Modelling and design of ultra-high stable Fabry–Pérot cavity

Abstract

Lasers having sub-Hz linewidth and long-term stability better than a few parts in 1016 is an unavoidable requisite to achieve unprecedented accuracy in the optical atomic clocks, intercomparing distributed atomic clocks and their networking, establishing coherent optical fibres, precision time & frequency transfer, production of optical qubits, and many more. For these wide ranges of applications, ultrastable Fabry–Pérot (FP) cavities, which act as the reference optical resonator, have got lots of attention. Designing such a FP cavity is a challenge due to the requirements of suppressing instabilities from all the thermo-mechanical noise sources at the highest degree. In this article, we report a comprehensive study to elucidate detailed design steps and associated numerical analysis procedures to build such a FP cavity. For this, we considered all sources of noises arising from: improper optical and opto-mechanical settings, ground vibrations transmitted to the cavity, deformations due to self-weight as it worsens the stability due to acoustic noise coupled to it, and temperature fluctuation. We present quantitative assessments of the instabilities for different shapes, geometries, and constituent materials of the cavities. In order to model the vibration-induced instability, we developed a novel forced-vibration based technique for accurate estimation of the instabilities, that reciprocates the experimental results reported in the literature, and the method is found to be superior compared to the other approaches, therefore estimating the overall cavity stability more accurately. We found in short term (¡ 10 s), the instability of the cavity is limited by temperature fluctuation, and in the long term (¿ 10 s), Brownian noise dominates the instability, therefore demands adequate precautions to reach the desired level of stability. Through systematic simulations, we have identified the best criteria for minimization of all these noises and obtain stabilities of 8.5×10−17 and 5.1×10−17 using dielectric and crystalline mirror coatings, respectively, which are similar to the best-reported results among its homologue cavities.