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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.

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