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Optics Letters

Simple model for the nonlinear optical response of gases in the transparency region

K. Schuh, M. Kolesík, Ewan M. Wright, Jerome V. Moloney

Published Aug 20, 2014• 5 citations
Publisher

Abstract

We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise.

DOI
10.1364/ol.39.005086

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We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise.
The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrödinger-like wave equation that considers only instantaneous Kerr nonlinearity.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
The nonlinear optical response of a dilute atomic gas to ultrashort high-intensity midinfrared pulse excitation is calculated fully microscopically. The optically induced polarization dynamics is evaluated for the interacting many-electron system in a gas of hydrogen atoms. It is shown that the many-body effects during the excitation distinctly influence not only the atomic ionization dynamics, but also the nonlinear polarization response in the midinfrared regime. The delicate balance between the Kerr focusing and the ionization-induced defocusing is dramatically modified and a significant decrease of the nonlinear refractive index is predicted for increasing wavelength of the exciting pulse.
The goal of this paper is to elucidate the theoretical underpinnings of the metastable electronic state approach (MESA) and demonstrate its utility for the evaluation of the nonlinear optical response of noble-gas atoms with emphasis on the application of the method to the propagation of multicolor optical fields in large-scale, spatially resolved simulations. More specifically, single-active-electron models of various atoms are employed to calculate their nonlinear properties both within the adiabatic approximation, involving a single metastable state and beyond, capturing inertial effects, and wavelength-dependent ionization. Simulations for excitation pulses at different center wavelengths as well as ionization in two-color pulses are presented and compared with numerical solutions of the time-dependent Schr\"odinger equation. Illustrative examples of the numerical simulation of high-power pulse propagation incorporating MESA data are also presented and showcase the successful application to optical filamentation in the midinfrared region.
It is commonly assumed that for low-intensity short optical pulses far from resonance, the third-order optical nonlinear response is instantaneous. We solve the three-dimensional time-dependent Schrödinger equation for the hydrogen atom and show that this is not the case: the polarization is not simply proportional to the cube of the electric field even at low intensities. We analyze the fundamental-frequency and third-harmonic nonlinear susceptibilities of hydrogen, investigate their dependence on intensity, and find that the delays in the Kerr response rapidly approach the femtosecond time-scale at higher intensities, while the delays in the third harmonic generation remain much lower. We also propose an experimental scheme to detect and characterize the above effects.
Introduction In 1961, just a few months after Maiman invented the ruby laser, Franken focused the pulses emitted from such a laser, of wavelength 694 nm, on a quartz plate, and examined the spectrum of the light transmitted using a simple prism (see Figure 7.1). He thus discovered that ultra-violet light of wavelength 347 nm was emerging from the quartz plate. Clearly, as it propagated through the quartz, the light of frequency ω had generated the second harmonic, of frequency 2ω. It thus transpires that in optics, as in any other part of physics, a system subjected to a strong enough sinusoidal excitation will leave the linear response regime. Nonlinearities cause harmonics of the excitation frequency to appear. But what intensity is needed before nonlinear effects will appear? One might think that a natural scale would be the electric field of the nucleus at the location of an atomic electron. In the case of the hydrogen atom in its ground state, this field is about, or 3 × 10 11 V.m −1 . (Here e is the charge of the electron, and a 0 the Bohr radius, of the order of 5 × 10 −11 m). In fact, experiment shows that, in the transparency zone of a dielectric material like quartz, a field of just 10 7 V.m −1 (corresponding to a light intensity of 2.5 kW.cm −2 ) is sufficient for nonlinear effects to appear perturbatively.