Abstract

A Fabry-Perot resonator filled with second-order nonlinear optical material is investigated. Attention is devoted to making the resonator act as a nonlinear mirror for ultralow-intensity light signals that can be switched by a control beam at the second-harmonic frequency. The interaction process is an input-phase-independent parametric downconversion. The theoretical problem is solved through implementation of a dummy variable method optimized for a parametric process. Efficient amplification and bistability of low-intensity signals have been found.

© 2002 Optical Society of America

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References

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  1. J. Paye, D. Hulin, “Femtosecond response of a semiconductor nonlinear Fabry-Perot etalon,” J. Opt. Soc. Am. B 10, 2371–2376 (1993).
    [CrossRef]
  2. N. J. Doran, D. Wood, “Nonlinear optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
    [CrossRef] [PubMed]
  3. N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
    [CrossRef]
  4. I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
    [CrossRef]
  5. A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
    [CrossRef]
  6. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. VanStryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]
  7. A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
    [CrossRef]
  8. G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
    [CrossRef]
  9. E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
    [CrossRef]
  10. E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
    [CrossRef]
  11. M. A. Krumbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245–247 (1997).
    [CrossRef] [PubMed]
  12. C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
    [CrossRef]
  13. L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
    [CrossRef]
  14. L. Lefort, 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]
  15. C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
    [CrossRef]
  16. C. Cojocaru, J. Martorell, R. Villaseca, J. Trull, E. Fazio, “Active reflection via a phase-insensitive quadratic nonlinear interaction within a microcavity,” Appl. Phys. Lett. 74, 504–506 (1999).
    [CrossRef]
  17. S. Kim, Z. Wang, D. J. Hagan, E. W. VanStryland, A. Koyakov, F. Lederer, G. Assanto, “Phase-insensitive all-optical transistors based on second-order nonlinearities,” IEEE J. Quantum Electron. 34, 666–672 (1998).
    [CrossRef]

1999

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

1998

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

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

1997

1996

C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
[CrossRef]

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

1995

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

L. Lefort, 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

I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
[CrossRef]

1993

C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
[CrossRef]

J. Paye, D. Hulin, “Femtosecond response of a semiconductor nonlinear Fabry-Perot etalon,” J. Opt. Soc. Am. B 10, 2371–2376 (1993).
[CrossRef]

1992

1989

N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
[CrossRef]

1988

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

N. J. Doran, D. Wood, “Nonlinear optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
[CrossRef] [PubMed]

Aitchinson, J. S.

C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
[CrossRef]

Arnold, J. M.

C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
[CrossRef]

Assanto, G.

S. Kim, Z. Wang, D. J. Hagan, E. W. VanStryland, A. Koyakov, F. Lederer, 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, 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]

Bertolotti, M.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
[CrossRef]

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

Cojocaru, C.

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

D’Aguanno, G.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

Davies, D. A. O.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

DeLong, K. W.

DeSalvo, R.

Dominici, S.

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

Doran, N. J.

N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
[CrossRef]

N. J. Doran, D. Wood, “Nonlinear optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
[CrossRef] [PubMed]

Ellis, A. D.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

Fabre, C.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

Fazio, E.

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

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
[CrossRef]

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

Ferrari, E.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Fittinghoff, D. N.

Flannery, D.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

Forrester, D. S.

N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
[CrossRef]

Giacobino, E.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

Glesk, I.

I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
[CrossRef]

Hagan, D. J.

S. Kim, Z. Wang, D. J. Hagan, E. W. VanStryland, A. Koyakov, F. Lederer, 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. VanStryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Horowicz, R. J.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

Hulin, D.

Ironside, C. N.

C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
[CrossRef]

Kim, S.

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

Koyakov, A.

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

Krumbugel, M. A.

Lederer, F.

S. Kim, Z. Wang, D. J. Hagan, E. W. VanStryland, A. Koyakov, F. Lederer, 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, 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]

Lugiato, L. A.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

Manning, R. J.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

Martorell, J.

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

Nayar, B. K.

N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
[CrossRef]

Oldano, C.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

Patrick, D. M.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

Paye, J.

Prucnal, P. R.

I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
[CrossRef]

Re, A.

C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
[CrossRef]

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

Senesi, F.

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

Sheik-Bahae, M.

Sibilia, C.

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

C. Sibilia, A. Re, E. Fazio, M. Bertolotti, “On the second harmonic generation in a ring cavity,” J. Opt. Soc. Am. B 13, 1151–1157 (1996).
[CrossRef]

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

Sokoloff, J. P.

I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
[CrossRef]

Spirit, D. M.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

Stegeman, G.

Sweetser, J. N.

Trebino, R.

Trull, J.

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

Vanherzeele, H.

VanStryland, E. W.

S. Kim, Z. Wang, D. J. Hagan, E. W. VanStryland, A. Koyakov, F. Lederer, 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. VanStryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Villaseca, R.

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

Wang, Z.

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

Wood, D.

Zitelli, M.

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

Appl. Phys. Lett.

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

Electron. Lett.

N. J. Doran, D. S. Forrester, B. K. Nayar, “Experimental investigation of all-optical switching in fiber loop mirror device,” Electron. Lett. 25, 267–269 (1989).
[CrossRef]

I. Glesk, J. P. Sokoloff, P. R. Prucnal, Demonstration of all-optical demultiplexing at TDM data at 250 Gbit/s, Electron. Lett. 30, 339–341 (1994).
[CrossRef]

IEEE J. Quantum Electron.

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

C. N. Ironside, J. S. Aitchinson, J. M. Arnold, “An all-optical switching employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
[CrossRef]

Il Nuovo Cimento

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Il Nuovo Cimento 16, 959–977 (1988).
[CrossRef]

J. Lightwave Technol.

A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, D. M. Spirit, “Ultra-high-speed OTDM networks using semiconductor amplifier-based processing nodes,” J. Lightwave Technol. 13, 761–770 (1995).
[CrossRef]

J. Mod. Opt.

A. Re, C. Sibilia, E. Fazio, M. Bertolotti, “Field dependent effects in a quadratic nonlinear medium,” J. Mod. Opt. 42, 823–839 (1995).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

L. Lefort, 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]

E. Fazio, M. Zitelli, S. Dominici, C. Sibilia, G. D’Aguanno, M. Bertolotti, “Phase-driven pulse-breaking during perfectly matched second-harmonic generation,” Opt. Commun. 148, 427–435 (1998).
[CrossRef]

E. Fazio, C. Sibilia, F. Senesi, M. Bertolotti, “All-optical switching during quasi-collinear second-harmonic generation,” Opt. Commun. 127, 62–66 (1996).
[CrossRef]

Opt. Lett.

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Figures (14)

Fig. 1
Fig. 1

Scheme of light paths inside the Fabry-Perot cavity. 0, input internal interface for the forward wave; 1, output internal interface for the forward wave; 2, 3, similarly output and input interfaces, respectively, for the backward wave, 4, undergoing a complete round trip and overlapping the external beam at position 0; ε, injection from outside.

Fig. 2
Fig. 2

Behavior of the internal mode α1 at the fundamental frequency as a function of the internal second-harmonic mode just behind the first mirror, i.e., at position 0. The three curves correspond to different cavity mismatches. Note that the peaks of the curves move to the left hand side, increasing the mismatch, even passing the graphic boundary. If this limit is passed, the curve monotonically decreases along the whole intensity range of the second-harmonic internal mode.

Fig. 3
Fig. 3

Behavior of the internal mode α3 at the second-harmonic frequency as a function of the fundamental internal mode α1 just behind the first mirror, i.e., at position 0. The curves correspond to different cavity mismatches. Note that different trends can be observed, corresponding to just one peak, two peaks, etc.

Fig. 4
Fig. 4

Graphic solution of the cavity performances by inserting the S single curve |α1(0)|2 versus |α3(0)|2 from Eq. (14) and the F curve family |α3(0)|2 versus |α1(0)|2 from Eq. (15). The F curves differ for dummy parameter ε3, which represents the external second-harmonic intensity. Intersections between the S curve and the F curves show the cavity solutions: In particular it can be seen that for different values of ε3 that we have one, two, or three intersections.

Fig. 5
Fig. 5

Cavity performances as derived from Fig. 4. In this case the internal intensity of the fundamental frequency at input position 0 is plotted as a function of the external second-harmonic intensity. In the region between 1 and 1.45 MW/cm2 the cavity accepts three contemporary solutions, typical of bistable behavior.

Fig. 6
Fig. 6

Nonlinear reflection of a low-intensity beam at the fundamental frequency from the Fabry-Perot active mirror driven by a second-harmonic control beam. These results correspond to the behavior of the internal mode described in Figs. 4 and 5. Starting from a linear reflection of 1, the signal is amplified 15–20 times, by a control beam as great as 1 MW/cm2. Above this value the reflected signal beam switches toward a higher reflection of approximately 80–90.

Fig. 7
Fig. 7

Graphic solution of the cavity performances, as described in Fig. 4, for a different mismatch of the second-harmonic cavity. Note that in this case the different behaviors of the F curves now show the trend decreasing, in the region where intersects curve S instead of the trend increasing as in Fig. 4. This difference corresponds to a completely different cavity performance, as shown in Fig. 8.

Fig. 8
Fig. 8

Cavity performances as derived from Fig. 7. The internal intensity of the fundamental frequency, plotted as a function of the external second-harmonic intensity, shows a bistable region between 0.24 and 0.42 MW/cm2. Compared with the bistable loop derived in Fig. 5, few differences can be identified: The present loop is reversed with respect to the previous one, mainly due to the modal resonances; it occurs at lower power and is larger.

Fig. 9
Fig. 9

Different cavity performances for three second-harmonic mode mismatches. When the mismatch is low, the bistable loop occurs when the pumping is lower; at a moderate mismatch no loops are present, only efficient amplification; at an elevated mismatch, the loop is reversed and occurs at a higher pump intensity than above. Note that in the last case the loop is folded toward a lower intensity: This characteristic takes into account the low internal intensity of the pump beam that increases cavity switching and, as a consequence, allows the energy stored inside the cavity to be higher.

Fig. 10
Fig. 10

Influence on cavity performances of the phase mismatch of the parametric process and of the linear absorption (dashed curve). This behavior is compared with the perfectly matched process without absorption (continuous curve). Both parametric mismatch and absorption decrease cavity efficiencies, making the loops larger.

Fig. 11
Fig. 11

Control of the convergence of the numerical model: From the theory the two terms, |α i (0)|2 (continuous curve) and |α i (4) + t i Ei ext|2 (dashed curve), must be usual for both wavelengths in any pumping regime. Here they are reported for the fundamental mode.

Fig. 12
Fig. 12

Relative errors recorded during the numerical calculation described in Fig. 11. The relative error never exceeds 1.2%.

Fig. 13
Fig. 13

Verification of the Manley-Rowe rule. Also, in this case, as shown in Fig. 12, the relative error is really low.

Fig. 14
Fig. 14

Reflection coefficients of the Fabry-Perot active nonlinear mirror for different Δϕ1. Amplifications as high as 220 have been observed at pump intensities of the order of 1 MW/cm2.

Equations (33)

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Ai2=riAi, Ai4=riAi3,
Ai1=Ai0fiA10, A20, A30exp-ikiL, Ai3=Ai2fiA12, A22, A32exp-ikiL.
Ai0=Ai4+tiEiext,
A1z=-βωA1-iΓ1A2*A3 exp-iΔkL, A2z=-βωA2-iΓ2A1*A3 exp-iΔkL, A3z=-β2ωA3-iΓ3A1A2 expiΔkL,
Γi=8π/ωiniωi deff
α1=-iΓ2Γ31/2A1 expβωz, α2=-iΓ1Γ31/2A2 expβωz, α3=-iΓ1Γ21/2A3 expβ2ωz,
α1z=-α2*α3 expγ12z, α2z=-α1*α3 expγ12z, α3z=α1α2 expγ3z,
γ12=-β2ω+iΔK, γ3=-2βω-β2ω-iΔK.
αiz=αi0+αiz0 z+2αiz20z22+3αiz3αiz0z36exp-ikiz+O4.
α1z=-α2*α3, α2z=-α1*α3, α3z=α1α2.
α1z0=0, 2α1z20=α10|α30|2, 3α1z30=0, α2z0=-α10α3*0, 2α2z20=0, 3α2z30=α10α3*0|α10|2-|α30|2, α3z0=0, 2α3z20=-α30|α10|2, 3α1iz30=0.
α1z=α101+|α30|2z22exp-ik1z, α2z=-α10α3*0z+|α30|2-|α10|2z36×exp-ik2z, α3z=α301-|α10|2z22exp-ik3z.
αi0=αi4+εi,
ε1=-iΓ2Γ31/2t1Eext1,ε2=0, ε3=-iΓ1Γ21/2t3Eext3,
α10=ε11-r12 exp-2ik1zF1|α10|2, |α30|2,
α30=ε31-r32 exp-2ik3zF3|α10|2, |α30|2,
F1|α10|2, |α30|2=1+|α30|2L221+|α30|2×1-|α10|2L222 r32L22,
F3|α10|2, |α30|2=1-|α10|2L221-|α10|2×1+|α30|2L222 r12L22.
F1=F1|α30|21+|α30|2L22×1+|α30|2 r32L22, F3=F3|α10|21-|α10|2L22×1-|α10|2 r12L22.
|ε1|21-cos22Δϕ1
|α30|2=1+r32+t34+4r32r12cos2Δϕ11/2r32L2.
|α10|2=1+r12r12L2;
|α10|2=1+r12+t14+4r12r32cos2Δϕ31/2r12L2
|α10|2=1+r12-t14+4r12r32cos2Δϕ31/2r12L2.
|α10|2=1+r12r12L2,
|ε3|2=|α30|21-r32 exp-2ik3L1-|α10|2L22×1-|α10|2r12L222.
3α1z30=2γ12+γ12*α10|α30|2, 3α3z30=2γ3+γ12α30|α10|2.
α1z=α101+|α30|2z22+2γ12+γ12*z36×exp-ik1z, α3z=α301-|α10|2z22+2γ3+γ12z36×exp-ik3z.
Λ1=L22+2γ12+γ12*L36, Λ3=L22+2γ3+γ12L36,
α10=ε11-r12 exp-2ik1L1+|α30|2Λ11+|α30|2r32Λ1, α30=ε31-r32 exp-2ik3L1-|α10|2Λ31-|α10|2r12Λ3.
F˜1=1+|α30|2Λ11+|α30|2r32Λ1=|F˜1|expiΦ1NL, F˜3=1-|α10|2Λ31-|α10|2r12Λ3=|F˜3|expiΦ3NL.
|αi4+tiEiext|2-|αi0|2|αi0|2
n1ω |α1z|2+n32ω |α3z|2=n1ω |α10|2+n32ω |α30|2

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