Saturation spectroscopy in optically thick three-level gas media

Abstract

High-contrast transmission spectra arising from saturated absorption in optically thick Doppler-broadened threelevel media are analyzed within the formalism of Maxwell-Bloch-type equations. It is found that although in the strong pumping engine propagation-induced line narrowing and light-shift elimination occur, spectral features lying within the natural linewidth cannot be resolved.Saturated absorption spectroscopy (SAS) is a widely used method for obtaining Doppler-free resonances on the absorption of a probe beam when atomic and molecular vapors are simultaneously interacting with a counterpropagating pump beam of the same frequency' (see Fig. 1 can be used to resolve spectral features that lie within the natural linewidth. The simplest model that can give us physical insight into the subnatural spectroscopy problem is a threelevel system with two nearly degenerate levels (see Fig. 2). A practical example could be an atom or molecule with a J = 1 ground state and an excited J = 0 state placed on a static magnetic field parallel to the direction of the two counterpropagating pump and detection beams, with the J = 1-J = 0 transition frequency cwo in the absence of external fields being far apart from all other absorption frequencies of the system.The absorbing gaseous medium composed of such three-level atoms is subjected to irradiation by a monochromatic field, E(z, t), composed of two counterpropagating plane waves of arbitrary strength,( 2) where ko = w/c. Note that the amplitudes of the a+ -waves depend on the penetration depth z. Specifically, we consider the simplest setup for SAS1" 2 shown in Fig. 1. The a-wave originates by retroreflection of the pump beam a+ on a back mirror after traversing the atomic sample of length L. Each a wave couples to both 0-1 and 0-2 transitions with respective detuningsA 1 =A-8andA 2 =A+a,whereA=w-woo. The coupling of the at fields is characterized by the Rabi frequencies 29A, which for simplicity are assumed to be equal for both 0-1 and 0-2 dipole-allowed transitions.The medium response to the optical field, taking into account population and coherence effects, is governed by the ensemble-averaged density matrix p (v, z, t) whose Fourier components can be expressed in terms of a continued fraction 5 and have been evaluated within a single-relaxation-rate (single--y) model.The induced nonlinear polarization P(z, t) can be expressed in terms of the steady-state susceptibilities as follows: P(z, t) = eo(X+a+ + x-a-)exp(-iwt) + c.c., (3) where eO is the vacuum permittivity and the saturated medium susceptibilities for the two counterpropagating waves, x+ and x-, depend on the two phasematched Fourier components of the velocity-averaged atomic coherence, probe beam is obtained by retroreflection of the transmitted pump beam, which is strongly attenuated despite considerable bleaching in the optically dense sample.

Investigation of shifts and interaction of signals in high-contrast transmission spectroscopy

“…The conclusion is that the line-narrowing mechanism active in the high-contrast regime does not enable resolution within the broadening of lines due to the Heisenberg uncertainty. Calculations, based on the Maxwell-Bloch equations, performed by Corbahln and co-workers [9,10] also yield the same result. Studying a transition with a hyperfine structure, like the D 1 line in this work, crossover signals will always be interacting with the true signals and further decrease the resolution capacity.…”

“…In particular, the question is posed, whether signals nonresolved within their natural width can be made to resolve under the influence of the line-narrowing mechanisms active in the high-contrast regime. The results from our spectral hole-burning model are related to calculations by Corbal~n et al [9,10] based on the Maxwell-Bitch equations.…”

“…To calculate the absorption for one of the laser beams (I+) we have to evaluate the generalized integral: (9) D (v) in the integral is the velocity distribution. At room temperature and at even higher temperatures the Doppler widths of emission lines from optical transitions are much (at least 100 times) broader than the natural linewidths.…”