Vector theory of self-focusing of an optical beam in Kerr media

The scalar theory of the self-focusing of an optical beam is not valid for a very narrow beam, and a correct description of the beam behavior requires a vector analysis in this case. A vector nonparaxial theory is developed from the vector Maxwell equations by application of an order-of-magnitude analysis method. For the same input beam, the numerical results of self-focusing from both scalar and vector theories are compared. It is found by the vector theory that a linearly polarized circular input beam becomes elliptical in the selffocusing process.