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 LiNbO_{3} 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]

G. D. Landry and T. A. Maldonado, “Switching and second harmonic generation in a mirrorless configuration,” J. Lightwave Technol. 17, 316–327 (1999).

[CrossRef]

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]

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]

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

[CrossRef]

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]

X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ^{(2)}:χ^{(2)} nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).

[CrossRef]

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]

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]

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 LiNbO_{3},” Opt. Lett. 22, 277–279 (1997).

[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 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]

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]

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]

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]

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]

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]

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]

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. 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]

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]

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]

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 LiNbO_{3} 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]

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 LiNbO_{3} 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]

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 LiNbO_{3} waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).

[CrossRef]

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]

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]

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]

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 LiNbO_{3} 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]

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]

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]

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]

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).

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. 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]

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]

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]

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

[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]

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 LiNbO_{3} waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).

[CrossRef]

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

[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]

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 LiNbO_{3} 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]

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]

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]

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]

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]

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 LiNbO_{3} 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]

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]

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 LiNbO_{3} waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (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]

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 LiNbO_{3} waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (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 LiNbO_{3} waveguides,” IEEE Photonics Technol. Lett. 12, 82–84 (2000).

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

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]

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]

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).

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]

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]

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]

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

[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]

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]

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]

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. 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]

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 LiNbO_{3} 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]

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]

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]

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]

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. 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).

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]

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 LiNbO_{3},” Opt. Lett. 22, 277–279 (1997).

[CrossRef]

X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ^{(2)}:χ^{(2)} nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).

[CrossRef]

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

[CrossRef]
[PubMed]

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]

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

[CrossRef]
[PubMed]

The initial phases of the signal and the SH counterpropagating in the medium meet the requirements for θ that (0)=Φ_{3}(0)–2Φ_{2}(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.