Abstract

We show that useful noninstantaneous, nonlinear phase shifts can be obtained from cascaded quadratic processes in the presence of group-velocity mismatch. The two-field nature of the process permits responses that can be effectively advanced or retarded in time with respect to one of the fields. There is an analogy to a generalized Raman-scattering effect, permitting both red and blueshifts of short pulses. We expect this capability to have many applications in short-pulse generation and propagation, such as the compensation of Raman-induced effects and high-quality pulse compression, which we discuss.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. I. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. J. 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), Chap. 2, pp. 49–76.
  2. C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2)(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
    [CrossRef]
  3. 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 (1997).
    [CrossRef]
  4. H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
    [CrossRef] [PubMed]
  5. X. Liu, L. J. Qian, and F. W. 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]
  6. F. Wise, L. Qian, and X. Liu, “Applications of cascaded quadratic nonlinearities to femtosecond pulse generation,” J. Nonlinear Opt. Phys. Mater. 11, 317–338 (2002).
    [CrossRef]
  7. S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
    [CrossRef]
  8. L. J. Qian, X. Liu, and F. W. Wise, “Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts,” Opt. Lett. 24, 166–168 (1999).
    [CrossRef]
  9. K. Beckwitt, F. W. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
    [CrossRef]
  10. P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
    [CrossRef] [PubMed]
  11. P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides,” Opt. Lett. 27, 2182–2184 (2002).
    [CrossRef]
  12. A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three-wave interaction,” Physica D 4, 122–134 (1981).
    [CrossRef]
  13. J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).
    [CrossRef]
  14. H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
    [CrossRef]
  15. A. Kundu, “Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations,” J. Math. Phys. 25, 3433–3438 (1984).
    [CrossRef]
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  17. X. Liu, K. Beckwitt, and F. W. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (2000).
    [CrossRef]
  18. O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
    [CrossRef]
  19. W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).
  20. P. T. Dinda, K. Nakkeean, and A. Labruyere, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
    [CrossRef]
  21. A. Galvanauskas, “Mode-scalable fiber-based chirped-pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7, 504–517 (2001).
    [CrossRef]
  22. 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]
  23. F. Ö. Ilday and F. W. Wise, “Nonlinearity management: a route to high-energy soliton fiber lasers,” J. Opt. Soc. Am. B 19, 470–476 (2002), and references therein.
    [CrossRef]
  24. C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28, 986–988 (2003).
    [CrossRef] [PubMed]
  25. S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).
    [CrossRef]
  26. P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
    [CrossRef]

2003 (2)

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28, 986–988 (2003).
[CrossRef] [PubMed]

2002 (6)

2001 (3)

S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
[CrossRef]

K. Beckwitt, F. W. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
[CrossRef]

A. Galvanauskas, “Mode-scalable fiber-based chirped-pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7, 504–517 (2001).
[CrossRef]

2000 (2)

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

X. Liu, K. Beckwitt, and F. W. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (2000).
[CrossRef]

1999 (2)

1997 (2)

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 (1997).
[CrossRef]

J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).
[CrossRef]

1994 (1)

1992 (1)

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]

1990 (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

1987 (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

1984 (1)

A. Kundu, “Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations,” J. Math. Phys. 25, 3433–3438 (1984).
[CrossRef]

1981 (1)

A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three-wave interaction,” Physica D 4, 122–134 (1981).
[CrossRef]

1979 (1)

H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
[CrossRef]

Ashihara, S.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Bang, O.

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Baronio, F.

Barthelemy, A.

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Beckwitt, K.

K. Beckwitt, F. W. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
[CrossRef]

X. Liu, K. Beckwitt, and F. W. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (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]

Canto-Said, E.

Carrasco, S.

S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
[CrossRef]

Chen, H. H.

H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
[CrossRef]

Chinglia, W.

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Couderc, V.

De Angelis, C.

Di Trapani, P.

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Dinda, P. T.

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]

Galvanauskas, A.

A. Galvanauskas, “Mode-scalable fiber-based chirped-pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7, 504–517 (2001).
[CrossRef]

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Ilday, F. Ö.

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]

Kanashov, A. A.

A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three-wave interaction,” Physica D 4, 122–134 (1981).
[CrossRef]

Kobyakov, A.

Krlikowski, W.

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

Krolikowski, W.

O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Kundu, A.

A. Kundu, “Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations,” J. Math. Phys. 25, 3433–3438 (1984).
[CrossRef]

Kuroda, K.

Labruyere, A.

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Lederer, F.

Lee, Y. C.

H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
[CrossRef]

Lefort, L.

Liu, C. S.

H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
[CrossRef]

Liu, X.

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]

Menyuk, C. R.

Min, Y.

Minardi, S.

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Nakkeean, K.

Nishina, J.

Pioger, P.

Piskarskas, A.

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Qian, L.

F. Wise, L. Qian, and X. Liu, “Applications of cascaded quadratic nonlinearities to femtosecond pulse generation,” J. Nonlinear Opt. Phys. Mater. 11, 317–338 (2002).
[CrossRef]

K. Beckwitt, F. W. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26, 1696–1698 (2001).
[CrossRef]

Qian, L. J.

Quiring, V.

Rasmussen, J.

O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Rasmussen, J. J.

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

Rubenchik, A. M.

A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three-wave interaction,” Physica D 4, 122–134 (1981).
[CrossRef]

Schiek, R.

Schmidt, E.

Shimura, T.

Sohler, W.

Torner, L.

S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
[CrossRef]

J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).
[CrossRef]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2)(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
[CrossRef]

Torres, J. P.

S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
[CrossRef]

J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).
[CrossRef]

Valiulis, G.

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Walker, L. A.

Weber, H. P.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Wise, F.

F. Wise, L. Qian, and X. Liu, “Applications of cascaded quadratic nonlinearities to femtosecond pulse generation,” J. Nonlinear Opt. Phys. Mater. 11, 317–338 (2002).
[CrossRef]

Wise, F. W.

Wyller, J.

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Xu, C.

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

Acta Phys. Pol. A (1)

W. Krlikowski, O. Bang, J. Wyller, and J. J. Rasmussen, “Optical beams in nonlocal nonlinear media,” Acta Phys. Pol. A 103, 133–148 (2003).

IEEE J. Quantum Electron. (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]

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. QE-23, 1938–1946 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Galvanauskas, “Mode-scalable fiber-based chirped-pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7, 504–517 (2001).
[CrossRef]

J. Math. Phys. (1)

A. Kundu, “Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations,” J. Math. Phys. 25, 3433–3438 (1984).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

F. Wise, L. Qian, and X. Liu, “Applications of cascaded quadratic nonlinearities to femtosecond pulse generation,” J. Nonlinear Opt. Phys. Mater. 11, 317–338 (2002).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

S. Carrasco, J. P. Torres, L. Torner, and F. W. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

J. P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. 29, 757–776 (1997).
[CrossRef]

Phys. Rev. A (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (2)

X. Liu, K. Beckwitt, and F. W. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (2000).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

P. Di Trapani, W. Chinglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef] [PubMed]

Phys. Scr. (1)

H. H. Chen, Y. C. Lee, and C. S. Liu, “Integrability of nonlinear Hamiltonian systems by inverse scattering method,” Phys. Scr. 20, 490–492 (1979).
[CrossRef]

Physica D (1)

A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three-wave interaction,” Physica D 4, 122–134 (1981).
[CrossRef]

Other (2)

G. I. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. J. 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), Chap. 2, pp. 49–76.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Illustration of the cascaded quadratic processes under phase-mismatch conditions. The FF is partially converted to the SH and then backconverted. Dashed (solid) curves are for the case of zero (nonzero) GVM.

Fig. 2
Fig. 2

(a) Evolution of the spectrum along the propagation direction. Shift is in units of the initial spectral FWHM, ∼3.7 THz. The scale bar shows spectral intensity in arbitrary units. (b) Weighted average frequency shift as a function of propagation distance. Dashed curve indicates fit to region of linear shift. Dashed–dotted curve shows similar results in the absence of χ(3) (n2=0).

Fig. 3
Fig. 3

Intensity profiles of the FF at z=0 mm (dashed–dotted curve), z=12 mm (solid curve), z=100 mm (dashed curve). For the launched pulse LDS,1=74 mm.

Fig. 4
Fig. 4

Frequency shift (crosses) and figure of merit (circles) as a function of phase mismatch. Similarly to Fig. 2, frequency shift is measured in units of the initial FWHM (here ∼4.4 THz). Note that GVD is chosen to be normal (anomalous) for Δk>0 (Δk<0) to support solitonlike pulses.

Fig. 5
Fig. 5

Phase impressed on the FF for zero (solid curve), positive (dashed curve), and negative (dashed–dotted curve) GVM.

Fig. 6
Fig. 6

Experimental (solid curves) and simulated (dashed curves) spectra for phase mismatches of 5π/mm and 36π/mm. The latter serves as control. Inset: experimental (symbols) and calculated (solid curve) frequency shift for different values of phase mismatch. As in Fig. 2, frequency shift is measured in units of the initial FWHM, ∼3.7 THz.

Fig. 7
Fig. 7

Pulse spectrum after propagation in fiber without precompensation (dashed–dotted curve) and after cascade precompensation stage (dashed curve) and subsequent propagation through fiber (solid curve). Dots indicate the launched pulse spectrum.

Fig. 8
Fig. 8

Temporal profile of compressed pulses before (dashed curve) and after spectral filtering (solid curve) of the unshifted frequencies. Inset: compressed pulse spectrum before (dashed curve) and after filtering (solid curve). Dashed–dotted curves indicate the launched temporal profile–spectrum.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

ia1ξ-δ122a1τ2+a1*a2 exp(iβξ)=0,
ia2ξ-δ222a2τ2-ia2τ+a12 exp(-iβξ)=0.
ia1ξ-δ122a1τ2-1β|a1|2a1-2i1β2|a1|2a1τ+1β2(δ1-δ2)|a1|22a1τ2-δ2β2a1*a1τ2
+O1|β|3=0.
ia1ξ-δ122a1τ2-1β|a1|2a1-2i1β2|a1|2a1τ=0.
iq(Z, T)Z-2q(Z, T)T2+i|q(Z, T)|2q(Z, T)T=0
a1(ξ, τ)=c0 exp[i(c1ξ+c2t)]q(ξ, τ),
T=-2/δ1τ-βδ1/2ξ,
Z=ξ.
ia1ξδ122a1τ2+γ|a1|2a1NLSETRa1|a1|2τRaman=0.
uξ=δ1uτϕτ+δ12u2ϕτ2+2β2u2uτ,
uϕξ=-δ122uτ2+δ12ϕτ2u-1βu3+2β2u3ϕτ.
uξ=2β2u2uτ,
uϕξ=-1βu3+2β2u3ϕτ.
ϕ(ξ, τ)=-1βu2(τ)ξ+O1β2.
ϕξ-1βu2-4β3u3uτ.
ϕ(ξ, τ)-1βsech2(τ)1+ξ2β2 sech (τ)tanh(τ)ξ+ϕ0,
1β|a1|2a1+2i1β2|a1|2a1τ
=π/2β(1+ω2)(3+2ω/β)sech(πω/2),
iA1z-ZI2LDS,12A1τ2+A1*A2 exp[iΔk(ZIz)]
+ZILNL,1(|A1|2+2|A2|2)A1=0,
iA2z-ZI2LDS,22A2τ2-iZILGVMA2τ
+n(ω1)n(ω2)A12 exp[-iΔk(ZIz)]
+n(ω1)n(ω2)ZILNL,2(2|A1|2+|A2|2)A2=0.

Metrics