Two-Photon Beer’s Law for Coherently Prepared Three-Level Media
The propagation of pairs of laser pulses interacting with resonant media has been recently recognized1,2 to be of interest in connection with lasing without inversions3 and electromagnetically induced transparency4. Here we have studied two different-frequency weak laser pulses propagating in one- and two-photon resonance with a coherently prepared medium with damping. In contrast to a two level system where a single weak pulse decays after a characteristic distance, we have shown that a coherently prepared three level medium forces the two weak fields to cooperate and evolve into a coherent superposition that propagates without loss. This can be regarded as a direct generalization of Beer’s law to the situation of two coupled pulses when the medium is strongly damped. Our analytical theory is confirmed by comparison with computer simulations.