Abstract
The physics of the continuous-wave gas ring laser is reexamined to allow for mode-coupling effects. Conditions are specified under which pulsations in the excitation density can be neglected, so that calculations can be done to infinite order in the electric field. Dispersion for the forward and backward traveling waves is modified by the inclusion of Lorentz transformations of field amplitudes. The role of dispersion relations in the interpretation of experimental data from a rotating ring is delineated, taking account of a double-valuedness derived in the companion paper as a result of mode coupling.