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Register a new userNonlinear Beam Propagation in a Class of Complex Non-PT -Symmetric Potentials
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The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schrodinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it might be the case in realistic applications. We utilize two parameters: the first one breaks PT-symmetry but retains a proportionality between the imaginary and the derivative of the real part of the potential; the second one, detunes from this latter proportionality. It is shown that the departure of the potential from the PT -symmetric form does not allow for the numerical identification of exact stationary solutions. Nevertheless, it is of crucial importance to consider the dynamical evolution of initial beam profiles. In that light, we define a suitable notion of optimization and find that even for non PT-symmetric cases, the beam dynamics, both in 1D and 2D -although prone to weak growth or decay- suggests that the optimized profiles do not change significantly under propagation for specific parameter regimes.
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The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikovs perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system and are located at specific positions with respect to the underlying potential. It is shown that the necessary conditions for the existence of continuous families of stationary solitary waves, as they arise from Melnikov theory, provide general constraints for the real and imaginary part of the potential, that are not restricted to symmetry conditions or specific types of potentials. Direct simulations are used to compare numerical results with the analytical predictions, as well as to investigate the propagation dynamics of the solitary waves.
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