Phase-bistable Kerr cavity solitons and patterns

Abstract

We study pattern formation in a passive nonlinear optical cavity on the basis of the classic Lugiato-Lefever model with a periodically modulated injection. When the injection amplitude sign alternates, e.g., following a sinusoidal modulation in time or in space, a phase-bistable response emerges, which is at the root of the spatial pattern formation in the system. An asymptotic description is given in terms of a damped nonlinear Schrödinger equation with parametric amplification, which allows gaining insight into the basic spatiotemporal dynamics of the system. One-and two-dimensional phase-bistable spatial patterns, such as bright and dark-ring cavity solitons and labyrinths, are demonstrated.

Phase-bistable patterns and cavity solitons induced by spatially periodic injection into vertical-cavity surface-emitting lasers

“…In the optical arena, rocking of small Fresnel number (small aspect ratio) nonlinear resonators results in a global phase bistability affecting the whole light beam [15,20], while for large Fresnel number systems more spatial degrees of freedom are available and rocking leads to the excitation of spatial phase-bistable patterns that form on the transverse section of the light beam, such as phase domains, rolls, and phase solitons [13,14]. In particular, spatial rocking, which is the concern of the present study, has been considered in a one-transverse-dimensional broad area semiconductor laser [17] and in a Kerr resonator [19].…”

“…That modulation must entail sign alternations (i.e., π -phase jumps) of the forcing in time (temporal rocking) or in space (spatial rocking) and must occur on sufficiently fast, nonresonant scales as compared to the typical scales of the oscillations' envelope dynamics. Theoretical [13][14][15][16][17][18][19] and experimental [16,20,21] studies have revealed that this type of forcing converts the initially phase-invariant oscillatory system into a phasebistable pattern forming one, similarly to the classic 2:1 resonant forcing (at twice the system's natural frequency) of a spatially homogeneous Hopf bifurcation [8,9]. The advantage of rocking with respect to the 2:1 resonance is that some systems (optical in particular) are insensitive to the latter, due to their extremely narrow frequency response.…”

Phase-bistable pattern formation in oscillatory systems via rocking: application to nonlinear optical systems

“…Figures 10 and 11 illustrate typical results of the numerical integration of a Kerr nonlinear system below the threshold, equation (6.1). We note that both the temporal and the spatial rocking is possible, as already shown in [70]. Here, we concentrate on spatial rocking by injecting a periodic pattern in the form of parallel stripes (figure 10), which can be called one-dimensional rocking, and by injecting a pattern of square symmetry (figure 11)-two-dimensional rocking.…”

Transverse phase shielding solitons in the degenerated optical parametric oscillator

“…Spatially extended systems described by this equation have been reported to exhibit periodic patterns (triangles, hexagons, rolls, and so forth) [15][16][17], localized structures without (dissipative soliton, fronts, kinks, localized states) and with [9,21,19,18,20] propagative domain walls [22] and many other dynamical dissipative structures. In the optical context, the PDNLS has been derived in a Kerr optical medium forced by modulated (spatially and temporally) injection [23].…”