Fabry Pérot (FP) cavity with a high degree of stability has garnered a lot of interest in precision laser spectroscopy, quantum measurements, and gravitational wave detection using interferometric techniques, etc. Typically, the fractional frequency stability of the cavity ( \(\sim 10^{-16}\) ) has a direct correlation to the length stability of the FP-cavity mode-locked under an electro-optics control loop. The control loop, however, can unintentionally get locked into a transverse higher-order mode (HOM), instead of the fundamental mode, causing instability to the system. Therefore in this study, for better performance of the cavity, suppression of HOMs has been achieved by the analysis of Gouy phase shifts which cause attenuation to the transverse HOMs, termed as the ‘Suppression Factor’. A desired suppression factor \(\sim 10^{10}\) can be obtained by additional introduction of coatings to both mirrors in the FP-cavity since a careful selection of proper coating profiles causes further reduction of HOMs. For the best possible choice of coating, multiple coating types such as etalon and metal coating profiles have been studied with the help of optical design software complemented by numerical simulation.
