Abstract

The effects of the phase mismatch due to cubic nonlinearity in the equations for second-harmonic generation are investigated. We show that the phase mismatch induced by the nonlinear refractive index of a doubling crystal can dramatically reduce the conversion efficiency of high-peak-power laser pulses. Simple, analytic expressions are derived for the conversion efficiency of cw radiation and for the estimation of the dispersion in the nonlinear refractive index of the doubling crystal, which is quite important in the determination of the magnitude of the nonlinear effects on maximum conversion. The consequences that these nonlinearities have on the frequency doubling of ultrashort (≤100 fs) pulses, including the additional effects of group-velocity walk-off between the pulses, are then numerically calculated.

© 1996 Optical Society of America

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1995

1993

1992

R. Adair, L. L. Chase, and S. A. Payne, "Dispersion of the nonlinear refractive index of optical crystals," Opt. Mater. 1, 185 (1992).

1991

1990

1989

R. Adair, L. L. Chase, and S. A. Payne, "Nonlinear refractive index of optical crystals," Phys. Rev. B 39, 3337 (1989).

1985

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Phys. Rep. 129, 286 (1985).

1984

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

1982

L. S. Telegin and A. S. Chirkin, "Interaction in frequency doubling of ultrashort laser pulses," Sov. J. Quantum Electron. 12, 1358 (1982).

D. J. Harter and D. C. Brown, "Effects of higher order nonlinearities on second-order frequency mixing," IEEE J. Quantum Electron. QE-18, 1146 (1982).

1978

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601 (1978).

1968

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

1966

H. B. Bebb and A. Gold, "Multiphoton ionization of hydrogen and rare-gas atoms," Phys. Rev. 143, 1 (1966).

1965

J. E. Midwinter and J. Warner, "The effects of phase matching method and of uniaxial symmetry on the polar distribution of second order non-linear optical polarization," Br. J. Appl. Phys. 16, 1135 (1965).

1964

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

1961

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, "Dispersion of the nonlinear refractive index of optical crystals," Opt. Mater. 1, 185 (1992).

R. Adair, L. L. Chase, and S. A. Payne, "Nonlinear refractive index of optical crystals," Phys. Rev. B 39, 3337 (1989).

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon and Breach, New York, 1972).

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

Bakker, H. J.

Banerjee, P. P.

Bebb, H. B.

H. B. Bebb and A. Gold, "Multiphoton ionization of hydrogen and rare-gas atoms," Phys. Rev. 143, 1 (1966).

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

Boer, M. P. de

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601 (1978).

Brown, D. C.

D. J. Harter and D. C. Brown, "Effects of higher order nonlinearities on second-order frequency mixing," IEEE J. Quantum Electron. QE-18, 1146 (1982).

Caimi, F. C.

Cao, X. D.

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, "Dispersion of the nonlinear refractive index of optical crystals," Opt. Mater. 1, 185 (1992).

R. Adair, L. L. Chase, and S. A. Payne, "Nonlinear refractive index of optical crystals," Phys. Rev. B 39, 3337 (1989).

Chien, C. Y.

Chirkin, A. S.

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

L. S. Telegin and A. S. Chirkin, "Interaction in frequency doubling of ultrashort laser pulses," Sov. J. Quantum Electron. 12, 1358 (1982).

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

Choe, W.

Coe, J. S.

Craxton, R. S.

Drabovich, K. N.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601 (1978).

Gold, A.

H. B. Bebb and A. Gold, "Multiphoton ionization of hydrogen and rare-gas atoms," Phys. Rev. 143, 1 (1966).

Harter, D. J.

D. J. Harter and D. C. Brown, "Effects of higher order nonlinearities on second-order frequency mixing," IEEE J. Quantum Electron. QE-18, 1146 (1982).

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Khokhlov, R. V.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon and Breach, New York, 1972).

Kholodnykh, A. I.

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

Korn, G.

Kovrigin, A. I.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

McKinstrie, C. J.

Midwinter, J. E.

J. E. Midwinter and J. Warner, "The effects of phase matching method and of uniaxial symmetry on the polar distribution of second order non-linear optical polarization," Br. J. Appl. Phys. 16, 1135 (1965).

Mourou, G.

Musher, S. L.

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Phys. Rep. 129, 286 (1985).

Noordam, L. D.

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601 (1978).

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, "Dispersion of the nonlinear refractive index of optical crystals," Opt. Mater. 1, 185 (1992).

R. Adair, L. L. Chase, and S. A. Payne, "Nonlinear refractive index of optical crystals," Phys. Rev. B 39, 3337 (1989).

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Razumikhina, T. B.

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

Rubenchik, A. M.

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Phys. Rep. 129, 286 (1985).

Squier, J.

Sukhorukov, A. P.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

Telegin, L. S.

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

L. S. Telegin and A. S. Chirkin, "Interaction in frequency doubling of ultrashort laser pulses," Sov. J. Quantum Electron. 12, 1358 (1982).

van den Heuvell, H. B. van Linden

Warner, J.

J. E. Midwinter and J. Warner, "The effects of phase matching method and of uniaxial symmetry on the polar distribution of second order non-linear optical polarization," Br. J. Appl. Phys. 16, 1135 (1965).

Weinreigh, G. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Zakharov, V. E.

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Phys. Rep. 129, 286 (1985).

Zernike, F.

Br. J. Appl. Phys.

J. E. Midwinter and J. Warner, "The effects of phase matching method and of uniaxial symmetry on the polar distribution of second order non-linear optical polarization," Br. J. Appl. Phys. 16, 1135 (1965).

IEEE J. Quantum Electron.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601 (1978).

D. J. Harter and D. C. Brown, "Effects of higher order nonlinearities on second-order frequency mixing," IEEE J. Quantum Electron. QE-18, 1146 (1982).

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, "Nonstationary nonlinear optical effects and ultrashort light pulse formation," IEEE J. Quantum Electron. QE-4, 598 (1968).

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Mater.

R. Adair, L. L. Chase, and S. A. Payne, "Dispersion of the nonlinear refractive index of optical crystals," Opt. Mater. 1, 185 (1992).

Phys. Rep.

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Phys. Rep. 129, 286 (1985).

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).

H. B. Bebb and A. Gold, "Multiphoton ionization of hydrogen and rare-gas atoms," Phys. Rev. 143, 1 (1966).

Phys. Rev. B

R. Adair, L. L. Chase, and S. A. Payne, "Nonlinear refractive index of optical crystals," Phys. Rev. B 39, 3337 (1989).

Phys. Rev. Lett.

P. A. Franken, A. E. Hill, C. W. Peters, and G. W. Weinreigh, "Generation of optical harmonics," Phys. Rev. Lett. 7, 118 (1961).

Sov. J. Quantum Electron.

T. B. Razumikhina, L. S. Telegin, A. I. Kholodnykh, and A. S. Chirkin, "Three-frequency interactions of high-intensity light waves in media with quadratic and cubic nonlinearities," Sov. J. Quantum Electron. 14, 1358 (1984).

L. S. Telegin and A. S. Chirkin, "Interaction in frequency doubling of ultrashort laser pulses," Sov. J. Quantum Electron. 12, 1358 (1982).

Other

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon and Breach, New York, 1972).

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