Nonadiabatic effects in optical pattern formation

Abstract

Pattern formation in cavity nonlinear optical systems subjected to a periodic modulation of frequency detuning is studied analytically and numerically with particular reference to the models of optical parametric oscillator and two-level laser. Owing to the nonautonomous dynamics, a new mechanism for pattern formation as a result of a primary instability, rather distinct from the most common tilted-wave mechanism found in autonomous systems, is predicted and explained in detail by means of a phase integral (WKB) analysis of the underlying field equations. This mechanism for pattern formation can be traced back to the existence of coherent field oscillations in the two-field dynamics and associated to the existence of turning points in the WKB expansion, which break the adiabatic following. In particular, it is shown that nonadiabatic effects are likely when the decay rates of interacting fields are equal, corresponding to the existence of real turning points. For different relaxation rates of interacting fields, the turning points are complex and nonadiabatic effects vanish at low modulation frequencies. Above threshold, weakly nonlinear analysis and numerical simulations indicate that traveling waves are selected by the nonlinearity.