Stability and dynamics of transverse field structures in the optical parametric oscillator near resonance signal detuning

Abstract

An order parameter equation is derived for an optical parametric oscillator near the resonance signal detuning limit in two dimensions. The parametric mixing between signal and pump fields with cavity diffraction leads to a quintic, fourth-order evolution equation of the Swift–Hohenberg type which supports the formation of cavity solitons, plane waves and periodic structures. The formation, interaction and stability of each of the nontrivial spatial structures is considered via extensive numerical simulations. Stable optical structures are created which can be used as the basis for a wide range of all-optical technologies.

Stability and interactions of transverse field structures in optical parametric oscillators near resonance detuning

“…to establish linear instability. In the Fourier domain, this results in [25]. The growth of this structure is extremely slow for the first few hundred time units.…”

“…In addition to assuming a resonance signal detuning, the derivation here also assumes 2). This gives the OPE [24,25]:…”

“…where δ = ±1 depending on the sign of 2 and the scalings of [24,25] have been used. The resulting spatial structures which arise after bifurcation and are governed by this OPE are the focus of this paper.…”

“…It was also derived previously in the context of a degenerate OPO near resonance detuning [12], but the construction of solutions and characterization of their stability remained open questions. Note that although solutions to (2) can be constructed in one dimension [25], the generalization to two dimensions does not hold due to nonlinear cross terms. Further, the previous solutions found do not have the underlying hexagonal symmetry so often observed in simulations.…”

“…It should be noted that the modulational stability/instability of plane wave solutions can be characterized completely [25]. However, for the fully nonlinear LS to be considered here, these plane wave results are of limited use and validity.…”