The nonlinear Schrödinger equation with dissipation and the moment method

Abstract The moment method is applied to study self-focusing and collapse of light beams in nonlinear media with losses. Approximate analytical expressions for collapse length and minimum losses avoiding collapse are found and compared to the exact ones obtained from numerical simulations of the nonlinear Schrodinger equation.

[1]  M. Porras,et al.  The relationship between the second order moment width and the caustic surface radius of laser beams , 1993 .

[2]  Gagnon,et al.  Adiabatic amplification of optical solitons. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[3]  Karlsson Optical beams in saturable self-focusing media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Mj Martin Bastiaans Second-order moments of the Wigner distribution function in first-order optical systems , 1988 .

[5]  Anthony E. Siegman,et al.  Defining the effective radius of curvature for a nonideal optical beam , 1991 .

[6]  B. Suydam Effect of refractive-index nonlinearity on the optical quality of high-power laser beams , 1975 .

[7]  Bishop,et al.  Kink stability, propagation, and length-scale competition in the periodically modulated sine-Gordon equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  L. Vázquez,et al.  Nonlinear Random Waves , 1994 .

[9]  M Karlsson,et al.  Dynamics of self-focusing and self-phase modulation in a parabolic index optical fiber. , 1992, Optics letters.

[10]  E Bernabeu,et al.  Nonlinear propagation and transformation of arbitrary laser beams by means of the generalized ABCD formalism. , 1993, Applied optics.

[11]  Javier Alda,et al.  Complex beam parameter and ABCD law for non-Gaussian and nonspherical light beams. , 1992, Applied optics.

[12]  J. Bjorkholm,et al.  CW self-focusing and self-trapping of light in sodium vapor , 1974 .

[13]  Vladimir E. Zakharov,et al.  Computer simulation of wave collapses in the nonlinear Schro¨dinger equation , 1991 .

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

[15]  J. Whinnery,et al.  THERMAL SELF‐FOCUSING OF LASER BEAMS IN LEAD GLASSES , 1968 .

[16]  P. Bélanger,et al.  Beam propagation and the ABCD ray matrices. , 1991, Optics letters.

[17]  O. Bang,et al.  Driving and collapse in a nonlinear Schrödinger equation , 1994 .

[18]  Peyrard,et al.  Kink dynamics in the periodically modulated phi4 model. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  M. Karlsson,et al.  Super-Gaussian approximation of the fundamental radial mode in nonlinear parabolic-index optical fibers , 1992 .

[20]  K. Spatschek,et al.  Nonlinear Coherent Structures in Physics and Biology , 1994 .

[21]  Magnus Karlsson,et al.  Wave-breaking-free pulses in nonlinear-optical fibers , 1993 .