High-Precision Static Alignment Scheme Based on the Eigenfrequency Separation Characteristics of Same-Order Hermite-Gaussian Mode in Triangular Ring-Down Cavities

Triangular cavities are increasingly used in cavity ring-down spectrometers (CRDS) to compensate for the existence of optical feedback and other disadvantages of straight cavities. However, at the same time, the difficulty of the cavity mounting alignment process is increased. Consequently, the fast and stable establishment of resonance between the optical source and the triangular ring-down cavity has been widely explored for CRDS-based applications. The Hermite-Gaussian theory has unique advantages for the description of the Gaussian resonant beams characteristics in triangular cavities, while the theory is of great importance for the alignment in high finesse triangular ring-down cavities. Along these lines, in this work, the eigenfrequency separation characteristics of the Hermite-Gaussian modes in the triangular cavity, in the meridional and sagittal planes, as well as the excitation and transmission characteristics of the first-order mode in the high finesse cavity were verified. A static alignment method was established for the high-finesse triangular ring-down cavity, and the transmission suppression of the Hermite-Gaussian modes by the high-finesse cavity was overcome in the experiment. Finally, by leveraging the advantageous features of the fundamental and the first-order mode that are complementary to each other, the tilt and axis shift errors of each specified plane with directional high accuracy can be aligned. The static alignment scheme of the triangular cavity based on the Hermite-Gaussian theory that was established here paves the way for the mounting alignment of the CRDS instrument before the ring-down experiment, whereas the system accuracy of CRDS is further improved.