Emergence of order, self-organization and instabilities in a 1-D array of solitons
2005 IEEE LEOS Annual Meeting Conference Proceedings
Nonlinear interactions between light and matter can lead to the formation of spatial patterns and self-trapped optical beams. A light pulse propagating in a nonlinear Kerr medium will come to a focus if its power is above a critical value. If the pulse power is much higher than the critical power then the optical beam will break up into multiple filaments    . Each filament will contain approximately the critical power. We have used carbon disulfide (CS 2 ) as the nonlinear material (n
... nlinear material (n 0 = 1.6, n 2 = 3x10 -15 cm 2 /W ), which has a critical power of 190 kW for our laser wavelength of 800 nm. We have used 150-femtosecond pulses with a maximum energy of 1 mJ to generate spatial solitons. Each pulse from the laser is split into pump and probe pulses. The pump pulse is focused into a line (using a cylindrical lens) at the entrance face of a 10 mm glass cell filled with CS 2 . The beam profile of the pump at the exit of the glass cell is imaged onto a CCD camera for different values of the input power ( Fig. 1 ). In the absence of nonlinearity the incident cylindrical beam would diverge, but for high power the beam self-focuses into a thin line (Fig. 1a-c) . For P > 100P cr , the beam breaks up into individual filaments ( Fig. 2d-e) . The filaments are seeded by small variations in the input beam and are stable in location and size to small variations in the input energy. In other words, the pattern of filaments is repeatable from shot to shot as long as the illuminating beam profile is kept constant. The diameter of the filaments is approximately 12 μm and does not change when the energy is increased, while the number of filaments increases with power. For P > 250P cr , the output beam profile becomes unrepeatable and the filaments start to fuse into a continuous line (Fig 2f-h) . We believe the instability in the beam profile results from interactions between the filaments when the spacing between them becomes small. Part of the energy is scattered out of the central maximum into side lobes. The side lobes are generated through the emission of conical waves from the filaments, during the self-focusing stage . Fig. 1. Beam profile of the pump pulse at the output of the CS2 cell. The power increases form left to right: a) P = 12P cr , b) 40P cr , c) 80P cr , d) 170P cr , e) 250P cr , f) 390P cr , g) 530P cr , h) 1200P cr . The beam profile inside the CS 2 cell is captured using Femtosecond Time-resolved Optical Polarigraphy (FTOP)  in a pump-probe setup. The trajectory of the pump pulse is obtained by numerically combining multiple pump-probe images of the pulse at different positions as it traverses the material. Figure 2 shows the trajectory of the beam obtained for pulses with P = 390P cr (a) and 1200P cr (c), from a distance of 0.5 cm to 5 cm from the cell entrance. The 1-D Fourier transforms of the beam profile are calculated and displayed in Figure 2b and 2d for each 292 0-7803-9217-5/05/$20.00©2005 IEEE TuN4 11:30 -11:45 Authorized licensed use limited to: CALIFORNIA INSTITUTE OF TECHNOLOGY. Downloaded on April 14,2010 at 18:58:08 UTC from IEEE Xplore. Restrictions apply.