Waveguide laser resonators with a tilted mirror

We present a multimode theory of square-bore waveguide laser resonators with one well-aligned and one tilted plane mirror. Our theoretical results for mode content, resonator loss, and power output agree reasonably well with experimental results from an RF-excited CO
2
laser with a
376 \times 1.5 \times 1.5
mm Al/Al
2
O
3
waveguide. The mode propagation coefficients of this structure are discussed. We model a diffraction grating as a plane mirror with a wavelength-dependent tilt, and conclude that previous single-mode theory has underestimated the severity of the line-hopping constraint on tunable waveguide CO
2
laser performance.