Frequency characteristics of a ring laser with a large-amplitude periodic frequency offset

A weak coupling approximation in the case of narrow static locking zones and large amplitudes of a periodic frequency offset is used to obtain a simple quadrature expression for the frequency characteristic describing the dependence of this characteristic on the frequency offset profile. By way of example, the expression is applied to five different frequency offsets, including those with the traditional rectangular and sinusoidal profiles. Complete expressions are obtained from the frequency characteristics. The offset profiles optimal from the point of view of linearity and the ratio of the widths of locking bands are also determined.