3-DIMENSIONAL REPRESENTATION OF 2-DIMENSIONAL VORTEX DYNAMICS IN LASERS

We observe that the dynamics of vortices in paraxial optics, including vortex pair-creation and pair-annihilation, can be represented in a s implified manner by the motion of a locus obtained from the complex op tical field, for which the real and imaginary parts of the field are e qual. When the locus lies within the transverse plane a dark line is p resent in the optical field with a phase change of pi across. When the locus intersects the transverse plane, a vortex exists at the interse ction point. Thus the locus line appears like a three-dimensional vort ex line. Examples are given ranging from emission in low order laser m ode families to patterns calculated for plane mirror resonators.