B.S.T.J. Briefs: A Circle Diagram for Optical Resonators
01 July 1964
T H E BELL SYSTEM TECHNICAL J O U R N A L , J U L Y 19G4 A Circle Diagram lor Optical Resonators By J. ! GORDON (Manuscript received June 1G, 10(5-4) A graphical representation of the relationships between the parameters of Hermite Gaussian light beams has been introduced recently 1 '" by S. A. Collins, .Jr. T. Li has pointed out 1 that Collins' chart has two equivalent forms. Collins' chart relates the spot radius and phase front curvature at any position on the 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 gx = 1 -- d/Tti ,ยท>= 1 -- d/R2 , where and R> are the radii of curvature of the phase fronts, and d is their separation. This new chart directly relates mirror curvatures and spot radii in a spherical mirror resonator. The equations on which the chart is based are 0 ' 6 g i _ w2~ (h WXWo = -- (1 - 0102) 7T (1)