Transformation of waist parameters of a Gaussian beam by a thick lens

This paper presents a theory of the transformation of the waist position and waist size of a Gaussian beam by a thick lens. We clarify the effects of lens thickness and shape on the transformed waist parameters. For equiconvex and equiconcave lenses, the effects of the thickness on the transformed parameters are significant when the Rayleigh length of the incident beam is small compared with the focal length of a thin positive lens. For plano-convex and plano-concave lenses, the waist parameters of the transmitted beam depend largely on whether the flat or curved side faces the incident beam. The conditions for locating the waist at a prescribed position in a spherical shell or a sphere are also given in terms of the waist parameters of the incident beam.