Theory of Mode Interaction in the Case of Small Mode Spacing

This paper deals with strong mode interaction in a short gas laser with plane parallel mirrors; in such a laser the mode spacings are of the order of the natural line width. The treatment here presented is based on Lamb's theoretical model, with the extension that the vector character of the electromagnetic field is not ignored. It is assumed that the gas remains isotropic and that the rate of induced transitions follows the beat frequencies. We shall focus attention particularly on the dispersive behavior of the active medium with and without laser action and derive the refractive index as a function of the frequency. It will be shown that, owing to the small mode spacing, there are strong variations of refractive index in the neighborhood of an oscillating mode. We shall see that, as a consequence of these variations, the conditions for obtaining more than one oscillating frequency with the same cavity resonance and with the same spatial distribution can be fulfilled. Finally, from this model some conclusions can be drawn regarding the directions of polarization of the two principal modes without and with the presence of combination tones.