Multiconical transverse patterns of monolithic mini-cavity optical parametric oscillator

Abstract

Transverse pattern formation in broad aperture lasers and in other nonlinear optical resonators like photorefractive oscillators and optical parametric oscillators (OPOs) is attracting an increasing interest. The interest stems from two viewpoints: (1) from the fundamental physical viewpoint, since the nonlinear optical systems are convenient systems for studies of self-organization and pattern formation in spatially extended systems; (2) from the viewpoint of applications, since optical patterns have an application potential for parallel information processing, for image processing, nonlinear microscopy, and related topics. Pattern formation in nonlinear mini-cavities is especially attractive from the application viewpoint due to the compactness of the system. Transverse patterns have been predicted to occur and have been observed in several different nonlinear optical systems (see e. g. [1, 2] for a review). In the case of a quadratic nonlinear interaction patterns have been predicted in OPOs [3–5], in degenerate OPOs [6, 7], and in second harmonic generation SHG [8–10]. Degenerate OPOs are particularly interesting due to the possibility of excitation of phase patterns [11, 12], and of phase solitons [13]. Experimentally transverse patterns have been observed for OPOs [14–16] and for second harmonic generation [17]. No patterns have been yet seen for degenerate OPOs, or for OPOs in monolithic microor mini-cavities. Most of the theoretical-numerical studies on transverse patterns in nonlinear optics consider mean field approximation, which means equivalently a single longitudinal mode assumption. Within this assumption the emission of a spatially extended system evolves on a resonant ring in the far field domain with the ring radius dependent on the detuning on the resonator: k ⊥ = 2|k|(ω − ω0)/c, where k⊥ is the transverse wave-number of the emitted radiation, |k| = ω/c, ω is the gain frequency (atomic gain frequency in lasers, half-pump-frequency for degenerate OPOs, and the frequency of injection in passive systems), ω0 is the eigenfrequency of the (closest) longitudinal mode of the resonator, and c is the velocity of light in material. Therefore the off-axis (conical) emission with the cone angle depending on the detuning is a “weakly nonlinear” precursor of the nonlinear transverse patterns. The basic mechanism of the “essentially nonlinear” pattern formation in lasers is the tilted wave selection, i. e. a selection of one or several waves from those allowed by the above resonant ring condition [18]. Analogously the basic mechanism of the “essentially nonlin-