John Wyller

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.

Classification of Kink Type Solutions to the Extended Derivative Nonlinear Schrödinger Equation

The Raman Extended Derivative Non Linear Schrodinger (R-EDNLS) equation which models single mode propagation in optical fibers, is shown to possess travelling and stationary kink envelope solutions of monotonic and oscillatory type. These structures have been called optical shocks in analogy with hydrodynamical shocks or optical double layers in analogy with electrostatic double layers in plasma physics. Hydrodynamical equations for the action density and local wave number are derived and shock wave solutions of the Rankine–Hugionot type are constructed. They are consistent with the kink structures when excluding the nongeneric case that the kink envelope approaches zero in a nonmonotonic way.

Dynamics of localized solutions to the Raman-extended derivative nonlinear Schrödinger equation

Using virial estimates we study the temporal evolution of localized solutions to the Raman-extended derivative nonlinear Schrodinger (R-EDNLS) equation, with a particular emphasis on collapse and non-collapse. By means of a Lagrangian approach, we investigate the possibility of realizing a finite-time self-similar collapse as it appears in solutions to the usual critical nonlinear Schrodinger (CNLS) equation.

Modulational instability in nonlocal Kerr media

We study the modulational instability of the plane wave solutions to nonlocal nonlinear Schrodinger equation. We show that nonlocality suppresses the instability in case of self-focusing nonlinearity while it has much weaker effect in the self-defocusing medium.

Nonlocal incoherent solitons in materials with a logarithmic nonlinearity

We study the propagation of partially coherent beams in spatially nonlocal nonlinear materials with a logarithmic nonlinearity. We describe analytically the beam evolution and find conditions for the formation of nonlocal incoherent solitons.

Rigorous proof of soliton stability and absence of collapse in Kerr media and Bose-Einstein condensates with a general nonlocal nonlinearity

We prove that nonlocality of the nonlinear response means that collapse cannot occur in Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response is symmetric, but of arbitrary shape.