Existence Of Modulational Instability Research Articles

Modulation instability in the presence of slowly varying saturable nonlinearity, dispersion and a PT-symmetric external potential over the length of waveguide

We study the modulation instability (MI) for optical wave propagation in the presence of slowly varying saturable nonlinearity, group velocity dispersion and a PT-symmetric external potential over the length of tapered graded-index waveguide. First we study the MI with space-dependent dispersion and saturated nonlinearity and then with constant dispersion and saturated nonlinearity. We analytically compute the growth rate and analyze the possibility of existence of MI for focussing and defocussing nonlinearities for different choices of group velocity dispersion terms and saturated nonlinearities. We observe that MI is independent of PT symmetric potential term and typically depends upon the choice of group velocity dispersion term, nonlinearity, saturated nonlinearity and wave amplitude. MI gain decreases with increase in cw amplitude however it increases with increase in saturated nonlinearity both for focussing and defocussing nonlinearities.

Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation

In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.

Collisional effects on the modulational instability of intense laser pulses in magnetoactive plasmas

AbstractThe modulational instability associated with propagation of an intense laser pulse through a transversely magnetized plasma is investigated in the presence of collisional effects. The source-dependent expansion method for analyzing the wave equation is employed. The dispersion relation is obtained and modulational instability and its growth rate are studied. It is shown that in the absence of collisional effects the modulational instability is restricted to the small wavenumber region and the constant magnetic field reduces the growth rate of the instability. In contrast, in the collisional plasma, there is no upper limit of wavenumber for the existence of modulational instability. In addition, in this case, the growth rate of instability increases as the collision frequency goes up.

Study of modulation instability for nonlinear Schrödinger equation phase locked with an external source

We study the modulation instability (MI) for nonlinear Schrödinger equation phase locked to an external source. We analytically compute the growth rate and analyze the possibility of existence of MI for self-focusing and self-defocusing nonlinearities for positive and negative values of the homogeneous source term coefficient. We further investigate the impact of variation of nonlinear coefficient and variation of source term coefficient on the existence of MI. Phase-locking is the key characteristic that enables us to conduct analytical investigations of MI in this dynamical system, that appertains to pulse propagation through asymmetric twin-core fibers.

Modulation instability of a two-mode packet of strongly interacting waves

The conditions for the appearance of modulation instability of a two-wave packet formed by two unidirectional strongly interacting modes traveling in a two-mode fiber waveguide are studied. The possibility of the existence of modulation instability in the region of normal dispersion and the effect of the initial conditions of fiber excitation on the development of modulation instability are demonstrated.