Two-pulse photon echo area theorem in an optically dense medium

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  ³H ₆(1)→³H ₄(1) (793 nm) of Tm ³⁺ 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.