Internal Dynamics of Partially Incoherent Optical Solitons

Wieslaw Krolikowski
Laser Physics Centre, Research School of Physical Sciences and Engineering, ANU

Ole Bang
Institute of Mathematical Modelling, Technical University of Denmark

Darran Edmundson
ANU Supercomputer Facility Vizlab

Imagine a laser beam bouncing off of a roughened rotating mirror and entering a crystal. The roughened mirror will introduce random phase variations in the wavefront. Each point across the beam will now contain components travelling in many directions. At any given instant, these components will sum to give a complicated intereference pattern at some distance z inside the crystal. However, this pattern will fluctuate quickly as the mirror is rotating. If the crystal cannot respond quickly to the fluctuations, the interference pattern will be "washed out" and the crystal will only see the sum of the average intensities of all the components in the beam. The beam is said to contain mutually incoherent components.

The following are visualizations of simulations of the propagation of an incoherent beam in a crystal whose index of refraction responds slowly but logarithmically to the total intensity. We simulate this on the ANUSF VPP supercomputer using a 256x256 x-y mesh with 256 components used to represent the incoherent beam. At any z along the crystal, we sum all 256 components to get the intensity of the beam. This intensity induces a change in the refractive index of the crystal which subsequently acts as a waveguide for the components.

In these first images, the incoherence is carefully chosen so that spreading due to both incoherence and diffraction is exactly compensated for by nonlinear self-focusing. Note that the isosurfaces are cylinders revealing that the total beam profile is constant. However, within this beam, individual components oscillate back and forth, changing shape in such a way to keep the beam fixed.

Selected 5% of the total components used to propagate the Log(I) soliton (incoherence sigma=2) visualized as tubes which follow the peak of each component. Blue half-cylinders show isosurfaces at 1% and 10% of the total intensity. For illustration, spatial extent of the field of two components is shown at two values of z.

Stripping away all tubes at left except for that corresponding to component 242, we also show the field at z=0 from which the tube location was gleaned. The raw data is a 3d scalar field for |f|. At each z we identify the centre of the pulse and have the tube pierce this location.

When the degree of incoherence of the beam doesn't exactly match a certain value, independent oscillations of the beam width in the two directions are seen. When the periods are incommensurate, a complicated (but predictable) intensity pattern is obtained.

Selected components used to propagate the oscillating beam visualized as tubes which follow the peak of each component. Isosurfaces at 1%, 10% and 25% of the total intensity are plotted.

Selected components used to propagate an elliptic beam (different degrees of incoherence in the x and y directions) visualized as tubes which follow the peak of each component. Notice that the component launched at 45% executes a helical path. Isosurfaces at 1%, 10% and 30% of the total intensity are plotted.