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Physical Review A

Nonlinear saturated absorption in resonant media: Level-degeneracy-induced polarization effects

Govind Prasad Agrawal

Published Feb 1, 1984• 13 citations
Publisher

Abstract

The effect of level degeneracy on saturated absorption in a resonant medium is considered using a simple but realistic three-level system to model $J=1\ensuremath{\rightarrow}J=0$ atomic transition. Assuming homogeneous broadening and exact resonance, an analytic nonperturbative expression for the medium susceptibility is obtained and used to study propagation of an arbitrarily polarized optical field. Optical saturation affects considerably Zeeman-coherence-induced circular dichroism. The analysis may find application in high-resolution spectroscopy and other branches of nonlinear optics.

DOI
10.1103/physreva.29.994

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Optics Letters•Jul 1, 1983•14 citations
The effect of level degeneracy on saturated absorption in a resonant medium is considered using a simple but realistic three-level system to model J=1\ensuremath→J=0J=1\ensuremath{\rightarrow}J=0J=1\ensuremath→J=0 atomic transition. Assuming homogeneous broadening and exact resonance, an analytic nonperturbative expression for the medium susceptibility is obtained and used to study propagation of an arbitrarily polarized optical field. Optical saturation affects considerably Zeeman-coherence-induced circular dichroism. The analysis may find application in high-resolution spectroscopy and other branches of nonlinear optics.
An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.
The shapes of the saturated absorption resonances at transitions from the ground 1S0 atom state in a gas medium in the field of two unidirectional waves are investigated both analytically and numerically. It is shown for the first time that the spectra of nonlinear resonances are formed by processes in the two-and three-level V-schemes resulting from the degeneracy of the upper P transition state, are qualitatively different at the resonant transition and transitions to the more excited atom states. It is established that the physical causes for differences of these spectra are due to the different degree of branching of the radiation from the excited to the ground state (the degree of openness) of transition. The degree of openness of transition determines the amount of contributions of coherent processes to the resonance shapes both in the system of two levels (coherent population beats) and three levels (nonlinear interference effect).
The propagation of strongly polarized electromagnetic waves through a resonance medium, with arbitrary angular momenta of the levels, is investigated in the adiabatic-following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarized wave are constructed and the picture of the shift of energy level splittings is discussed. Exact formulae for the nonlinear refractive index of the medium in the field of the circularly (linearly) polarized wave are found. The propagation of counterpropagating polarized waves—an intense pump wave and a probe light signal—through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced rotation of the plane of polarization for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
Abstract The physical processes forming the saturated absorption resonance spectra at a number of degenerate atomic transitions at their interaction with coherent optical fields and incoherent ield of spontaneous radiation of excited atoms are studied numerically. The features of behavior of nonlinear resonance spectra depending on the degree of degeneration and relaxation parametersof level transitions, character of polarizations and intensities, as well as direction of propagation of optical fields are analyzed.
We investigate the properties of a homogeneously broadened three-level system interacting with two optical fields, Eω1(x,t) and Eω2(x,t), with central frequencies ω1 and ω2 whose amplitudes are assumed to be slowly varying in time compared with dephasing times of the optical transitions. We calculate Raman susceptibilities allowing each transition to be induced by both fields and without employing the rotating wave approximation (RWA); this enables correct calculation of the optical response of the medium when the fields are on-resonance or arbitrarily far off-resonance with the Raman transition. In some frequency regions the RWA causes substantial errors. A distinction is drawn between two different types of RWA: (a) a neglect of off-resonant components of the polarization for direct optical transitions, and (b) neglect of off-resonant components of off-diagonal density matrix elements of order Eω1(x,t)Eω2(x,t)* in the field amplitudes. The first RWA is known to become inaccurate when the pump frequency is significantly off-resonance with the pump transition. We show that the second RWA becomes inaccurate when ‖ω1−ω2‖ is small or comparable to the active Raman mode frequency (even when the field are close to resonance). Calculations based upon our expressions show that when the pump frequency is close to resonance with the optical transition from the ground state, a nonlinear absorption at the Stokes shifted frequency occurs. This absorption can significantly decrease the Raman gain. Also, we find that Rabi splittings in a three-level system can occur even when the pulse durations of the incident fields are short compared with the T1 times of the system. We solve analytically for the optical response of the system to two fields of arbitrary strength and frequency. We analyze this solution and its perturbative expansion in the field amplitudes. We use the Maxwell–Bloch equations developed here to propagate time-dependent pulses.
The effect of Zeeman coherence on phase conjugation is investigated in the saturation regime by using a nonperturbative analysis of resonant degenerate four-wave mixing with orthogonally polarized pump beams in a A-type homogeneously broadened three-level system. The dependence of the phase-conjugation efficiency on phase-interrupting collisions and pump imbalance is particularly studied. Significant phase-conjugate reflectivities can be obtained at pump intensities much below those required for a two-level system.