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Physical Review

"Negative" Tensor Susceptibility in Media Exhibiting Population Inversion

R. L. Fork, C. Kumar N. Patel

Published Mar 15, 1963• 10 citations
Publisher

Abstract

This paper describes the results of a theoretical and experimental investigation of the tensor dielectric susceptibility of a plasma in which some of the participating atoms exhibit population inversion. The measurement of the real part of the tensor dielectric susceptibility in the vicinity of an optical resonance has previously been very difficult due to the large absorption near resonance; however, by examining a resonance for which the levels exhibit population inversion we have obtained a direct measure of the real part of the susceptibility by observing the "negative" Faraday rotation, i.e., "negative" circular birefringence associated with the resonance. We also observed for levels with inverted populations the complement of the inverse Zeeman effect, that is, we observed a Zeeman splitting of the gain curve in the amplifying medium. The high-gain $5d[\frac{3}{2}]_{1}^{}{}_{}{}^{0}\ensuremath{-}6p{[\frac{3}{2}]}_{1}$ transition of atomic xenon at 2.026 \ensuremath{\mu} in a helium-xenon mixture was used for these measurements. The observed results were consistent with the theory.

DOI
10.1103/physrev.129.2577

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This paper describes the results of a theoretical and experimental investigation of the tensor dielectric susceptibility of a plasma in which some of the participating atoms exhibit population inversion. The measurement of the real part of the tensor dielectric susceptibility in the vicinity of an optical resonance has previously been very difficult due to the large absorption near resonance; however, by examining a resonance for which the levels exhibit population inversion we have obtained a direct measure of the real part of the susceptibility by observing the "negative" Faraday rotation, i.e., "negative" circular birefringence associated with the resonance. We also observed for levels with inverted populations the complement of the inverse Zeeman effect, that is, we observed a Zeeman splitting of the gain curve in the amplifying medium. The high-gain 5d[32]10\ensuremath−6p[32]15d[\frac{3}{2}]_{1}^{}{}_{}{}^{0}\ensuremath{-}6p{[\frac{3}{2}]}_{1}5d[23​]1​​0\ensuremath−6p[23​]1​ transition of atomic xenon at 2.026 \ensuremath{\mu} in a helium-xenon mixture was used for these measurements. The observed results were consistent with the theory.
A theory of the optical Zeeman effect is developed in terms of the angular polarisability, **i, a fundamental property of both atoms and molecules. It is shown that **i is negative to motion reversal T and parity inversion P, and forms an interaction hamiltonian with the T negative, P positive conjugate product pi(i) of a circularly polarised pump laser. This activates the T negative **i, which is the axial vector equivalent of the imaginary part of the atomic or molecular electronic polarisability, an antisymmetric polar tensor. The quantity pi(i) is proportional to the square of the electric field strength of the laser, and disappears if the latter is not circularly polarised. This distinguishes the optical Zeeman effect from the experimentally measured optical Autler Townes effect, which is mediated by the symmetric, T positive, real part of the dynamic electronic polarisability. The optical Zeeman effect is accompanied by circular birefringence and the bulk magnetisation of the inverse Faraday effect.
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.
The effect of changing the value of Rabi frequency has been studied in six level atomic system, Optical Bloch equations where used as the main tool to get the final shape of the model to treat the model. In this work we present a theoretical study of the non-linear optical properties of materials as a result of their interaction with laser radiation in resonance state. Density matrix was used in our formulation of Optical Bloch Equation. These equations were solved using Matlap program for Six-levels Inverted-Y Atomic Systems. A formula for calculation of electrical susceptibility was obtained. With increasing the real and imaginary parts of the electric susceptibility have also increased gradually which effects the index of refraction of the medium (real part), and the absorption window (described by the imaginary part). Moreover, when increasing the real and imaginary parts of the electric susceptibility decreased and we noticed that with increasing the value of the signal laser field related to transition |2⟩ ↔ |6⟩a distortion starts to appear on both real and imaginary parts. Key Words: Rabi frequency, Density matrix, electrical susceptibility, laser, Optical Bloch equations.
We report the observation of light amplification without population inversion. A linear superposition of an m=1 and an m=-1 magnetic substate is populated coherently. Absorption from this superposition to a higher state is canceled by interference of channels, a so-called dark resonance. An inverse transition is used for amplification of light. The temporal behavior of the amplified pulse and the gain are studied as a function of the energy splitting due to a magnetic field. In a vapor of cadmium-112 gain factors of up to 4.3 are observed.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].