Second (quantum) threshold of a laser

A. A. Bakasov, N. B. Abraham

Vincenzo Gino Benza, E. Montaldi

Vladimir P Bykov

The quantum-mechanical state of laser radiation near the generation threshold is studied. It is shown that there is a second threshold in laser generation which lies above the first one. At the second threshold coherence appears in laser radiation. In a small region between the two thresholds the laser radiation is in an essentially quantum state, in which the average field strength is close to zero, but the average energy keeps a macroscopic value. Active atoms in superposition states are the sources of coherence in lasers. The laser active medium sufficiently enlarges the characteristic time of coherence.

Pierre Meystre, Murray Sargent

A. A. Bakasov, N. B. Abraham

An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold, for arbitary physical values of the relaxation rates, and at an arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have been previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is reconsidered and specified more clearly, including an analysis of what reasonably can be attained in lasers or masers. A general analytical proof is given of the fact that, for a larger detuning of the laser cavity from resonance, a higher value of the laser excitation is required to destabilize the steady-state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and for the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the minima ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate.