Gaussian beam reflection and refraction by a spherical or parabolic surface: comparison of vectorial-law calculation with lens approximation.

A ray-tracing approach is used to demonstrate efficient application of the vectorial laws of reflection and refraction to computational optics problems. Both the full width at half-maximum (fwhm) and offset of Gaussian beams resulting from off-center reflection and refraction are calculated for spherical and paraboloidal surfaces of revolution. It is found that the magnification and displacement depend nonlinearly on the miscentering. For these geometries, the limits of accuracy of the lens approximation are examined quantitatively. In contrast to the ray-tracing solution, this paraxial approximation would predict a magnification of a beam's fwhm that is independent of miscentering, and an offset linearly proportional to the miscentering. The focusing property of paraboloidal surfaces of revolution is also derived in setting up the calculation.