When a lens is not prepared with an exact quadratic profile but is approximated by such a profile, there is considerable arbitrariness in the choice of the quadratic profile. Only one of these choices is optimal and gives the correct description of the physical optics involved. Laser beam self-focusing is chosen as the example in case, and it is shown that the optimal energy-conserving solution is equivalent to the variational and moments theories of self-focusing while at the same time it is paraxial in nature. Hankel-transformation techniques are used to prove this.
© 2004 Optical Society of America
D. Subbarao, "Paraxial lens approximation and self-focusing theory," J. Opt. Soc. Am. B 21, 323-329 (2004)