Abstract
We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry. These structures are unstable with respect to the upswitching process, leading to a premature transition to the upper branch in the homogeneous hysteresis cycle.
Highlights
Self-organization in large area two-dimensional optical devices is an active topic in nonlinear optics [1,2,3,4]
These structures consist of self-organized light bullets traveling in the cavity and have been reported in nonlinear Kerr cavities [6], optical parametric oscillators [7], type II second harmonic generation [8], and wide aperture lasers with a saturable absorber [9]
This means that up-switching in the homogeneous hysteresis cycle of a Kerr cavity with negative diffraction and direct dispe√rsion will occur at the bifurcation point |Ac|2 = 1/Γ rather than at the limit point |A−|2 = (2Δ ± Δ2 − 3)/(3Γ), effectively reducing the width of the cycle
Summary
Self-organization in large area two-dimensional optical devices is an active topic in nonlinear optics [1,2,3,4]. When diffraction and dispersion have a comparable influence on the system, 3D dissipative structures are formed These structures consist of self-organized light bullets traveling in the cavity and have been reported in nonlinear Kerr cavities [6], optical parametric oscillators [7], type II second harmonic generation [8], and wide aperture lasers with a saturable absorber [9]. 3, we study numerically the dissipative structures that emerge from the unstable homogeneous steady states (HSS) and show that the light distribution evolves through a number of different 3D patterns. These patterns are unstable and the cavity switches to the higher homogeneous state. The latter phenomenon leads to a narrower homogeneous hysteresis cycle
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