Induced and Spontaneous Emission in a Coherent Field. IV

Abstract

In the previous articles of this series, dealing with the interaction between a number of molecules and the electromagnetic field in a resonant cavity, both the molecules and the field were treated by perturbation theory. The perturbation restriction on the field is removed in the present article, allowing large changes in the field, but the molecules are still assumed to undergo a small change during the time under consideration. The justification for this type of analysis, involving the generalization of the conventional concepts of induced and spontaneous emission, the applicability to a molecular amplifier during the buildup period, and the re-examination of a calculation by Serber and Townes concerning the fundamental limits of molecular amplification, is discussed.Two different molecular distributions are considered. In one (the resonant case) all molecules have the same frequency as the cavity, and in the other (the nonresonant case) there is a uniform frequency distribution. The molecules are assumed to be initially in an emissive state. Several types of driving fields are considered. Expressions are obtained for the field operators by the solution of a Volterra integral equation, and expectation values are obtained for the field strength and field energy.In the resonant case, both the coherent and incoherent fields increase exponentially after a sufficiently long time, no matter how small the initial gain is. Their ratio becomes constant and is equal to the number of photons in the driving field only in the absence of dissipation. An interesting related result is the fact that the signal-to-noise ratio for constant signal input power increases as the cavity dissipation increases. An estimate of the total time for which the theory is valid is obtained from a consideration of the energy emitted by the molecules. Contact is made with perturbation theory for sufficiently small gain and short time.In the nonresonant case the effect of the molecules is shown to be that of a negative dissipation. In contrast to the resonant case, the gain becomes exponential only if the negative dissipation exceeds, in absolute value, the true dissipation. The ratio of induced to spontaneous emission is, in this case also, equal to the number of photons in the driving field only in the absence of disipation. However, the signal-to-noise ratio for constant input power drops with increasing cavity dissipation.