The 2 x 2 Jones matrix method is used in a theoretical analysis of the
cavity amplitude and phase nonreciprocities of monolithic nonplanar s
olid-state ring lasers. An approach is developed to the optimisation o
f the perimeter and parameters of the cavity to ensure the necessary a
mplitude and phase nonreciprocities. Calculations are reported of the
cavity parameters optimal for the two most important applications: uni
directional single-frequency lasing and bidirectional lasing in a self
-modulation regime which is of interest in laser gyroscopy.