Abstract

We propose a novel type of cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves. Self-phase modulation of the fundamental wave results from a cascading process consisting of four second-order subprocesses, the direct and reverse subprocesses of Type I second-harmonic generation (SHG) and the direct and reverse subprocesses of Type II SHG. It is found analytically and numerically that the fundamental wave passing through a quadratic medium, tuned for simultaneous near phase matching for these two processes, collects 60% more nonlinear phase shift than does the corresponding two-step cascading. We also obtain the conditions for stationary waves (nonlinear modes) supported by such multistep cascading processes.

© 2000 Optical Society of America

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  1. G. Stegeman, D. 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).
    [Crossref]
  2. G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.
  3. S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2):χ(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.
  4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992).
    [Crossref] [PubMed]
  5. K. Koynov, S. Saltiel, and I. Buchvarov, “All-optical switching by means of an interferometer with nonlinear frequency doubling mirrors,” J. Opt. Soc. Am. B 14, 834–838 (1997).
    [Crossref]
  6. M. Cha, “Casaded phase shift and intensity phase modulation in aperiodic quasi-phase matched gratings,” Opt. Lett. 23, 250–252 (1998).
    [Crossref]
  7. S. Saltiel, K. Koynov, and M. Fejer, “Aperiodic quasi-phase-matching as a method to reduce switching intensity in devices based on second-order cascading,” in Conference on Lasers and Electro-Optics (CLEO Europe) (Optical Society of America, Washington, D.C., 1998), paper CWF68, p. 193.
  8. K. Koynov and S. Saltiel, “Nonlinear phase shift via multistep cascading,” Opt. Commun. 152, 96–100 (1998).
    [Crossref]
  9. G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in second-order cascading: novel approaches,” Opt. Lett. 19, 1720–1722 (1994).
    [Crossref] [PubMed]
  10. A. L. Belostotsky, A. S. Leonov, and A. V. Meleshko, “Nonlinear phase change in type II second-harmonic generation under exact phase-matched conditions,” Opt. Lett. 19, 856–858 (1994).
    [Crossref] [PubMed]
  11. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
    [Crossref]
  12. S. Saltiel and Y. Deyanova, “Polarization switching as a result of cascading of two simultaneously phase-matched processes,” Opt. Lett. 24, 1296–1298 (1999).
    [Crossref]
  13. 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]
  14. O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. Van Baak, M. D. Levenson, and W. R. Bosenberg, “Continuous-wave frequency tripling and quadrupoling by simultaneous three-wave mixing in periodically poled crystals: application to a two-step 1.19–10.71-mm frequency bridge,” Opt. Lett. 22, 1211–1213 (1997).
    [Crossref] [PubMed]
  15. Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, “Two-colour multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056–R5059 (1999).
    [Crossref]
  16. Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979).
    [Crossref]
  17. R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
    [Crossref]
  18. S. Saltiel, S. Tanev, and A. Boardman, “High-order nonlinear phase shift due to cascaded third-order processes,” Opt. Lett. 22, 148–150 (1997).
    [Crossref] [PubMed]
  19. S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
    [Crossref]
  20. R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, “Modification of solitary waves by third-harmonic generation,” Opt. Lett. 22, 1385–1387 (1997).
    [Crossref]
  21. G. Cerullo, S. De Silvestri, A. Monduzzi, D. Segala, and V. Magni, “Self-starting mode-locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746–748 (1995).
    [Crossref] [PubMed]
  22. V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
    [Crossref]
  23. S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
    [Crossref]
  24. C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999).
    [Crossref]
  25. Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, “Spatial optical solitons resulting from multistep cascading,” Opt. Lett. 24, 759–761 (1999).
    [Crossref]
  26. I. Towers, R. Sammut, A. V. Buryak, and B. A. Malomed, “Soliton multistability as a result of double-resonance wave mixing in χ(2) media,” Opt. Lett. 24, 1738–1740 (1999).
    [Crossref]
  27. A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3290 (1997).
    [Crossref]

1999 (5)

1998 (4)

M. Cha, “Casaded phase shift and intensity phase modulation in aperiodic quasi-phase matched gratings,” Opt. Lett. 23, 250–252 (1998).
[Crossref]

K. Koynov and S. Saltiel, “Nonlinear phase shift via multistep cascading,” Opt. Commun. 152, 96–100 (1998).
[Crossref]

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
[Crossref]

1997 (6)

1996 (2)

R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
[Crossref]

G. Stegeman, D. 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).
[Crossref]

1995 (2)

G. Cerullo, S. De Silvestri, A. Monduzzi, D. Segala, and V. Magni, “Self-starting mode-locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746–748 (1995).
[Crossref] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

1994 (2)

1992 (2)

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992).
[Crossref] [PubMed]

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]

1979 (1)

Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979).
[Crossref]

Afanasjev, V. V.

R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
[Crossref]

Alexander, T. J.

Assanto, G.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in second-order cascading: novel approaches,” Opt. Lett. 19, 1720–1722 (1994).
[Crossref] [PubMed]

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Baboiu, D.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Baek, Y.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Bang, O.

C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999).
[Crossref]

Barthelemy, A.

V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
[Crossref]

Belostotsky, A. L.

Boardman, A.

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

S. Saltiel, S. Tanev, and A. Boardman, “High-order nonlinear phase shift due to cascaded third-order processes,” Opt. Lett. 22, 148–150 (1997).
[Crossref] [PubMed]

Bosenberg, W. R.

Buchvarov, I.

K. Koynov, S. Saltiel, and I. Buchvarov, “All-optical switching by means of an interferometer with nonlinear frequency doubling mirrors,” J. Opt. Soc. Am. B 14, 834–838 (1997).
[Crossref]

S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2):χ(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.

Buryak, A. V.

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]

Cerullo, G.

Cha, M.

Christiansen, P. L.

C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999).
[Crossref]

Clausen, C. B.

C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999).
[Crossref]

Couderc, V.

V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
[Crossref]

De Silvestri, S.

DeSalvo, R.

Deyanova, Y.

Fejer, M.

S. Saltiel, K. Koynov, and M. Fejer, “Aperiodic quasi-phase-matching as a method to reduce switching intensity in devices based on second-order cascading,” in Conference on Lasers and Electro-Optics (CLEO Europe) (Optical Society of America, Washington, D.C., 1998), paper CWF68, p. 193.

Fejer, M. M.

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]

Ge, C.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Guy, O.

V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
[Crossref]

Hagan, D.

G. Stegeman, D. 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).
[Crossref]

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Hagan, D. J.

Hollberg, L.

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]

Kivshar, Yu. S.

Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, “Two-colour multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056–R5059 (1999).
[Crossref]

C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999).
[Crossref]

Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, “Spatial optical solitons resulting from multistep cascading,” Opt. Lett. 24, 759–761 (1999).
[Crossref]

A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3290 (1997).
[Crossref]

R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, “Modification of solitary waves by third-harmonic generation,” Opt. Lett. 22, 1385–1387 (1997).
[Crossref]

R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
[Crossref]

Koynov, K.

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

K. Koynov and S. Saltiel, “Nonlinear phase shift via multistep cascading,” Opt. Commun. 152, 96–100 (1998).
[Crossref]

K. Koynov, S. Saltiel, and I. Buchvarov, “All-optical switching by means of an interferometer with nonlinear frequency doubling mirrors,” J. Opt. Soc. Am. B 14, 834–838 (1997).
[Crossref]

S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2):χ(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.

S. Saltiel, K. Koynov, and M. Fejer, “Aperiodic quasi-phase-matching as a method to reduce switching intensity in devices based on second-order cascading,” in Conference on Lasers and Electro-Optics (CLEO Europe) (Optical Society of America, Washington, D.C., 1998), paper CWF68, p. 193.

Leonov, A. S.

Levenson, M. D.

Love, J. D.

R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
[Crossref]

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]

Magni, V.

Malomed, B. A.

Meleshko, A. V.

Micalef, R. W.

R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996).
[Crossref]

Ming, N.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Monduzzi, A.

Pfister, O.

Pushkarov, D. I.

Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979).
[Crossref]

Pushkarov, Kh. I.

Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979).
[Crossref]

Qin, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Roisse, E.

V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998).
[Crossref]

Saltiel, S.

Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, “Spatial optical solitons resulting from multistep cascading,” Opt. Lett. 24, 759–761 (1999).
[Crossref]

Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, “Two-colour multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056–R5059 (1999).
[Crossref]

S. Saltiel and Y. Deyanova, “Polarization switching as a result of cascading of two simultaneously phase-matched processes,” Opt. Lett. 24, 1296–1298 (1999).
[Crossref]

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

K. Koynov and S. Saltiel, “Nonlinear phase shift via multistep cascading,” Opt. Commun. 152, 96–100 (1998).
[Crossref]

K. Koynov, S. Saltiel, and I. Buchvarov, “All-optical switching by means of an interferometer with nonlinear frequency doubling mirrors,” J. Opt. Soc. Am. B 14, 834–838 (1997).
[Crossref]

S. Saltiel, S. Tanev, and A. Boardman, “High-order nonlinear phase shift due to cascaded third-order processes,” Opt. Lett. 22, 148–150 (1997).
[Crossref] [PubMed]

S. Saltiel, K. Koynov, and M. Fejer, “Aperiodic quasi-phase-matching as a method to reduce switching intensity in devices based on second-order cascading,” in Conference on Lasers and Electro-Optics (CLEO Europe) (Optical Society of America, Washington, D.C., 1998), paper CWF68, p. 193.

S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2):χ(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.

Sammut, R.

Sammut, R. A.

Scheik, R.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Segala, D.

Sheik-Bahae, M.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992).
[Crossref] [PubMed]

Stegeman, G.

G. Stegeman, D. 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).
[Crossref]

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992).
[Crossref] [PubMed]

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Sukhorukov, A. A.

Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, “Two-colour multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056–R5059 (1999).
[Crossref]

Tanev, S.

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

S. Saltiel, S. Tanev, and A. Boardman, “High-order nonlinear phase shift due to cascaded third-order processes,” Opt. Lett. 22, 148–150 (1997).
[Crossref] [PubMed]

Tomov, I. V.

Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979).
[Crossref]

Torelli, I.

Torner, L.

G. Stegeman, D. 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).
[Crossref]

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Torruellas, W.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Towers, I.

Trillo, S.

Tzankov, P.

S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
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Van Baak, D. A.

Van Stryland, E.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Van Stryland, E. W.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
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R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992).
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Wang, H.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Wang, Z.

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Wells, J. S.

Zhu, S.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Zhu, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Zink, L.

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S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998).
[Crossref]

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Other (3)

G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2):χ(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.

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Figures (5)

Fig. 1
Fig. 1

Nonlinear phase shift ΔφA of fundamental wave A as a function of the phase mismatch of the Type I SHG process. Dashed–dotted–dotted curves are analytical results [Eq. (5)]; solid curves are numerical solutions of the system of Eqs. (1).

Fig. 2
Fig. 2

Nonlinear phase shift and the intensity transmittance of fundamental wave A as a function of its normalized input amplitude for the two-color MSC scheme (solid and dashed curves) and for Type I SHG (dashed–dotted–dotted curve). The chosen phase-mismatch parameters are for collection of (a) π NPS or (b) π/2 NPS at the point of full reconstruction of the intensity of fundamental wave A.

Fig. 3
Fig. 3

Values of the phase mismatches for achieving π NPS (darker-colored curves) and π/2 NPS (lighter-colored curves). The switching intensities Is=(σaL)2 are indicated as well. Only data for which the transmittance of the fundamental wave is more than 0.9 are shown.

Fig. 4
Fig. 4

Dependence of the NPS of fundamental wave A and phase mismatches Δk1L and Δk2L on the input amplitude of fundamental wave A in a regime of stationary-wave propagation. The normalized input amplitudes of waves B and S are Bst=1 and Sst=1, respectively (σ1=σ2=σ).

Fig. 5
Fig. 5

Conditions for stable propagation of phase-locked stationary waves. The numbers indicate the values of Sst, the normalized input amplitude of the second-harmonic wave (β=σ2/σ1=1). Black and white areas correspond to unstable and stable stationary modes, respectively.

Equations (32)

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dSdz=-iσ1A2 exp(iΔk1z)-2iσ2AB exp(iΔk2z),
dAdz=-iσ1SA* exp(-iΔk1z)-iσ2SB* exp(-iΔk2z),
dBdz=-iσ2SA* exp(-iΔk2z),
dS˜dz+iΔk1S˜=-iσ1A2-i2σ2B˜A,
dAdz=-iσ1S˜A*-iσ2B˜*S˜,
dB˜dz+iΔkB˜=-iσ2S˜A*.
S˜=-σ1A2[1-exp(-iQz)]/Q,
B˜=σ1σ2|A|2A[1-exp(-iQz)]/QΔk,
ΔφA=ΔφATSC+ΔφAMSC,
ΔφATSC=σ12a2LQ1-sin(Qz)Qz,
ΔφAMSC=2σ12σ22a4LQ2Δk1-sin(Qz)Qz.
dAdz-i σ12Q|A|2A-i σ12σ22Q2Δk|A|4A=0,
ΔφAσ12a2Q1+2σ22a2QΔkL,
σ1AL=An exp[i(φA+hAξ)],
σ1BL=Bn exp[i(φA+hBξ)],
σ1SL=Sn exp[i(2φA+hSξ)],
hS-2hA=Δk1L,hS-hA-hB=Δk2L,
i dSndξ-hSSn-An2-2βBnAn=0,
i dAndξ-hAAn-SnAn*-βSstBn*=0,
i dBndξ-hBBn-βSstAn*=0,
Δk1L=1+2β BstAst Sst2-Ast2Sst+Sst,
Δk2L=1+β BstAst Sst2-Ast2Sst+βAstSstBst(Sst2-Bst2).
An=Ast+(a1+ia2)exp(λξ),
Bn=Bst+(b1+ib2)exp(λξ),
Sn=Sst+(s1+is2)exp(λξ),
Lˆ(-)m=λIˆr,
Lˆ(+)r=-λIˆm,
Lˆ(±)=ha±Sst±βSstAst+βBst±βSsthbβAst2Ast+2βBst2βAsths.
Asta1+Bstb1+Ssts1=0.
λ4+C2λ2+C0=0,
C2=Ast2Bst2Sst24β2+4β AstBst+Ast2Bst2+Sst2β22BstβAst+Bst2Ast2+Ast2Bst2+2β2(2Bst2+2Ast2-Sst2)+4Ast2+8βAstBst,
C0=Ast4Sst2Bst2β24+8β BstAst+Ast2Sst2+Ast2β2(6Ast2+4Sst2-3Bst2)-2βAst3Bst+8β3AstBst(Ast2+Sst2).

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