The parabolic equation (nonlinear Schrödinger equation) that appears in problems of stationary nonlinear beam propagation (self-focusing) is reconsidered. It is shown that an additional term, which involves changes of the propagation constant along the propagation direction, should be taken into account. The physical consequences of this departure from the standard approximation, which uses the parabolic equation, are discussed. A numerical simulation showing the difference between the new approach and the standard nonlinear Schrödinger equation is given as an example.
© 1993 Optical Society of America
Nail Akhmediev, Adrian Ankiewicz, and Jose Maria Soto-Crespo, "Does the nonlinear Schrödinger equation correctly describe beam propagation?," Opt. Lett. 18, 411-413 (1993)