Modulational instability in nonlinear oppositely directed coupler with saturable delayed nonlinear response

Abstract

A theoretical analysis of the modulational instability (MI) in a nonlinear oppositely directional coupler with one channel fabricated from nonlinear medium having negative refraction index is discussed. The saturation of the nonlinearity is incorporated in the relaxation dynamics of Kerr response. In particular, we discuss the influence of system parameters such as the ratio of the forward to backward propagating wave’s power $$ f $$ , the incident input power, the saturation and the finite time response on the MI spectrum. It is shown that MI generation is thresholdless for $$ f $$ , and increasing the input power can enhance the MI gain. The relaxation extends the range of unstable frequencies while it disturbs the instability bands. This happens because the finite response time in the nonlinear response is equivalent to assuming a complex nonlinearity. Moreover, combine relaxation and saturation form new instability regions and hence, can provide more ways to generate solitons or ultrashort pulses. We also analyze the impact of different nonlinear configurations of coupler channels on the MI spectrum. It is found that when one channel is self-focusing and the other is self-defocusing, the nonlinear coefficients induce the appearance of new instability regions. Our study suggest how to generate and manipulate MI and solitons in relaxing nonlinear oppositely directed coupler with an emphasis on a negative refraction index channel. However, numerical simulations are carried out following the analytical consideration of the MI to explore nonlinear development of the MI, revealing the generation of periodic solitons with growing amplitudes.