Analytical calculation of Hermite-Gauss and Laguerre-Gauss modes on a   bullseye photodiode
  This note describes the analytical derivation of the response of bullseye detectors to optical beats between higher-order spatial modes of the Laguerre-Gauss form, and subsequently the Hermite-Gauss form. Also included is a comparison with numerically calculated beat coefficients, and a simple example of the use of the resulting beat coefficients in simulating a mode mismatch sensor for a Fabry-Perot cavity. 
Charlotte Bond, Paul Fulda, Andreas Freise
physics.optics