Generalized mean-field or master equation for nonlinear cavities with transverse effects.

We present a general form of master equation for nonlinear-optical cavities that can be described by an ABCD matrix. It includes as special cases some previous models of spatiotemporal effects in lasers.

Kerr lens effects in a ring resonator with an aperture:mode locking and unidirectional operation.

A ring resonator containing a Kerr lens and a Gaussian slit is analyzed. From the point of view of Kerr lens mode locking, it is shown that a self-defocusing nonlinear element is as effective as a self-focusing one and that the positioning of the Kerr element introduces trade-offs between self-starting and operational stabilization. The nonlinearity can lead to unidirectional lasing.

Spatial ring emission and filament formation in an optical fiber with a saturable nonlinear cladding.

We present numerical simulations of Gaussian beam propagation in an optical fiber with a linear core and a saturable self-focusing cladding. Cylindrical nonlinear waves are emitted from the core into the cladding and are initially localized only in the radial direction, forming rings. These rings can break their cylindrical symmetry through a transverse instability, which yields filaments localized both azimuthally and radially, most of which stay close to the core for long propagation distances.

Nonlinear directional coupler with a diffusive Kerr-type nonlinearity.

We present numerical results showing the effects of a diffusive Kerr-type nonlinearity on the switching characteristics of a nonlinear directional coupler. It is found that switching can still occur even when the diffusion length is equal to the waveguide separation but that then its threshold increases and becomes less pronounced.