Frequency locking of modes in a ring laser

The locking of two countertraveling ring laser modes due to light scattering is investigated. It is found that the mutual locking of two free-running oscillating modes is different from locking due to an externally injected signal. The text defines two kinds of mode-to-mode scattering: conservative and nonconservative. The former leads to no locking, to a high degree of approximation. Examples of conservative scatterers are nonabsorbing particles, small compared to a wavelength, and loss-free objects of larger size that represent only a weak perturbation of the dielectric constant in the cavity. The presence of two types of scatterers makes it impossible, in general, to calculate lockbands from measured scattering intensities from optical components such as mirrors. The relationship between the present theory, the conventional Adler theory, and measurable laser component properties such as scattering coefficients is discussed. The findings are of importance for the development of mirrors and optical coating processes in ring lasers.