Microscopic model for the higher-order nonlinearity in optical filaments

Abstract

Using an exactly soluble one-dimensional atomic model we explore the idea that the recently observed high-order nonlinearity in optical filaments is due to virtual transitions involving the continuum states. We show that the model's behavior is qualitatively comparable with the experimentally observed cross-over from self-focusing to de-focusing at high intensities, and only occurs at intensities which result in significant ionization. Based on these observations, we conjecture that this continuum electron nonlinear refraction exhibits strong memory effects, and most importantly, the change of its sign is effectively masked by the de-focusing due to free electrons.Comment: 4 pages, 2 figure

Optical Nonlinearity in Ar andN2near the Ionization Threshold

“…One measurement [13] found that the electron density was two orders of magnitude higher than predicted by a calculation including higher-order nonlinearities, but agreed with a simulation based on plasma defocusing alone [5]. A physical mechanism for the saturation and negative response was proposed based on the nonlinear response near the threshold of ionization [17,18]. What is missing from this debate is a direct measurement of the nonlinearity that corroborates or refutes the intensity dependence observed by Loriot et al Here, we describe such a measurement in Ar and N 2 using spectral interferometry.…”

Model for atomic dielectric response in strong, time-dependent laser fields

“…The time savings over typical TDSE treatments is manifest by the absence of any spatial dependence in Eq. (10). One might protest that we've traded the problem of a large spatial simulation domain for an infinite time integral, but solving for S(t) via Eq.…”

“…However, in the limit σ → 0, u(r) becomes a delta function and the NLI potential reduces to a more familiar local potential term, −λδ 3 (r)ψ(r, t); while the delta potential has been considered in 1D treatments of Eq. (3) [10], the 3D extension produces solutions to ψ(r) that are singular at the origin. The NLI potential can be considered an extension of the 3D delta function that permits normalizable solutions to the wavefunction.…”

“…(9), the explicit form of S(t ′ ) on −∞ < t ′ ≤ 0 is obtained with the condition that the electron is bound on this interval, while subsequent values of S(t) can be calculated numerically via Eq. (10). A more detailed discussion of the numerical treatment of Eq.…”

Interpretation of negative birefringence observed in strong-field optical pump-probe experiments: High-order Kerr and plasma grating effects

“…[1,2]. In this respect, several theoretical studies have been focused on the microscopic origin of the HOK effect either by solving the 1D or 3D Schrödinger equation for an atom exposed to a strong laser field [17][18][19][20][21][22][23][24] or by applying the concept of nonlinear Kramers-Kronig relations [25,26]. Although the literature published on this issue has contributed to get a much better insight into the temporal dynamics responsible for the nonlinear atomic response at the driving field frequency, the relevance of the HOK model for shortpulse long-wavelength propagation is still controversial.…”