We report the formulation of an <i>ABCD</i> matrix for reflection and refraction of Gaussian light beams at the surfaces of the hyperboloid of revolution that separate media of different refractive indices. The analysis includes an arbitrary angle of incidence and is based on matching the optical phase at the interface. Finally, we deduce expressions for spot sizes and wave-front radii and use them to obtain the <i>ABCD</i> matrix. Based on the formulated <i>ABCD</i> matrix for refraction under paraxial approximation, we also report a simple theoretical investigation of the coupling efficiency of a laser diode to a single-mode fiber with a hyperbolic lens formed on its tip.
© 1997 Optical Society of America
Sankar Gangopadhyay and Somenath Sarkar, "ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip," Appl. Opt. 36, 8582-8586 (1997)