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Journal of the Optical Society of America B

Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: normal incidence

Victor A Malyshev, Enrique Conejero Jarque

Published May 1, 1997• 19 citations
Publisher

Abstract

We study the nonlinear resonant reflection of an intense linearly polarized plane wave from a vacuum-dense two-level-medium interface under normal-incidence conditions. A domain of parameters is specially selected for which one needs to take into account strong atom–field coupling, which results in the appearance of a gap in the spectrum of mixed states (polaritons). For the linear problem, the presence of the gap causes a strong reflection of an incident signal with a frequency within the gap. The near-zone dipole–dipole interaction is also included within the framework of the local-field approach. By performing the time-domain analysis of the reflectivity at different spectral points, we observe certain peculiarities, such as the possibility of a steady-state high-contrast optical switching with low-level operation, stable and unstable hysteresis loops, and an auto-oscillation regime of reflectivity for a certain range of the parameters driving the evolution of the system.

DOI
10.1364/josab.14.001167

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
We study the nonlinear resonant reflection of an intense linearly polarized plane wave from a vacuum-dense two-level-medium interface under normal-incidence conditions. A domain of parameters is specially selected for which one needs to take into account strong atom–field coupling, which results in the appearance of a gap in the spectrum of mixed states (polaritons). For the linear problem, the presence of the gap causes a strong reflection of an incident signal with a frequency within the gap. The near-zone dipole–dipole interaction is also included within the framework of the local-field approach. By performing the time-domain analysis of the reflectivity at different spectral points, we observe certain peculiarities, such as the possibility of a steady-state high-contrast optical switching with low-level operation, stable and unstable hysteresis loops, and an auto-oscillation regime of reflectivity for a certain range of the parameters driving the evolution of the system.
The field acting on the atoms in a medium is different from the averaged macroscopic field. The problem of the effective local field caused by dipole–dipole interaction has been discussed several times since Lorentz. In describing the nonlinear optical properties of optically thin resonant layers, it is of principal importance to take into consideration the dipole–dipole interaction of the atoms. These effects manifest themselves when certain relations between the parameters of the atomic system and the incident field are fulfilled. The presence of the excitonic lines shows that the dipole–dipole interaction is larger than the homogeneous and inhomogeneous broadenings. This gives reason to hope that the required inequalities are satisfied in such systems. The chapter considers boundary value problem and a linearly polarized plane wave, with amplitude slowly varying during one optical period, falls perpendicularly onto the surface of a plane-parallel, optically thin, resonant layer consisting of two-level atoms.
We consider a boundary value problem of reflection of a powerful light wave from a dense resonant medium that exhibits intrinsic optical bistability because of the dipole–dipole interaction of two-level atoms. On the basis of analytical solutions and numerical simulations we establish that intrinsic optical bistability results in the dependence of the reflection coefficient on the adiabatically varying intensity of an external field. The reflection coefficient is an oscillating function of the intensity because of the additional reflectivity that is due to a light-induced sharp discontinuity in the nonlinear permittivity of a dense resonant medium.
We investigate the boundary-value problem of nonresonant reflection and transmission of probe light wave passing through excited nonlinear semi-infinite medium of three- level atoms. The two lower levels are excited by intensive resonant stationary or nonstationary radiation to obtain the interference of atomic states. Some properties of near field effect in this problem are investigated taking into account retarded polarizing fields and the density-dependent near dipole-dipole interactions. We separate in our consideration three waves: the inversion wave and two polarization waves with corresponding nonlinear indices of refraction.
In this work the authors will present analytical results that explain the numerical simulations of M. E. Crenshaw et al.1 on the extended optical Bloch equations that include near dipole–dipole interactions. These simulations have shown the possibility of an ultrafast switch, caused by an incident unaltered pulse in a thin dense medium of two-level atoms. The switching parameter, defined as Ω 0 ε , is a ratio of the Rabi frequency to the strength of the near dipole–dipole interaction Our analysis will show an exact solution for the first switching condition, Ω 0 ε ≈ 1 . Furthermore, an asymptotic analysis will show that to leading order in the asymptotic expansion, only three possible final states of the medium occur. These states, if characterized by the population inversion w, are total inversion (w f = 1), no inversion (w f = -1), or half inversion (w f = 0). For the case w f = 0, a reduced system in a phase plane is derived. This reduced system will help us understand this self-transparent behavior. We will conclude by presenting the results on the stability analysis in parameter space.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
A system of coherently driven spatially distributed two-level atoms, coupled with each other via dipole–dipole interaction, exhibits intrinsic optical bistability (IOB) at solid-state densities,1 i.e., optical bistability without optical feedback. The origin of the IOB was shown to be due to inversion-dependent renormalization of the single-atom resonance frequency caused by dipole–dipole interaction among the atoms located mainly within an atomic resonance wavelength.2 For normally incident plane waves of intensity beyond threshold, a spatially dependent discontinuity in the nonlinear refractive index was shown to exist inside the medium,1 corresponding to spatial separation of the high and low absorption phases of the IOB. We present numerical results for the time-dependent solutions of the equations of motion and dynamics of the field propagation.