Beam propagation in nonlinear multimode interference waveguide

A variational technique is introduced to analyse the beam propagation features in nonlinear multimode interference. The differential equations for beam width and beam centre are given by the variational method. The steady-state solution of the differential equations is analysed. Detailed features of the nonlinear multimode interference when the input beam centre is at the centre and off the centre are investigated. It is found that, when the input power is high enough that the beam can be looked at as an integer, the beam will bend and experiences a zigzag path. These features are power dependent. Some results of the variational method are verified by a numerical method.