Unstable resonator modeling has been carried out for an injection-
seeded CO2 transversely excited atmosphere (TEA) laser in the NOAA/ERL/Wave Propagation Laboratory (WPL) Doppler lidar to examine the effects of various cavity designs on the quality of the output beam. The results show the effects of an injection pinhole, electrode spacing, mirror tilt, and radial reflectivity function of the output coupler. The electrode spacing in our laser has negligible effect. The injection pinhole, however, produces complicated structures in the output patterns. If the pinhole is removed, the output pattern is much smoother, and the frequency jitter is smaller. Misalignment sensitivity is very closely related to the radial reflectivity function. The superparabolic function provides the highest coupling efficiency, largest beam size, and good collimation, but produces a slightly higher misalignment sensitivity compared with a parabolic function. The Gaussian function provides the lowest misalignment sensitivity, but it produces the smallest beam size and the largest beam divergence. Also, the coupling coefficient is 50% lower than the optimum value. Methods for using a flat diffraction grating in unstable resonators are also investigated. The best way is to use a flat grating/positive lens combination to replace the back concave mirror.