We provide an analytic study of the dynamics of semiconductor lasers with injection (pump) of spin-polarized electrons, previously considered in the steady-state regime. Using complementary approaches of quasi-static and small signal analyses, we elucidate how the spin modulation in semiconductor lasers can improve performance, as compared to the conventional (spin-unpolarized) counterparts. We reveal that the spin-polarized injection can lead to an enhanced bandwidth and desirable switching properties of spin-lasers.

It is well known that a velocity perturbation can travel through a mass spring chain with strongly nonlinear interactions as a solitary and antisolitary wave pair. In recent years, nonlinear wave propagation in 2D structures have also been explored. Here we first consider the propagation of such a velocity perturbation for cases where the system has a 2D "Y"-shaped structure. Here each of the three pieces that make up the "Y" are made of a small mass spring chain. In addition, we consider a case where multiple "Y"-shaped structures are used to generate a "tree." We explore the early time dynamical behavior associated with the propagation of a velocity perturbation initiated at the trunk and at the extremities for both cases. We are looking for the energy transmission properties from one branch to another of these "Y"-shaped structures. Our dynamical simulations suggest the following broad observations: (i) for strongly nonlinear interactions, mechanical energy propagation resembles pulse propagation with the energy propagation being dispersive in the linear case; (ii) for strong nonlinear interactions, the tree-like structure acts as an energy gate showing preference for large perturbations in the system while the behavior of the linear case shows no such preference, thereby suggesting that such structures can possibly act as switches that activate at sufficiently high energies. The study aspires to develop insights into the nature of nonlinear wave propagation through a network of linear chains.