We consider the nonlinear Schrödinger equation with variable coefficients that describes beam propagation in inhomogeneous graded-index waveguides. By using the direct transformation of variables and functions, we present the exact general bright and dark spatial self-similar solutions. As an application, we discuss the nonlinear tunneling of optical similaritons. The results show that under an integrable condition, the optical waves can similarly pass through the nonlinear barrier or well, and the interaction between the neighboring waves is elastic collision. Under a nonintegrable condition, when they pass through the nonlinear barrier, the optical beams can effectively be compressed for the relatively small value of height of the nonlinear barrier. However, the beam splits into some filaments when the height of the nonlinear barrier is large enough.
© 2008 Optical Society of America
Original Manuscript: March 18, 2008
Revised Manuscript: May 13, 2008
Manuscript Accepted: May 16, 2008
Published: July 11, 2008
Juanfen Wang, Lu Li, and Suotang Jia, "Nonlinear tunneling of optical similaritons in nonlinear waveguides," J. Opt. Soc. Am. B 25, 1254-1260 (2008)