Abstract

From the viewpoint of photon flux, the evolution of phases and intensities in the eigenmode state in three-wave mixing (TWM) is studied, and the requirements for the initial phases and incident intensities in this state are derived. Another special state in which there is an exchange of intensities without a phase change in the TWM is also investigated, for the first time to the authors’ knowledge. By use of the two special states of cascaded quadratic nonlinear effects, an all-optical switch based on the push–pull Sagnac loop is proposed, and its properties are calculated. The numerical results show that the switch is quite stable, and the intensity and phase of the output signal can easily be established and controlled.

© 2001 Optical Society of America

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  1. P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webijorn, and P. St. J. Russell, “Larger nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3,” Opt. Lett. 22, 277–279 (1997).
    [CrossRef]
  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 solitions,” Opt. Commun. 28, 1691–1740 (1996).
  3. G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
    [CrossRef]
  4. J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  5. G. Assanto and I. Torelli, “Cascading effects in type II second-harmonic generation: application to all-optical processing,” Opt. Commun. 119, 143–148 (1995).
    [CrossRef]
  6. G. S. Kanter and P. Kumar, “Optical devices based on internally seeded cascaded nonlinearities,” IEEE J. Quantum Electron. 35, 891–896 (1999).
    [CrossRef]
  7. K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
    [CrossRef]
  8. X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ(2)(2) nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).
    [CrossRef]
  9. A. E. Kaplan, “Eigenmodes of χ(2) wave mixings: cross-induced second-order nonliear refraction,” Opt. Lett. 18, 1223–1225 (1993).
    [CrossRef] [PubMed]
  10. G. Baldenberger, S. L. Rochelle, and A. Villeneuve, “Cascaded nonlinear phase shift in a novel anharmoic phase-mismatch configuration,” J. Opt. Soc. Am. B 16, 1894–1903 (1999).
    [CrossRef]
  11. A. Kobyakov and F. Lederer, “Cascading of quadratic nonlinearities: an analytical study,” Phys. Rev. A 54, 3455–3471 (1996).
    [CrossRef] [PubMed]
  12. H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
    [CrossRef]
  13. M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
    [CrossRef]
  14. M. J. T. Milton, “General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
    [CrossRef]
  15. G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
    [CrossRef]
  16. T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1270 (1990).
    [CrossRef]
  17. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  18. A. Kobyakov, E. Schmidt, and F. Lederer, “Effect of group-velocity mismatch on amplitude and phase modulation of picosecond pulses in quadratically nonlinear media,” J. Opt. Soc. Am. B 14, 3242–3252 (2000).
    [CrossRef]
  19. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of the second-order nonlinear optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [CrossRef]
  20. C. N. Ironside, J. S. Aitchison, and J. M. Arnold, “An all-optical switch employing the cascaded second-order nonlinear effect,” IEEE J. Quantum Electron. 29, 2650–2654 (1993).
    [CrossRef]
  21. G. D. Landry and T. A. Maldonado, “Switching and second harmonic generation in a mirrorless configuration,” J. Lightwave Technol. 17, 316–327 (1999).
    [CrossRef]
  22. K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
    [CrossRef]
  23. H.-F. Chou, C.-F. Lin, and G.-C. Wang, “An iterative finite difference beam propagation method for modeling second-order nonlinear effects in optical waveguides,” J. Lightwave Technol. 16, 1686–1693 (1998).
    [CrossRef]
  24. The initial phases of the signal and the SH counterpropagating in the medium meet the requirements for θ that (0)=Φ3(0)–2Φ2(0)=0, π and that their photon fluxes correspond to Eq. (6). In Fig. 5, if θ(0)=0 for clockwise propagation, then θ(0)=π for anticlockwise propagation by the action of the half wave.
  25. H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
    [CrossRef]

2000 (5)

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

A. Kobyakov, E. Schmidt, and F. Lederer, “Effect of group-velocity mismatch on amplitude and phase modulation of picosecond pulses in quadratically nonlinear media,” J. Opt. Soc. Am. B 14, 3242–3252 (2000).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
[CrossRef]

1999 (6)

1998 (2)

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

H.-F. Chou, C.-F. Lin, and G.-C. Wang, “An iterative finite difference beam propagation method for modeling second-order nonlinear effects in optical waveguides,” J. Lightwave Technol. 16, 1686–1693 (1998).
[CrossRef]

1997 (2)

1996 (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 solitions,” Opt. Commun. 28, 1691–1740 (1996).

A. Kobyakov and F. Lederer, “Cascading of quadratic nonlinearities: an analytical study,” Phys. Rev. A 54, 3455–3471 (1996).
[CrossRef] [PubMed]

1995 (1)

G. Assanto and I. Torelli, “Cascading effects in type II second-harmonic generation: application to all-optical processing,” Opt. Commun. 119, 143–148 (1995).
[CrossRef]

1993 (2)

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

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

1992 (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

M. J. T. Milton, “General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
[CrossRef]

1990 (1)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1270 (1990).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Aitchison, J. S.

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

Alber, M. S.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Arnold, J. M.

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

Asobe, M.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Assanto, G.

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” J. Opt. Soc. Am. B 16, 267–269 (1999).
[CrossRef]

G. Assanto and I. Torelli, “Cascading effects in type II second-harmonic generation: application to all-optical processing,” Opt. Commun. 119, 143–148 (1995).
[CrossRef]

Baldenberger, G.

Banfi, G. P.

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Brener, I.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Chaban, E. E.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Chou, H.-F.

Chou, M. H.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

Datta, P. K.

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

Degiorgio, V.

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

Duculing, J.

J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Fejer, M. M.

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Fortusini, D.

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

Fujimura, M.

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

Gallo, K.

Hagan, D. J.

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 solitions,” Opt. Commun. 28, 1691–1740 (1996).

Ironside, C. N.

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

Ito, R.

Itoh, H.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kanbara, H.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Kanter, G. S.

G. S. Kanter and P. Kumar, “Optical devices based on internally seeded cascaded nonlinearities,” IEEE J. Quantum Electron. 35, 891–896 (1999).
[CrossRef]

Kaplan, A. E.

Kim, B. Y.

H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
[CrossRef]

Kitamoto, A.

Kobyakov, A.

Kondo, T.

Kosinski, S.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Kumar, P.

G. S. Kanter and P. Kumar, “Optical devices based on internally seeded cascaded nonlinearities,” IEEE J. Quantum Electron. 35, 891–896 (1999).
[CrossRef]

Landry, G. D.

Lederer, F.

Lee, H. W.

H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
[CrossRef]

Lenz, G.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Levenson, J. A.

Lin, C.-F.

Liu, X.

Lovering, D. J.

Luther, G. G.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Maldonado, T. A.

Marsden, J. E.

Milton, M. J. T.

M. J. T. Milton, “General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
[CrossRef]

Miyazawa, H.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Nishihara, H.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1270 (1990).
[CrossRef]

Noguchi, K.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Parameswaran, K. R.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Duculing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Philen, D.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Qian, L.

Rhy, H. Y.

H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
[CrossRef]

Robbins, J. M.

Rochelle, S. L.

Russell, P. St. J.

Schmidt, E.

Scotti, R.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Shirane, M.

Shmulovich, J.

M. H. Chou, I. Brener, G. Lenz, R. Scotti, E. E. Chaban, J. Shmulovich, D. Philen, S. Kosinski, K. R. Parameswaran, and M. M. Fejer, “Efficient wide-band and tunable midspan spectral inverter using cascaded nonlinearities in LiNbO3 waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).
[CrossRef]

Shoji, I.

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 solitions,” Opt. Commun. 28, 1691–1740 (1996).

Suhara, T.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1270 (1990).
[CrossRef]

Torelli, I.

G. Assanto and I. Torelli, “Cascading effects in type II second-harmonic generation: application to all-optical processing,” Opt. Commun. 119, 143–148 (1995).
[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 solitions,” Opt. Commun. 28, 1691–1740 (1996).

Vidakovic, P.

Villeneuve, A.

Wang, G.-C.

Webijorn, J.

Wise, F.

Yanagawa, T.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Yokohama, I.

H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, and I. Yokohama, “All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide,” IEEE Photonics Technol. Lett. 11, 328–330 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

G. P. Banfi, P. K. Datta, V. Degiorgio, and D. Fortusini, “Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate,” Appl. Phys. Lett. 73, 136–138 (1998).
[CrossRef]

IEEE J. Quantum Electron. (6)

G. S. Kanter and P. Kumar, “Optical devices based on internally seeded cascaded nonlinearities,” IEEE J. Quantum Electron. 35, 891–896 (1999).
[CrossRef]

M. J. T. Milton, “General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
[CrossRef]

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1270 (1990).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi phase-matched second-harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

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

H. Y. Rhy, B. Y. Kim, and H. W. Lee, “Self-switching with a nonlinear birefringent loop mirror,” IEEE J. Quantum Electron. 36, 89–93 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low power all-optical gate based on sum frequency mixing in APE wave guides in PPLN,” IEEE Photonics Technol. Lett. 12, 654–657 (2000).
[CrossRef]

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Other (1)

The initial phases of the signal and the SH counterpropagating in the medium meet the requirements for θ that (0)=Φ3(0)–2Φ2(0)=0, π and that their photon fluxes correspond to Eq. (6). In Fig. 5, if θ(0)=0 for clockwise propagation, then θ(0)=π for anticlockwise propagation by the action of the half wave.

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Figures (7)

Fig. 1
Fig. 1

Evolution of intensities and phases of the FF and SF waves propagating through the medium under the condition that θ(ζ0)=0, where Δk1,2=1.5, 0 mm-1; l1,2=7, 3 mm; I1,2,3(0)=3×103, 2×103, 1194.97 kW/cm2; and ϕ1,2,3(0)=0.5, 0, 0 rad. When the three waves propagate to ζ0(=l1/C), θ(ζ0)=0 and I1,2,3(ζ0) meet the conditions of Eq. (5a), and the three intensities are maintained steady and the phases are increased linearly for ζ>ζ0. (a), (b), (c) Two FF and SF waves, respectively.

Fig. 2
Fig. 2

Evolution of intensities and phases of the FF and SF waves propagating through the medium under the condition that θ(ζ0)=π. Initial parameters are the same as in Fig. 1 but I3(0)=4722.07 kW/cm2 and ϕ1(0)=-2.6416 rad. When the three waves propagate to ζ0, θ(ζ0)=π and I1,2,3(ζ0) meet the conditions of Eq. (5b), and the three intensities remain steady and the phases decrease linearly for ζ>ζ0. (a), (b), (c) Two FF and SF waves, respectively.

Fig. 3
Fig. 3

Evolution of intensities and phases of the FF and SF waves propagating through the medium under the condition that θ(ζ0)=-π/2. Initial parameters are the same as in Fig. 1 but Δk1=1.02547 mm-1 and I3(0)=0. When the three waves propagate to ζ0, the result of θ(ζ0)=-π/2 causes the phases of three waves to remain coherent for ζ>ζ0. (a), (b), (c) Two FF and SF waves, respectively.

Fig. 4
Fig. 4

Evolution of intensities and phases of the FF and SH waves in the PP SL AOS, where Δk=0, λ2=1550 nm, l=10 mm, and deff=20.5 pm/V. (a) Evolution of waves without the input SH, which corresponds to the closed state of the AOS. (b), (c) Evolution with the initial conditions ϕ3(0)2ϕ2(0)=0,π, respectively, corresponding to clockwise and anticlockwise directions in (a), i.e., the open state.

Fig. 5
Fig. 5

(a) Schematic diagram and (b) functional diagram of the PP SL AOS, where Δk=0, BPF filters the SH wave at the switch port, HW produces a half-wave phase shift for the anticlockwise direction, and I2 is the intensity of output signal ω2 controlled by the SH ω3. The AOS operates in the push–pull state, and the controlling wave (i.e., the SH wave) is assumed to comprise rectangular pulses. When I3(0)=0, the device performs as in the closed state. When θ(0)=ϕ3(0)2ϕ2(0)=0,π, and their photon fluxes correspond to Eq. (6), it performs as in the open state. If θ(0)=0 for the clockwise direction, θ(0)=π for the anticlockwise direction by the action of the HW.

Fig. 6
Fig. 6

Pulse shaping for (a) the rectangular and (b) the bell-shaped pulses, from the input to the output port of the PP SL AOS. I2 and I3 are normalized. In the calculation, all parameters are consistent with Fig. 4, and the group-velocity mismatch is ignored. (a) Ideal result, (b) similar to the practical configuration.

Fig. 7
Fig. 7

Transmissivity of the switching port for the PP SL AOS influenced by the fluctuation of the intensities and the phases of (a) the signal and (b) the SH wave, where ΔI2,3=I2,3-I2e,3e and Δϕ2,3=ϕ2,3-ϕ2e,3e, and I2e,3e and I2e,3e, are the intensities and phases of the signal and the SH for the eigenmode state in Fig. 4. All parameters, except the fluctuation of intensities and phases of the signal and SH, are consistent with those of Fig. 4. It is shown that the transmissivity of the signal is dependent only on the magnitude of Δϕ2,3 but is independent of the sign of Δϕ2,3.

Equations (15)

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Ejz=-iDjE(3-j)*E3 exp(-iΔkz)(j=1, 2),
E3z=-iD3E1E2 exp(iΔkz),
fj=njε0c2ωj1/2Ej exp(iϕj)(j=1, 2, 3),
ζ f1f2f3=-f2f3-f1f3f1f2sin ϕ,
ζ ϕ1ϕ2ϕ3=f2f3/f1f1f3/f2f1f2/f3cos θ.
ϕ1(ζ)ϕ2(ζ)ϕ3(ζ)=±f2f3/f1f1f3/f2f1f2/f3(ζ-ζ0)+ϕ1(ζ0)ϕ2(ζ0)ϕ3(ζ0),
f1f2f3-f1f3f2-f2f3f1+ΔkC=0,(θ(ζ0)=0)
-f1f2f3+f1f3f2+f2f3f1+ΔkC=0,(θ(ζ0)=π).
f3=f1f22(f12+f22) ΔkC2+4f12+4f221/2±ΔkC.
ϕNL(ζ)=ϕ2(ζ)-ϕ2(0)=±(f1f3/f2)(ζ-ζ0)+ϕ2(ζ0)-ϕ2(0),
ϕ3(ζ0)-ϕ2(ζ0)-ϕ1(ζ0)=-π/2, π/2.
E3zz0=-i ω3deffn3c|E1(0)||E2(0)|×exp{-i[ϕ1(0)+ϕ2(0)]}.
E3(Δz)-E3(0)ΔzΔz0
=-i ω3deffn3c|E1(0)||E2(0)|exp{-i[ϕ1(0)+ϕ2(0)]}.
E3(Δz)=-i ω3deffn3c|E1(0)||E2(0)|×exp{-i[ϕ1(0)+ϕ2(0)]}Δz.

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