Topological phase in a nonparaxial Gaussian beam

An analysis is made of the structure and evolution of the singularities of a nonparaxial Gaussian beam. It is shown that a Gaussian beam may be repres ented by a family of straight lines lying on the surface of a hyperboloid a nd that the wavefront of this beam is a function of a point source situated at a point on the z axis with the imaginary coordinate iz(0). The argument of this complex function is the topological phase of the beam which charac terizes the rotation of the wavefront. The singularities of a nonparaxial G aussian beam are located in the focal plane and are annular edge dislocatio ns. Dislocation processes near the constriction of the Gaussian beam only o ccur as a result of aperture diffraction. (C) 1999 American Institute of Ph ysics. [S1063-7850(99)01811-X].