Abstract
Paraboloid form is a commonly used element in optical or quasioptical systems. It is necessary to calculate the reflection and/or refraction of Gaussian beams at the surface of a paraboloid. Based on boundary-value relation in electromagnetic field, the expressions are derived for reflection and refraction of Gaussian beams on the interface of an elliptic paraboloid that divides media of different refractive indices. We extend the analysis to an arbitrary angle of incidence, and convert the obtained results to ABCD ray matrix form. By using these matrices, one can easily design and calculate some actual optical or quasioptical systems, including components with paraboloidal interfaces.
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