Nonlinear tunneling of self-similar periodic waves in inhomogeneous two mode optical fibers

Distinct types of self-similar periodic waveforms of the generalized coupled nonlinear Schr & ouml;dinger equations with varying nonlinearity, gain or loss and group velocity dispersion are obtained. The coupled system applies to the description of light pulse propagation in an inhomogeneous two mode optical fiber. The self-similar solutions are expressed in terms of Jacobian elliptic functions, thus enabling us to identify various kinds of propagating self-similar soliton pulses in their long-wave limit. It is found that these periodic structures exhibit a linear chirp property, which can be utilized to achieve efficient pulse compression and amplification. As a physically relevant application, we discuss the nonlinear tunneling process of these linearly chirped self-similar periodic waves through both dispersion and nonlinear barriers.