Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells.

We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of controlled ejection of solitons with significantly high speeds. At the outset, we describe the scattering setup and characterize the soliton ejection in terms of the different parameters of the system. Then, we formulate a theoretical model revealing the underlying physics of soliton ejection. The model is based on energy and norm exchange between the incident soliton and a stable trapped mode corresponding to an exact solution of the governing nonlinear Schrödinger equation. Remarkably, stationary solitons can lead to high-speed soliton ejection where part of the nonlinear interaction energy transforms to translational kinetic energy of the ejected soliton. Our investigation shows that soliton ejection always occurs whenever the incident soliton norm is greater than that of the trapped mode whereas their energy is almost the same. Once the incident soliton is trapped, the excess in norm turns to an ejected soliton in addition to a small amount of radiation that share translational kinetic energy. We found that higher ejection speeds are obtained with multinode trapped modes that have higher binding energy. Simultaneous two-soliton ejection has been also induced by two solitons scattering with the potential from both of its sides. An ejection speed almost twice as that of single soliton ejection was obtained. Ejection outcome and ejection speed turn out to be sensitive to the relative phase between the two incoming solitons, which suggests a tool for soliton phase interferometry.

Influence of self-steepening and intrapulse Raman scattering on modulation instability in oppositely directed coupler.

We investigate the modulation instability in oppositely directed coupler in the presence of higher-order effects. Using linear stability analysis, we obtain an expression for instability gain. Special attention is paid to find out the influence of self-steepening effect and intrapulse Raman scattering on modulation instability. The study shows that in normal dispersion, regime instability gain exists even if perturbation frequency (Ω) is zero. But the instability gain at Ω=0 is zero, when the dispersion is anomalous. Moreover, self-steepening effect and intrapulse Raman scattering form new instability regions and, hence, provide a new way to generate solitons or ultrashort pulses. Further, efficient control of modulation instability by adjusting self-steepening effect and intrapulse Raman scattering also successfully demonstrated.