Self-guided beams in a diffractive χ(2) medium: variational approach

Abstract It is demonstrated that the (1+1)- and (2+1)-dimensional self-guided beams (two-wave parametric spatial solitons ) in a diffractive dielectric medium with purely quadratic nonlinearity (the so-called χ (2) material) can be effectively approximated by means of a familiar variational approach. In particular, for the physical conditions for which no analytical solutions exist, the variational approach yields Gaussian approximations of the (1+1) beams such that the ratio of the harmonic energy to the total beam energy equals, with ∼ 0.1% error, to the ratio obtained numerically.

[1]  S. A. Akhmanov,et al.  Optics of Femtosecond Laser Pulses , 1991 .

[2]  Alexander M. Rubenchik,et al.  On diffraction and dispersion effect on three wave interaction , 1981 .

[3]  Mietek Lisak,et al.  Self-trapped cylindrical laser beams , 1979 .

[4]  C R Menyuk,et al.  Excitation of solitons with cascaded chi((2)) nonlinearities. , 1994, Optics letters.

[5]  R. Schiek,et al.  Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures , 1993 .

[6]  Malomed,et al.  Internal dynamics of a vector soliton in a nonlinear optical fiber. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Y. Kivshar,et al.  Solitons due to second harmonic generation , 1995 .

[8]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

[9]  Yaochun Shen.  Principles of nonlinear optics , 1984 .

[10]  G. Stegeman,et al.  Self-focusing and self-defocusing by cascaded second-order effects in KTP. , 1992, Optics letters.

[11]  Diana Anderson,et al.  Variational approach to nonlinear pulse propagation in optical fibers , 1983 .

[12]  Y. Kivshar,et al.  Spatial optical solitons governed by quadratic nonlinearity. , 1994, Optics letters.

[13]  Koshiba,et al.  Multidimensional solitons in quadratic nonlinear media. , 1993, Physical review letters.

[14]  L. Torner,et al.  Two-dimensional solitons with second-order nonlinearities. , 1995, Optics letters.

[15]  D. G. Vass,et al.  OSA Technical Digest Series , 1990 .