Abstract
We perform a theoretical and experimental study of the two-pulse photon echo area conservation law in an optically dense medium. The experimental properties of the echo signal are studied at 4K on the optical transition 3H6(1)→3H4(1) (793 nm) of Tm3+ in a YAG crystal for a wide range of pulse areas of the two incoming light pulses, up to θ 1 r o x4π and θ 2≈7π respectively, with optical depth 1.5. We analyze the experimental data by using the analytic solution of the photon echo area theorem for plane waves. We find that the transverse Gaussian spatial profile of the beam leads to an attenuation of the echo area nutation as function of θ1 and θ2. Additional spatial filtering of the photon echo beam allows to recover this nutation. The experimental data are in good agreement with the solution of photon echo pulse area theorem for weak incoming pulse areas θ 1,2≲π. However at higher pulse areas, the observations diverge from the analytic solution requiring further theoretical and experimental studies.
Highlights
The optical analogue of the spin echo [1], the photon echo [2, 3] is an efficient method in modern coherent spectroscopy [4]
Experimental studies of the pulse amplitude, spatial beam profile, temporal pulse shape and medium optical thickness on the photon echo intensity are usually described by the Maxwell-Bloch numerical simulation [35,36,37,38,39] or by using area theorem for a small input pulse area [40,41]
We experimentally test the photon echo area theorem in more general conditions, namely high incoming pulse areas θ1(0) > π, θ2(0) > 2π and different spatial filtering profiles
Summary
The optical analogue of the spin echo [1], the photon echo [2, 3] is an efficient method in modern coherent spectroscopy [4]. We take a widely used definition of optical density: the absorption coefficient multiplied by the sample thickness In this broad context, the McCall-Hahn pulse area theorem provides a global description of light pulse propagation in optically dense resonant atomic media [26]. Experimental studies of the pulse amplitude, spatial beam profile, temporal pulse shape and medium optical thickness on the photon echo intensity are usually described by the Maxwell-Bloch numerical simulation [35,36,37,38,39] or by using area theorem for a small input pulse area [40,41]. The analytical solution of the photon echo pulse area was obtained in [44] for arbitrary areas of the incoming pulses. We partially retrieve the plane wave solution by using spatial filtering of the light beams
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