Nonlinear tunneling effect in the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation with variable coefficients

By means of the similarity transformation, we obtain exact solutions of the (2+1)-dimensional generalized nonlinear Schrödinger equation, which describes the propagation of optical beams in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain. A one-to-one correspondence between such exact solutions and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss nonlinear tunneling effect of self-similar solutions. Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and then we perform direct numerical analysis with initial 5% white noise for the bright similariton passing through the diffraction barrier and well. Numerical calculations indicate stable propagation of the bright similariton over tens of diffraction lengths.