A New Method for Interpreting the Effective Radius of Curvature: Two-Dimensional Case

Starting from the vector field theory,the expression of the time average energy flow densityof a paraxial scalar light beam is deduced.In terms of this expression,the x(or y)directional weighted deviation is reasonably defined between the real-beam wavefrontand an imaginary ellipsoidal wavefront which is used to replace the real-beam wavefront.It is proved that,when Rx and Ry are just the x and y directional effective radii of curvature,respectively,the ellipsoidal wavefront Le=x^(2)/(2Rx)+y^(2)/(2 Ry)is the best-fit one for the real-beam wavefront L.Finally,the above results are generalized for a general polychrornatic light beams.