From the geometrical path statistics of rays in an anomalous-diffraction theory (ADT) [Opt. Lett. 28, 179 (2003)] closed-form expressions for the geometrical path distribution of rays and analytical formulas for the optical efficiencies of finite circular cylinders oriented in an arbitrary direction with respect to the incident light are derived. The characteristics of the shapes of the cylinders produce unique features in the geometrical path distributions of the cylinders compared with spheroids. Gaussian ray approximations, which depend only on the mean and the mean-squared geometrical paths of rays, of the optical efficiencies of finite circular cylinders and spheroids are compared with the exact optical efficiencies in ADT. The influence of the difference in shape between cylinders and spheroids on the optical efficiencies in ADT is illustrated by their respective geometrical path distributions of rays.

© 2003 Optical Society of America

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