Nonlocal description of X waves in quadratic nonlinear materials

Abstract

We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist-one needs to use the nonlocal description, because the nonlocal response function does not converge toward a ␦ function.Also, we use the nonlocal theory to show that the coupling to the second harmonic is able to generate an X shape in the fundamental field despite having anomalous dispersion, in contrast to the predictions of the cascading limit.

Modulational instability in the nonlocal -model

“…A similar type of behavior occurs in the multidimensional analogue of (1) and (2), which recently has been used to model light bullets and X -waves in quadratic media [22]. When neglecting the slowly varying term i∂ z e 2 by assuming (7), one ends up with a multidimensional analogue to (8)- (12).…”

Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality

“…In what follows we will use the normalization (6) 013826-1 ©2010 The American Physical Society nonlocal response is determined by the details of the physical process responsible for the nonlocality. For all diffusion-type nonlinearities [26], orientational-type nonlinearities (like nematic liquid crystal) [23], and for the general quadratic nonlinearity describing parametric interaction [27][28][29][30], the response function is an exponential R(x) = (2σ ) −1 exp(−|x|/σ ) originating from a Lorentzian in the Fourier domain, with σ > 0 defining the degree of nonlocality. Interestingly, for parametric interaction, the response function can also be periodic, R(x) ∝ sin(|x|/σ ) in certain regimes of the parameter space [31].…”

Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression

“…Until now, the stationary regime was argued to be when the characteristic GVM length is 4 times longer than the SHG coherence length [1], while a more accurate perturbative description showed that the FW has a GVM-induced Raman-like term [4,5], which must be small for the system to be in the stationary regime [4]. However, no precise definition of the transition between the regimes exists.On the other hand, the concept of nonlocality provides accurate predictions of quadratic spatial solitons [6,7], and many other physical systems (see [8] for a review). Here we introduce the concept of nonlocality to the temporal regime and soliton pulse compression in quadratic nonlinear materials.…”

“…On the other hand, the concept of nonlocality provides accurate predictions of quadratic spatial solitons [6,7], and many other physical systems (see [8] for a review). Here we introduce the concept of nonlocality to the temporal regime and soliton pulse compression in quadratic nonlinear materials.…”