Novel coordinate system for Gaussian beam reflection

A novel coordinate system for Gaussian beam reflection has been proposed in this Letter. Reflection from a spherical mirror is used to describe the novel coordinate system. One single segment of a general resonator is chosen to describe coordinate rotation in detail. Nonplanar ring resonators are chosen to show the application of the novel coordinate system. This novel coordinate system has been proved by two simple experiments and the problem existing in using the traditional coordinate system has been pointed out. This novel coordinate system is valuable for not only the designing of laser resonators but also Gaussian beam propagation analysis.