Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators

Abstract

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.PACS numbers:

Analytic instability thresholds in folded Kerr resonators of arbitrary finesse

“…[16] with our expression (12) by setting G = 0 in ψ 2 (only). There is perfect agreement, once the parameters of the two models are matched up using the vertical-slope condition (11). For zero GVD we note that all finite-frequency instabilities occur on the negative-slope branch, as for the non-Ikeda instabilities in Ref.…”

“…It holds for all values of r and φ and matches all previous special case analyses. It is also valid for all values of the XPM parameter G [11], and thus (9) holds for Kerr liquids, or indeed any Kerr-like material, as well as for dielectrics where G = 2. For a given input reflectivity r, cavity phase φ 0 , and input intensity I in , IL is known from the zero-order solution, and so ( 9) is effectively an analytic formula from which the threshold values of θ, and hence the transverse wavevector K, can be calculated.…”

“…This degeneracy does not make (7) trivial, and all the gain circle considerations still apply for G = 0, as do the threshold formulae (9), (10), (12). However, because there is no walk-off at zero-order we retain G = 2 in the nonlinear phase shift φ nl , which enters the boundary conditions (5) and the OB equation (11).…”

Dirac solitons in optical microresonators

“…As the repetition rate shift results from the imbalance of self-phase modulations, increasing the proportion of g 12 leads to more stability in the repetition rate, while decreasing the proportion of g 12 allows more tunability. We note that, depending on the nonlinear nature of the resonator material and the mode overlap, the cross-phase modulation may be larger or smaller than the self-phase modulation 52 , 53 . Moreover, theoretical DS solutions exist for almost all combinations of nonlinear coefficients.…”

Dissipative Polarization Domain Walls in a Passive Coherently Driven Kerr Resonator

“…Symmetry breaking in this system has recently been investigated in Refs. [6,26,27]. We consider A ¼ 1 and B ¼ 2, since our resonator is nondiffusive [1,28].…”