Resonators on the Stability Limits

Abstract

If the g-parameters of the stable resonator approach the stability boundaries at g ₁ g ₂ = 0 or g ₁ g ₂ = 1, the beam radii at the mirrors of the Gaussian beam go to zero or infinity. On the stability boundaries, the Gaussian beam is not an eigensolution of the resonator. The field distributions of the eigenmodes are still solutions of the diffraction integral equation (5.66), but the mode structure and the diffraction losses have to be calculated numerically. A helpful property of resonators on the stability limits is their equivalency since they all exhibit the same absolute value of the equivalent g-parameter G=2g ₁ g ₂ -1 = ±1. If the properties are known for one resonator as a function of the aperture radius, the mode structure and the losses of all other resonators on the stability limits can be determined.