  We describe spontaneous symmetry breaking in the powers of two optical modes
coupled into a ring resonator, using a pair of coupled Lorentzian equations,
featuring tunable self- and cross-phase modulation terms. We investigate a wide
variety of nonlinear materials by changing the ratio of the self- and
cross-phase interaction coefficients. Static and dynamic effects range from the
number and stability of stationary states to the onset and nature of
oscillations. Minimal conditions to observe symmetry breaking are provided in
terms of the ratio of the self-/cross-phase coefficients, detuning, and input
power. Different ratios of the nonlinear coefficients also influence the
dynamical regime, where they can induce or suppress bifurcations and
oscillations. A generalised description on this kind is useful for the
development of all-optical components, such as isolators and oscillators,
constructed from a wide variety of optical media in ring resonators.
