Phase variations due to dispersion in inhomogeneously broadened lasers

One-dimensional analytical solutions for irradiance and phase are obtained for a two-level ring resonator model of a long inhomogeneously broadened chemical laser with strong velocity changing collisions (momentum cross relaxation). The solutions give the longitudinal mode spectrum of the laser line in terms of the ratio of elastic to inelastic collision rate, the Doppler linewidth, the product of small-signal gain times the length of the gain medium, and the resonator loss. The intensity is given in terms of the width of the mode spectrum, the saturation intensity, and the gain-length product. The phase in a single pass is given in terms of the mode spectrum, the loss, and the ratio of homogeneous to inhomogeneous width. For typical conditions the phase difference relative to line center for a detuning frequency near the edge of a laser line is less than about one twentieth of a wavelength for a single pass through the resonator. Application to unstable resonator geometries suggests that the total phase difference at the edge of such a laser may reach a few tenths of a wave, although most of the power in the line has a much smaller phase variation.