Generalized beam matrices. IV. Optical system design

Abstract

Systematic procedures are presented for determining the optical components needed to produce an arbitrary transformation of a Gaussian light beams's spot size, radius of curvature, displacement, and direction of propagation. As an example, an optical system is considered that spatially separates the two coincident Gaussian beams produced by a high-diffraction-loss resonator that uses a Gaussian variable-reflectivity output coupler. In addition, an ABCDGH reverse matrix theorem and an ABCDGH Sylvester theorem are also derived. These matrix theorems may be used to satisfy special constraints inherent in the design of multipass and periodic optical systems.