Gap solitons in nonlinear electrical superlattices

Abstract

We investigate the amplitude dependence of the gap transmission properties of nonlinear electrical superlattices of finite length, sandwiched between two linear electrical transmission lines. We show that once the amplitude of the incident sinusoidal wave, with a frequency which lies in the first linear gap, is greater than a certain threshold, the system switches to a transmitting state: the transmittance of the system which can become unity presents gap soliton-mediated bistability and hysteresis. The voltage-current characteristic also exhibits bistability. The transmittance curve calculated by using the characteristic matrix method is in good agreement with the results of our numerical simulations performed with conditions close to those of real experiments. The gap soliton envelope calculated analytically fits both the results obtained by the characteristic matrix method and those obtained by numerical simulations on the dynamics of the wave transmission inside the electrical superlattice, after subtracting out the harmonics effects.