Eigenmode changes in a misaligned triangular optical cavity

We derive relationships between various types of small misalignments in a triangular optical cavity and associated geometrical eigenmode changes. We focus on the changes of beam spot positions on cavity mirrors, the beam waist position and its angle. A comparison of analytical and numerical results shows excellent agreement. The results are applicable to any triangular cavity close to an isosceles triangle, with the lengths of two sides much bigger than the third, consisting of a curved mirror and two flat mirrors (the curved mirror is the distant one) yielding a waist equally separated from the two flat mirrors. This cavity shape is most commonly used in laser interferometry. The analysis presented here can easily be extended to more generic cavity shapes. The geometrical analysis not only serves as a method of checking a simulation result, but also gives an intuitive and handy tool to visualize the eigenmode of a misaligned triangular cavity.