Abstract

A technique for numerically simulating second-order nonlinear interactions of light waves modulated spatially and temporally in both amplitude and phase in a uniaxial medium with arbitrary polarization and propagation directions is presented. A three-dimensional grid technique that automatically adapts grid parameters to the evolving sampled amplitudes by means of an analytical fit function is described. By means of spatiotemporal split-step fast-Fourier-transform propagation, diffraction and group-velocity dispersion can be included. We employ this technique for femtosecond noncollinear white-light-seeded parametric amplification in experimental designs presented earlier [Opt. Lett. 22, 1494 (1997); 23, 1283 (1998)]. The dependence of phase mismatch on signal wavelength provides a quantitative measure of the achromaticity of phase matching. Our results indicate that the pump pulse characteristics and not phase mismatching limit the amplification and the bandwidth of the parametric amplifier.

© 1999 Optical Society of America

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  1. P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).
  2. P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).
  3. P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).
  4. S. R. Greenfield and M. R. Wasielewski, “Optical parametric amplification of femtosecond pulses tunable from the blue to the infrared with microjoule energies,” Appl. Opt. 34, 2688–2691 (1995).
  5. F. Hache, T. J. Driscoll, M. Cavallari, and G. M. Gale, “Measurement of ultrashort pulse durations by interferometric autocorrelation: influence of various parameters,” Appl. Opt. 35, 3230–3236 (1996).
  6. T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494–1496 (1997).
  7. G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).
  8. G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).
  9. A. Shirakawa and T. Kobayashi, “Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared,” Opt. Lett. 23, 1292–1294 (1998).
  10. H. J. Bakker, P. C. M. Planken, and H. G. Muller, “Numeri-cal calculation of optical frequency-conversion processes: a new approach,” J. Opt. Soc. Am. B 6, 1665–1672 (1989).
  11. T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
  12. E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58, 1235–1237 (1968).
  13. E. Lalor, “The angular spectrum representation of electromagnetic fields in crystals,” J. Math. Phys. 13, 437–449 (1972).
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
  15. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  16. M. Trippenbach and Y. B. Band, “Propagation of light pulses in nonisotropic media,” J. Opt. Soc. Am. B 13, 1403–1411 (1996).
  17. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996).
  18. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer-Verlag, Berlin, 1997).
  19. R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).
  20. J. Manz and L. Wöste, eds., Femtosecond Chemistry (VCH, Weinheim, Germany, 1995), Vols. 1 and 2.
  21. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
  22. J. Lindener-Roenneke, “Pump-Tast-Spektroskopie mit durchstimmbaren Femtosekundenpulsen: Realisierung eines experimentellen Aufbas und Untersuchungen zur Dynamik von Cr(CO)6 und Cr(CO)6 ⋅ (CH3OH)nHeteroclustern,” Ph.D. dissertation (Universität zu Köln, Cologne, Germany, 1998).
  23. F. Hache, M. Cavallari, and G. M. Gale, “Ultrafast visible optical parametric oscillators: a route to tunable sub-10-femtosecond pulses?” in Ultrafast Phenomena X, Vol. 62 of Springer Series in Chemical Physics, P. F. Barbara, J. G. Fujimoto, W. H. Knox, and W. Zinth, eds. (Springer-Verlag, Berlin, 1996), pp. 33–35.
  24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

1998 (2)

1997 (3)

T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494–1496 (1997).

G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

1996 (3)

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

M. Trippenbach and Y. B. Band, “Propagation of light pulses in nonisotropic media,” J. Opt. Soc. Am. B 13, 1403–1411 (1996).

F. Hache, T. J. Driscoll, M. Cavallari, and G. M. Gale, “Measurement of ultrashort pulse durations by interferometric autocorrelation: influence of various parameters,” Appl. Opt. 35, 3230–3236 (1996).

1995 (4)

S. R. Greenfield and M. R. Wasielewski, “Optical parametric amplification of femtosecond pulses tunable from the blue to the infrared with microjoule energies,” Appl. Opt. 34, 2688–2691 (1995).

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

1989 (1)

1975 (1)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).

1972 (1)

E. Lalor, “The angular spectrum representation of electromagnetic fields in crystals,” J. Math. Phys. 13, 437–449 (1972).

1968 (1)

Andreoni, A.

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Bakker, H. J.

Band, Y. B.

Banfi, G. P.

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Bischel, W. K.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).

Cavallari, M.

Cerullo, G.

G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).

G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).

Danielius, R.

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

De Silvestri, S.

G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).

G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).

Di Trapani, P.

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

Driscoll, T. J.

Fisher, R. A.

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).

Foggi, P.

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Gale, G. M.

Greenfield, S. R.

Hache, F.

Kobayashi, T.

Lalor, E.

E. Lalor, “The angular spectrum representation of electromagnetic fields in crystals,” J. Math. Phys. 13, 437–449 (1972).

E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58, 1235–1237 (1968).

Lin, Q.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

Matousek, P.

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Monguzzi, M.

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Muller, H. G.

Nishikawa, T.

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).

Nisoli, M.

G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).

G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).

Parker, A. W.

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Piel, J.

Piskarskas, A.

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

Planken, P. C. M.

Riedle, E.

Shirakawa, A.

Solcia, C.

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Sozzi, C.

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Stagira, S.

Taday, P. F.

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Toner, W. T.

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Towrie, M.

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Trippenbach, M.

Uesugi, N.

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).

Wang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

Wasielewski, M. R.

Wilhelm, T.

Xu, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

Zhang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

G. Cerullo, M. Nisoli, and S. De Silvestri, “Generation of 11 fs pulses tunable across the visible by optical parametric amplification,” Appl. Phys. Lett. 71, 3616–3618 (1997).

IEEE J. Quantum Electron. (1)

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).

J. Appl. Phys. (2)

R. A. Fisher and W. K. Bischel, “Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses,” J. Appl. Phys. 46, 4921–4934 (1975).

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).

J. Math. Phys. (1)

E. Lalor, “The angular spectrum representation of electromagnetic fields in crystals,” J. Math. Phys. 13, 437–449 (1972).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

P. Di Trapani, A. Andreoni, P. Foggi, C. Solcia, R. Danielius, and A. Piskarskas, “Efficient conversion of femtosecond blue pulses by travelling-wave parametric generation in non-collinear phase matching,” Opt. Commun. 119, 327–332 (1995).

P. Matousek, A. W. Parker, P. F. Taday, W. T. Toner, and M. Towrie, “Two independently tunable and synchronised femtosecond pulses generated in the visible at the repetition rate 40 kHz using optical parametric amplifiers,” Opt. Commun. 127, 307–312 (1996).

Opt. Lett. (3)

Phys. Rev. A (1)

P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51, 3164–3168 (1995).

Other (8)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

J. Manz and L. Wöste, eds., Femtosecond Chemistry (VCH, Weinheim, Germany, 1995), Vols. 1 and 2.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer-Verlag, Berlin, 1997).

J. Lindener-Roenneke, “Pump-Tast-Spektroskopie mit durchstimmbaren Femtosekundenpulsen: Realisierung eines experimentellen Aufbas und Untersuchungen zur Dynamik von Cr(CO)6 und Cr(CO)6 ⋅ (CH3OH)nHeteroclustern,” Ph.D. dissertation (Universität zu Köln, Cologne, Germany, 1998).

F. Hache, M. Cavallari, and G. M. Gale, “Ultrafast visible optical parametric oscillators: a route to tunable sub-10-femtosecond pulses?” in Ultrafast Phenomena X, Vol. 62 of Springer Series in Chemical Physics, P. F. Barbara, J. G. Fujimoto, W. H. Knox, and W. Zinth, eds. (Springer-Verlag, Berlin, 1996), pp. 33–35.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

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