A Circle Diagram for Optical Resonators

A graphical representation of the relationshiops between the parameters of Hermite Gaussina light beams has been introduced recently 1,2 by S. A. collins, Jr. T. Li has pointed out 3 that collins' chart has tow equivalent forms. Collins' chart related the spot redius and phase front curvature at any position ont he beam to the position and spot radius of the beam waist. In this note we point out that a similar chart can be made which relates the curvature parameters 4,5 of any two phase fronts along a Gaussian beam and the spot radii on those phase fronts. The curvature parameters are defined as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g₁ = 1 - d/R₁, g₂ = 1-d/R₂,</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R₁</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R₂</tex> are the raddi of curvature of the phase fronts, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> is their separation. This new chart directly relates mirror curvatures and spot radii in a spherical mirror resonator.