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 density < S > of 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 R_x and R_y are just the x and y directional effective radii of curvature, respectively, the ellipsoidal wavefront L_e = x²/(2R_x) + y²/(2 R_y) is the best-fit one for the real-beam wavefront L. Finally, the above results are generalized for a general polychrornatic light beams.