Influence of the shape of a discharge-gap cross section on the gas-laser gain

A geometric contribution to the active-medium gain is estimated for laser tubes of circular, rectangular, and elliptic cross sections. The gain averaged over an elliptic cross section is found to decrease with increasing ellipse eccentricity and this gain is intermediate between those obtained for circular and rectangular cross sections (the gain on the axis is assumed to be the same in all cases). A smoother distribution of the gain over elliptic and rectangular cross sections and lower diffraction losses suggest that tubes with these cross sections should be used in ring lasers.