Controllable Raman soliton self-frequency shift in nonlinear metamaterials

Controllable and dispersive magnetic permeability in the metamaterials (MMs) provides us more freedom to harness the propagation of ultrashort electromagnetic pulses at will. Here we discuss the controllability of the Raman soliton self-frequency shift (SSFS) in the MMs with a nonlinear electric polarization. First, we derive a generalized nonlinear Schrodinger equation suitable for few-cycle pulse propagation in the MMs with delayed Raman response, and demonstrate the Raman effect, high-order Raman-related nonlinearity, and high-order nonlinear dispersion terms occurring in this equation. Second, we present a theoretical investigation on the controllability of the Raman SSFS in the MMs. In particular, we identify the combined effects of the anomalous self-steepening (SS), third-order dispersion (TOD), and Raman effect on SSFS. It is shown that the positive SS effect suppresses SSFS; however, the negative SS effect enhances SSFS, and the positive TOD leads to the deceleration of SSFS. Finally, the effects of SS on the SSFS of the second-order soliton are also discussed.