Resonant Frequency Separation Characteristics of the Same-Order Hermite-Gaussian Mode in the Astigmatic Triangular Cavity of a Cavity Ring-Down Spectroscope

Triangular planar ring resonant cavities are widely used in cavity ring-down spectroscopes (CRDS) because of the unique optical path advantage. Hermite-Gaussian theory is the classical method used to describe the beam in the resonant cavity. Since this theory can express the transverse electromagnetic mode (TEM) in the meridian plane and sagittal surface separately in an astigmatic triangular cavity, it has a unique advantage in the analysis of triangular cavities. However, among the many analyses of triangular ring-down cavities, existing theories of Hermite-Gaussian modes have not been able to reasonably explain the many phenomena observed in alignment and ring-down experiments. In this paper, the mechanisms of the effects of first-order Hermite-Gaussian mode on mounting alignment in CRDS instruments are investigated in depth. The frequency separation characteristics of the lower-order mode in the triangular cavity are verified in the mounting alignment stage. The separation characteristics of first-order mode can guide the misalignment of the two orthogonal planes separately. The resonant frequency separation property of the Hermite-Gaussian mode in a triangular ring-down cavity can also be applied to more complex odd-numbered cavity mirror resonant systems.