Abstract

We summarize and discuss the results of our second-harmonic generation experiments in titanium-indiffused lithium niobate optical channel waveguides. The wave-vector mismatch in the nonlinear wave interaction was varied with temperature tuning around the second-harmonic resonances. Fundamental depletion and second-harmonic tuning curves show a strong power dependence, which is an indication of an intensity-dependent wave-vector modification of the interacting modes. This nonlinear refractive effect (which is called cascaded nonlinearity) is characterized with interferometric measurements of the resulting nonlinear phase shift of the fundamental. Large nonlinear phase shifts (>2π) appear in regions of low fundamental depletion (<10%) because of a nonuniform wave-vector mismatch along the waveguide. At resonance a maximum fundamental depletion of more than 90% was observed. All the measured results are explained well theoretically with a coupled-mode model that has proved to be a reliable design tool for fabricating waveguide devices for applications of the cascaded nonlinearity.

© 1998 Optical Society of America

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  27. K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

1997 (3)

1996 (5)

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

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

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).

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

1995 (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

Y. Baek, R. Schiek, and G. I. Stegeman, “All-optical switching in a hybrid Mach–Zehnder interferometer as a result of cascaded second-order nonlinearity,” Opt. Lett. 20, 2168–2170 (1995).

1994 (1)

1993 (3)

1992 (2)

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

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

1989 (1)

N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. (USSR) 66, 806–808 (1989).

1988 (1)

E. Strake, G. P. Bava, and I. Montrosset, “Guided modes of Ti:LiNbO3 channel waveguides: a novel quasi-analytical technique in comparison with a scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).

1987 (1)

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

1984 (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).

1979 (1)

W. K. Burns, P. H. Klein, and E. J. West, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).

1962 (1)

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

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

Armstrong, J. A.

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

Asobe, M.

Assanto, G.

Baek, Y.

Baumann, I.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

Bava, G. P.

E. Strake, G. P. Bava, and I. Montrosset, “Guided modes of Ti:LiNbO3 channel waveguides: a novel quasi-analytical technique in comparison with a scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

Belashenkov, N. R.

N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. (USSR) 66, 806–808 (1989).

Beranek, M. W.

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

Bierlein, J. D.

Bloembergen, N.

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

Bosshard, C.

Burns, W. K.

W. K. Burns, P. H. Klein, and E. J. West, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).

DeSalvo, R.

Ducuing, J.

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

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

Gagarskii, S. V.

N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. (USSR) 66, 806–808 (1989).

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 solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

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

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

Inochkin, M. V.

N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. (USSR) 66, 806–808 (1989).

Itoh, H.

Kaino, T.

Kim, D. Y.

Klein, P. H.

W. K. Burns, P. H. Klein, and E. J. West, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).

Kobyakov, A.

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

Krijnen, G.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

Krug, W.

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).

Lederer, F.

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

Levenson, J. A.

Lovering, D. J.

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

Miao, E.

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

Montrosset, I.

E. Strake, G. P. Bava, and I. Montrosset, “Guided modes of Ti:LiNbO3 channel waveguides: a novel quasi-analytical technique in comparison with a scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

Pershan, P. S.

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

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

Rochford, K. B.

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

Russell, P. St. J.

Schiek, R.

R. Schiek, “Soliton-like pulse propagation and second harmonic generation in waveguides with second-order optical nonlinearities,” AEÜ Int. J. Electron. Commun. 51, 77–86 (1997).

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

Y. Baek, R. Schiek, and G. I. Stegeman, “All-optical switching in a hybrid Mach–Zehnder interferometer as a result of cascaded second-order nonlinearity,” Opt. Lett. 20, 2168–2170 (1995).

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).

R. Schiek, “Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures,” J. Opt. Soc. Am. B 10, 1848–1855 (1993).

Seibert, H.

Sheik-Bahae, M.

Sohler, W.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

Stegeman, G. I.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).

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).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

Y. Baek, R. Schiek, and G. I. Stegeman, “All-optical switching in a hybrid Mach–Zehnder interferometer as a result of cascaded second-order nonlinearity,” Opt. Lett. 20, 2168–2170 (1995).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).

M. I. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, and J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides due to cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18, 13–15 (1993).

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

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

Strake, E.

E. Strake, G. P. Bava, and I. Montrosset, “Guided modes of Ti:LiNbO3 channel waveguides: a novel quasi-analytical technique in comparison with a scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).

Suche, H.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

Sundheimer, M. I.

Sundheimer, M. L.

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).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

Van Stryland, E.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

M. I. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, and J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides due to cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).

Vanherzeele, H.

Vidakovic, P.

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

Webjörn, J.

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

West, E. J.

W. K. Burns, P. H. Klein, and E. J. West, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).

Yokohama, I.

Zanoni, R.

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

AEÜ Int. J. Electron. Commun. (1)

R. Schiek, “Soliton-like pulse propagation and second harmonic generation in waveguides with second-order optical nonlinearities,” AEÜ Int. J. Electron. Commun. 51, 77–86 (1997).

Appl. Phys. Lett. (1)

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).

IEEE J. Quantum Electron. (2)

K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, “Pulse-modulated interferometer for measuring intensity-induced phase shifts,” IEEE J. Quantum Electron. 28, 2044–2050 (1992).

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3 integrated optical parametric oscillators,” IEEE J. Quantum Electron. 23, 42–51 (1987).

J. Appl. Phys. (1)

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E. Strake, G. P. Bava, and I. Montrosset, “Guided modes of Ti:LiNbO3 channel waveguides: a novel quasi-analytical technique in comparison with a scalar finite-element method,” J. Lightwave Technol. 6, 1126–1135 (1988).

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

Opt. Lett. (8)

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

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18, 13–15 (1993).

M. I. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, and J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides due to cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).

Y. Baek, R. Schiek, and G. I. Stegeman, “All-optical switching in a hybrid Mach–Zehnder interferometer as a result of cascaded second-order nonlinearity,” Opt. Lett. 20, 2168–2170 (1995).

M. Asobe, I. Yokohama, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).

P. Vidaković, D. J. Lovering, J. A. Levenson, J. Webjörn, and P. St. J. Russell, “Large nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3,” Opt. Lett. 22, 277–279 (1997).

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).

Opt. Quantum Electron. (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).

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Opt. Spectrosc. (USSR) (1)

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Phys. Rev. (1)

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Phys. Rev. A (1)

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

Phys. Rev. E (1)

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).

Phys. Rev. Lett. (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).

Other (4)

H. Seibert, “Neue Methoden der Phasenanpassung optisch nichtlinearer Wechselwirkungen in Ti:LiNbO3- und HxLi1−xNbO3-Streifenwellenleitern,” Ph.D. dissertation (Universität Paderborn, Paderborn, Germany, 1992).

M. Fejer, Ginston Laboratory, Stanford University, Stanford, California 94305–4085 (personal communication, 1996).

R. Schiek, H. Fang, and G. I. Stegeman, “Measurement of the non-uniformity of the wave-vector mismatch in waveguides for second-harmonic generation,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 256–258.

R. Schiek, “Die Selbstbeeinflussung von Licht in nichtlinearen dielektrischen Schichten,” Ph.D. dissertation (Technische Universität München, Munich, Germany, 1987).

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