Theory of a two-photon laser amplifier

TLDR

An inverted two‑level medium of the same parity is considered for pulse propagation. The study investigates whether a signal at half the atomic transition frequency can be amplified in such a medium. The authors use a self‑consistent atom–field model, derive a spatial evolution equation for pulse energy, and simulate the envelope dynamics with a hybrid computer approach. They find that a nonlinear polarization at the pulse frequency can be generated, yielding a threshold for amplification and multiple steady‑state solutions, and that long amplifiers exhibit pulse‑envelope modulation and multiple‑pulse formation.

Abstract

We discuss the propagation of an electromagnetic pulse through an active medium prepared in a state of inversion between two levels of the same parity. Since no electric dipole transition is possible between the chosen atomic levels, we investigate the possibility of amplification of an injected signal having a carrier frequency equal to one-half the atomic-transition frequency. We show that under suitable conditions a nonlinear atomic polarization can be generated which oscillates at the same frequency as the incident electromagnetic pulse. The coupled atom-field evolution is described by the usual self-consistent approach. When atomic relaxation effects are negligible, we derive an equation describing the spatial evolution of the energy of the propagating pulse. From this equation we characterize the threshold condition for power amplification and classify the multiple steady-state solutions of the propagation problem. The evolution of the pulse envelope through the amplifier is analyzed with the help of a hybrid computer simulation. Pulse-envelope modulation and multiple-pulse formation even in the asymptotic limit of long amplifiers are displayed.