Imaging of optical modes — resonators with internal lenses

This paper discusses the modes of optical resonators, and optical modes of propagation or Gaussian beams of light. The passage of Gaussian beams through lenses, telescopes, sequences of lenses, and lenslike media is studied. Mode matching formulae are derived. A complex beam parameter is introduced for which the law of transformation by any given optical structure can be written in the simple form of a bilinear transformation (ABCD law). Resonators with internal optical elements and their transmission line duals are also investigated. Effective Fresnel numbers and curvature parameters are determined which allow one to infer the diffraction losses, the resonant conditions, and the mode patterns of the various systems. Results are obtained for resonators with internal lenses, sequences of lenses with irises inserted between the lenses, resonators with internal lenslike media, transmission lines consisting of a lenslike medium with periodically spaced irises, and resonators with one very large mirror.