From electrostatics to optics: The study on the soliton propagation in lead glass using the image beams method

We investigate the soliton propagation in lead glass with rectangle boundary by the method of image beams. This method is the analogue of the electric image method which is used to solve the Poisson type equation. In the general case that the beam width is much smaller than the boundary size, the soliton formation and the soliton steering are analytically studied independently. The critical power of the soliton formation is boundary independent. The boundary effect only provides, for the soliton steering, the dynamic force which is equivalent to the force between the soliton beam and the infinite number of image beams. The closed-form steering trajectories of the solitons are in good agreement with the experimental results.