Effective group velocity plotted as a function of the fundamental wave number kr when χ(2)E(2ω0)=4.3×10-3 and the relative phase difference is equal to Δϕ1 (short-dashed curve) and Δϕ2 (solid curve). The dotted curve corresponds to the linear case. The effective group velocity is normalized to its value in a homogeneous material with the same index of refraction as neff(ω0) of the linear structure.

Fig. 8
Fig. 8

(a) Dispersion curve for the fundamental beam and (b) effective group velocity plotted as functions of the fundamental wave number. In both cases the dotted curve corresponds to the linear case and the solid curve corresponds to χ(2)E(2ω0)=8×10-2 and a relative phase difference of 0.6π. The group velocity is normalized to its value in a homogeneous material with the same index of refraction as neff(ω0) of the linear structure.

Equations (4)

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-2z2Eω(z)-kω2Eω(z)=kω2nω2χ(2)E2ω(z)Eω*(z),
-2z2E2ω(z)-k2ω2E2ω(z)=k2ω22n2ω2χ(2)Eω2(z),
t(ω)=EωtrEωinc=exp i[Ψt(ω)+iγ(ω)L]=exp ik(ω)L,
kr(ω)=Ψt(ω)L,ki(ω)=γ(ω),

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