Influence of a difference between the resonator $\Omega$ factors on the interaction of opposite waves in solid-state ring lasers

A theoretical analysis is made of the characteristics of a solid-state ring laser with a small difference between the resonator $\Omega$ factors for the opposite waves. It is found that in a certain range of frequency biases $\Omega$, a difference between the $\Omega$ factors results in equalization of the opposite wave intensities and in the appearance of a beat regime. The amplitude and frequency characteristics are found to be asymmetric functions of $\Omega$. In the asymptotic range of large $\vert\Omega\vert$ the same wave is found to be suppressed for $\Omega>0$ and $\Omega<0$.