Abstract

An expression for the field transmitted through a dielectric spherical lens when a spherical Gaussian beam is incident is derived with the use of Maslov’s method. Through the application of the stationary phase method, it is verified that the expression reduces to the geometrical-optics solution in the region far from any caustic. The solutions are compared with the result obtained by the Kirchoff–Huygens principle and by the exact solution of the wave equation. Numerical results are presented for the variations of the field distributions in the focal region as a function of the source distance from the lens surface and the index of refraction of the lens. These results are useful for the design of ball lenses for couplers in optical-fiber communication systems.

© 1991 Optical Society of America

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