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Communications in Theoretical Physics

Nonlinear Absorption and Dispersion Response in Optically Dense Media Driven by a Single-Mode Laser

Jiahua Li, Ji-Bing Liu, Xiao-Tao Xie, Luo Jin-Ming

Published Jul 1, 2006• 0 citations
Publisher

Abstract

Taking the density-dependent near dipole-dipole (NDD) interaction into consideration, we theoretically investigate the response of nonlinear absorption and dispersion in optically dense media of three-level atoms driven by a single-mode probe laser. The influence of the NDD effects on the absorption and dispersion spectra of the probe field is predicted via numerical calculations. It is shown that the NDD effects reduce gradually to transient absorption and amplification with the increase of the strengths of the NDD interaction, but do not change the steady-state behavior. Due to the presence of the NDD effects, steady-state absorption spectra exhibit asymmetric double-peak structure and overall shifts when a continuous-wave (cw) probe field is applied. However, frequency dispersion spectra are insensitive to them near the zero detuning.

DOI
10.1088/0253-6102/46/1/029

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Taking the density-dependent near dipole-dipole (NDD) interaction into consideration, we theoretically investigate the response of nonlinear absorption and dispersion in optically dense media of three-level atoms driven by a single-mode probe laser. The influence of the NDD effects on the absorption and dispersion spectra of the probe field is predicted via numerical calculations. It is shown that the NDD effects reduce gradually to transient absorption and amplification with the increase of the strengths of the NDD interaction, but do not change the steady-state behavior. Due to the presence of the NDD effects, steady-state absorption spectra exhibit asymmetric double-peak structure and overall shifts when a continuous-wave (cw) probe field is applied. However, frequency dispersion spectra are insensitive to them near the zero detuning.
We theoretically investigate the response of nonlinear absorption and population dynamics in optically dense media of four-level atoms driven by a single-mode probe laser, via taking the density-dependent near dipole-dipole (NDD) interactions into consideration. The influence of the NDD effects on the absorption of the probe field and population dynamics is predicted via numerical calculations. It is shown that the NDD effects can reduce gradually to transient absorption with the increase of the strengths of the NDD interactions, and transient amplification can be achieved. In the steady-state limit, the probe field exhibits transparency for strong NDD interactions. Alternatively, the population entirely remains at the ground state due to the NDD effects.
In this paper we analyze theoretically the influence of the local-field effects on reflection spectra of a degenerate four-wave mixing in a dense medium of two-level atoms. We discuss the spectral dependence of the nonlinear absorption and dispersion of the signal and probe fields as well as their coupling for various strengths of the external field and atomic densities. For weak external fields the local-field effects reduce to the well known Lorentz redshift of the reflection spectra. When the external field saturates the transition in a dense sample significant modifications of the probe reflectivity and of the wave mixing spectra occur, resulting in asymmetric, multipeak line shapes. \textcopyright{} 1996 The American Physical Society.
The nonstationary pump-probe interaction between short laser pulses propagating in a resonant optically dense coherent medium is considered. Special attention is paid to the case where the density of two-level particles is high enough that a considerable part of the energy of relatively weak external laser fields can be coherently absorbed and reemitted by the medium. Thus, the field of the medium reaction plays a key role in the interaction processes, which leads to collective behavior of an atomic ensemble in the strongly coupled light-matter system. Such behavior results in fast excitation interchanges between the field and a medium in the form of optical ringing, which is analogous to polariton beating in solid-state optics. This collective oscillating response, which can be treated as successive beats between light wave packets of different group velocities, is shown to significantly affect the propagation and amplification of the probe field under its nonlinear interaction with a nearly copropagating pump pulse. Depending on the probe-pump time delay, the probe transmission spectra show the appearance of either a specific doublet or coherent dip. The widths of these features are determined by the density-dependent field-matter coupling coefficient and increase during the propagation. Besides that, the widths of the coherent features, which appear close to resonance in the broadband probe spectrum, exceed the absorption-line width, since under the strong-coupling regime, the frequency of optical ringing exceeds the rate of incoherent relaxation. Contrary to stationary strong-field effects, the density- and coordinate-dependent transmission spectra of the probe manifest the importance of collective oscillations and cannot be obtained in the framework of a single-atom model.
In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.
We performed a numerical investigation of the dynamics of the optical Bloch equations, extended for near dipole-dipole (NDD) interactions in dense collections of two-level systems. As a function of peak field strength, the inversion that remains in the medium following excitation by an ultrashort optical pulse has step-like transitions between the ground state and the excited state. The medium is left fully inverted if the peak Rabi frequency (peak field strength written in units of frequency) is equal to the NDD interaction strength. Remarkably, this result is independent of pulse area. About this point is a region of peak field strength for which the dense medium is left fully, or nearly fully, inverted. On the weak side of this region, the dense medium is left in the ground state. On the strong side of this region, the medium alternates between absorbing (ground state) and amplifying (inverted) as a function of peak field strength. This response can be used to measure the strength of the NDD interaction, for coherent optical pumping, and also constitutes a new and unique intrinsic optical switch, which, unlike optical bistability, does not have hysteresis and is independent of dissipation from incoherent effects.
The probe absorption–dispersion spectra of a driven three-level atom in a double-band photonic crystal have been investigated. We use the model which assumes the upper levels of the atomic transitions coupled via a classical driving field. One of the transitions interacts with the free vacuum modes, and the other transition couples to the modes of the modified reservoir (photonic band gap). The effect of the classical driving field on the absorption–dispersion spectra of an atom is investigated in detail. Most interestingly, it is shown that the atom becomes transparent to a probe laser field coupled to the free space transition, and slow group velocities are obtained near the transparency window.