COMPLEX RAY-TRACING OF NONLINEAR PROPAGATION

A new scale transformation of complex ray parameters is introduced in an unified manner to treat the nonlinear propagation in Kerr media. It is shown that the nonlinear propagation, including soliton propagatio n, can be consistently traced by complex rays specific to the linear p ropagation with the imposed scale effects of self-shortening, self-foc using and phase self-modification. The solution obtained is explicitly described as the propagation in a free-space modified by three propag ation effects, namely, the nonlinear changes of the beam or pulse wais t position, waist width and on-axis phase. A field of cylindrical symm etry and arbitrary transverse dimension is analyzed for power levels r anging from the linear propagation to the soliton self-trapping. It is shown that the method can be formulated within a frame of the nonline ar ABCD matrix formalism and specified to comply with the variational analysis of the problem.