Fat Rays: A Synthesis of Physical and Geometrical Optics with Gaussian Beamlets

Abstract

Optical systems are primarily designed and analyzed by tracing bundles of rays. These rays are actually discrete points on the geometrical wavefront propagating through the system. The local field amplitude is inversely proportional to the radius of curvature of the wavefront or the distance from a neighboring ray point. Since by definition diffraction effects are excluded from geometrical optics, the energy density is infinite at focus or, in general, on a caustic. These singularities can be removed if the rays are expanded into physical-optics beamlets which are solutions to at least the reduced (paraxial or parabolic) wave equation. The individual fields would then be finite and continuous everywhere, and their superposition would represent the cumulative effects of aberrations, interference, obscurations, and diffraction in the system. This "fattening" of the infinitesimal geometrical rays is analogous to "thinning" the infinite plane waves used in the Fourier transform solutions of physical optics.