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Journal of Nonlinear Optical Physics & Materials

SATURATION OF NONLINEAR SUSCEPTIBILITY

Muhammad Nurhuda, Akira Suda, Katsumi Midorikawa

Published Jun 1, 2004• 14 citations
Publisher

Abstract

The nonlinear susceptibility of atoms interacting with an intense laser field has been investigated using numerical solution of the time-dependent Schrödinger equation. It was found that the behavior of nonlinear susceptibility strongly depends on the intensity; it increases linearly in low intensity regime (Kerr nonlinearity), then saturates at higher intensity. Furthermore, it has also been found that the nonlinear susceptibility is substantially influenced by the onset of ionization.

DOI
10.1142/s0218863504001906

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The nonlinear susceptibility of atoms interacting with an intense laser field has been investigated using numerical solution of the time-dependent Schrödinger equation. It was found that the behavior of nonlinear susceptibility strongly depends on the intensity; it increases linearly in low intensity regime (Kerr nonlinearity), then saturates at higher intensity. Furthermore, it has also been found that the nonlinear susceptibility is substantially influenced by the onset of ionization.
We have investigated the nonlinear susceptibility of atoms induced by high intensity, ultrashort laser pulses using a numerical solution of the time-dependent Schrödinger equation. We found that the instantaneous nonlinear susceptibility becomes saturated at high intensity. We also found that the saturation is closely linked to depletion of the ground state. Based on the numerical results, a simple model that generalizes the nonlinear susceptibility of atoms for high intensity, ultrashort laser pulses is proposed. We also investigated the ionization-induced dipole moment and found that the amplitude of the dipole moment induced by an ionized electron is, in general, smaller than that induced by a free-electron, and is attributable to a residual interaction between the ionized-electron and its parent ion.
We discuss the connection between strong-field ionization, saturation of the Kerr response and the formation of the Kramers–Henneberger (KH) atom and long-living excitations in intense infrared (IR) external fields. We present a generalized model for the intensity-dependent response of atoms in strong IR laser fields, describing deviations in the nonlinear response at the frequency of the driving field from the standard model. We show that shaping the driving laser pulse allows one to reveal signatures of the excited KH states in the Kerr response of an individual atom.
By photoionizing hyperfine (HF) levels of the Cs state 62P3/26{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}62P3/2​ in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of ``dark'' and ``bright'' resonances leading to power-dependent branching coefficients.
Abstract The book so far is almost entirely concerned with linear optical processes, where the response of a material to incident light is described by its linear susceptibility and the rates of optical processes are proportional to the incident intensity. However, examples of nonlinear behaviour occur in the saturation of atomic transitions, discussed in §1.7, and in the power-broadened susceptibility, derived in eqn (2.8.6). Atomic saturation is also an important component in the laser theory of§§t.10 and 7.3. The expressions derived in these examples contain the electromagnetic energy density or photon number in denominators whose expansions include terms proportional to all positive powers of the optical energy. The higherorder, or nonlinear, terms are normally much smaller than the linear term for conventional light sources but their influence is often significant in experiments that use laser sources. The present chapter treats the effects of the nonlinear terms in modifying the properties of incident light beams.
There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.