Dynamic behavior of gas lasers

The purpose of this paper is to treat systematically the properties of gas lasers with respect to internal modulation, mode locking, perturbation of modes due to combination tones, and noise due to spontaneous emission. The response of gas lasers to the resonator loss modulation and the small external signal injection has been investigated on the basis of Lamb's optical maser theory. The analysis on the low-frequency loss modulation indicates that each oscillating mode in a gas laser has its proper damping constant or cutoff frequency for both the perturbations. Although this damping constant is determined in the vicinity of threshold by twice the difference between the first-order term of the negative conductivity due to laser action and the resonator loss conductivity, it converges to that determined by the resonator loss conductivity with the increase of oscillation intensity. The analysis on the small external signal injection gives the criteria of mode locking and clarifies the complex perturbation of oscillating modes due to it. In the case of forced locking where the resonator loss is modulated at a frequency nearly equal to the axial mode interval, the sideband components of each mode falling near its neighboring modes are equivalent to externally injected signals. Accordingly, the required modulation voltage across the KDP intracavity modulator for forced locking can be estimated from the foregoing locking criteria for the small external signal injection. It is also explained that the combination tones due to the nonlinearity of the laser medium, which are equivalent to externally injected signals, produce the complex frequency spectra around the oscillating modes, which result in a principal noise of unlocked gas lasers, and give rise to self locking in a certain condition. Besides, the perturbation by spontaneous emission also corresponds to the small external signal injection. The noise due to spontaneous emission is, therefore, easily calculated using the analytical results on the small external signal injection. The representation of the macroscopic polarization of laser medium developed into power series is shown to be inappropriate to a practical He-Ne gas laser with medium output power, and the analysis is extended to the more general case, where the polarization is represented by a monotonically saturating function.