Abstract

We develop a generalized model for studying second-order parametric interactions in 1-D multilayered photonic structures, accounting for collinear oblique waves and partial pump depletion. This model is used to assess the performance of parametric devices in photonic-crystal microcavity (PCM) structures. Our model shows dramatic enhancement of nonlinear interactions at frequencies for which the waves are localized. Also, we demonstrate the exponential dependence of the conversion efficiency of second harmonic generation (SHG) on the number of layers as was recently pointed out. In addition, in optical parametric amplification (OPA), we find that the gain has a resonance-like dependence on the pump intensity, turning large peak gain into strong attenuation at greater intensities, which suggests that the device can operate as an optical switch.

© 2008 Optical Society of America

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2007 (3)

2006 (1)

L.-M Zhao, and B.-Y. Gu, "Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material," Appl. Phys. Lett. 88, 122904 (2006).
[CrossRef]

2005 (2)

M. Centini, J. Peina, Jr., L. Sciscione, C. Sibilia, M. Scalora, M. J. Bloemer, and M. Bertolotti, "Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals," Phys. Rev. A 72, 033806 (2005).
[CrossRef]

T. Ochiai and K. Sakoda, "Scaling law of enhanced second harmonic generation in finite Bragg stacks," Opt. Express 13, 9094-9114 (2005).
[CrossRef]

2004 (4)

MSoljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature (London) 3, 211-219 (2004).

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Theory of spontaneous parametric downconversion from photonic crystals," Phys. Rev. A 70, 043810 (2004).
[CrossRef]

M. Cherchi, "Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers," Phys. Rev. E 69, 066602 (2004).
[CrossRef]

M. Liscidinia and L. Andreani, "Highly efficient second-harmonic generation in doubly resonant planar microcavities," Appl. Phys. Lett. 85, 1883-1885 (2004).

2003 (2)

A. R. Cowan and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 046606 (2003).
[CrossRef]

M. Ghulinyan C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

2002 (3)

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, "Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals," Appl. Phys. Lett. 81, 2725-2727 (2002).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Generalized coupled-mode theory for |(2) interactions in finite multilayered structures," J. Opt. Soc. Am. B 19, 2111-2121 (2002).
[CrossRef]

2001 (1)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to Χ(2) interactions," Phys. Rev. E 64, 016609 (2001).
[CrossRef]

1999 (2)

Y. Jeong and B. Lee, "Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion," IEEE J. Quantum Electron. 35, 162-172 (1999).
[CrossRef]

W. E. Angerer, N. Yang, A. G. Yodh, M. A. Khan, and C. J. Sun, "Ultrafast second-harmonic generation spectroscopy of GaN thin films on sapphire," Phys. Rev. B 59, 2932-2946 (1999).
[CrossRef]

1998 (2)

J.W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimei, "Enhanced second-harmonic generation in media with a weak periodicity," Phys. Rev. A 57, 2120-2128 (1998).
[CrossRef]

A. Arraf and C. M. de Sterke, "Coupled-mode equations for quadratically nonlinear deep gratings," Phys. Rev. E 58, 7951-7958 (1998).
[CrossRef]

1997 (1)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).

1996 (1)

1989 (1)

1988 (1)

Appl. Opt. (1)

Appl. Phys. Lett. (3)

L.-M Zhao, and B.-Y. Gu, "Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material," Appl. Phys. Lett. 88, 122904 (2006).
[CrossRef]

T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, and G. Mattei, "Giant microcavity enhancement of second-harmonic generation in all-silicon photonic crystals," Appl. Phys. Lett. 81, 2725-2727 (2002).
[CrossRef]

M. Liscidinia and L. Andreani, "Highly efficient second-harmonic generation in doubly resonant planar microcavities," Appl. Phys. Lett. 85, 1883-1885 (2004).

IEEE J. Quantum Electron. (1)

Y. Jeong and B. Lee, "Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion," IEEE J. Quantum Electron. 35, 162-172 (1999).
[CrossRef]

J. Appl. Phys. (1)

M. Ghulinyan C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

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

Nature (London) (1)

MSoljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature (London) 3, 211-219 (2004).

Opt. Express (1)

Phys. Rev. A (4)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Theory of spontaneous parametric downconversion from photonic crystals," Phys. Rev. A 70, 043810 (2004).
[CrossRef]

M. Centini, J. Peina, Jr., L. Sciscione, C. Sibilia, M. Scalora, M. J. Bloemer, and M. Bertolotti, "Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals," Phys. Rev. A 72, 033806 (2005).
[CrossRef]

J.W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimei, "Enhanced second-harmonic generation in media with a weak periodicity," Phys. Rev. A 57, 2120-2128 (1998).
[CrossRef]

Phys. Rev. B (1)

W. E. Angerer, N. Yang, A. G. Yodh, M. A. Khan, and C. J. Sun, "Ultrafast second-harmonic generation spectroscopy of GaN thin films on sapphire," Phys. Rev. B 59, 2932-2946 (1999).
[CrossRef]

Phys. Rev. E (5)

A. R. Cowan and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 046606 (2003).
[CrossRef]

A. Arraf and C. M. de Sterke, "Coupled-mode equations for quadratically nonlinear deep gratings," Phys. Rev. E 58, 7951-7958 (1998).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to Χ(2) interactions," Phys. Rev. E 64, 016609 (2001).
[CrossRef]

M. Cherchi, "Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers," Phys. Rev. E 69, 066602 (2004).
[CrossRef]

J. J. Li, Z. Y. Li, and D. Z. Zhang, "Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method," Phys. Rev. E 75, 056606 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef]

Other (1)

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 2007).

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