A polarization-insensitive recirculating delayed self-heterodyne method (PI-RDSHM) is proposed and demonstrated for the precise measurement of sub-kilohertz laser linewidths. By a unique combination of Faraday rotator mirrors (FRMs) in an interferometer, the polarization-induced fading is effectively reduced without any active polarization control. This passive polarization-insensitive operation is theoretically analyzed and experimentally verified. Benefited from the recirculating mechanism, a series of stable beat spectra with different delay times can be measured simultaneously without changing the length of delay fiber. Based on Voigt profile fitting of high-order beat spectra, the average Lorentzian linewidth of the laser is obtained. The PI-RDSHM has advantages of polarization insensitivity, high resolution, and less statistical error, providing an effective tool for accurate measurement of sub-kilohertz laser linewidth.

Thermal noise in optical cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Numata et al. derived three equations based on strain energy and the fluctuation–dissipation theorem to estimate the thermal noise contributions of the spacer, substrates, and coating. These equations work well for cylindrical cavities. Extending from that, an expression for the thermal noise for a cubic spacer based on the fluctuation–dissipation theorem is derived, and the thermal noise in cubic optical cavities is investigated in detail by theoretical analysis and finite element simulation. The result shows that the thermal noise of the analytic estimate fits well with that of finite element analysis. Meanwhile, the influence of the compressive force F_p on the thermal noise in cubic optical cavities is analyzed for the first time. For a 50 mm long ultra-low expansion cubic cavity with fused silica substrates and GaAs/AlGaAs crystalline coating, the displacement noise contributed from every F_p of 100 N is about three times more than that of the substrate and coating.

In many scientific fields, the continuous operation of ultra-stable lasers is crucial for applications. To speed up the frequency stabilization process in case of the occurence of unexpected interruptions, a prompt frequency stabilization approach based on an improved mean shift algorithm is proposed and verified with a homemade laser system. We developed a double-loop feedback controller to steer the laser frequency with fast and slow channels, respectively. In this study, an improved mean shift algorithm is utilized to intelligently search for the transmission signal, which involves adaptively updating the sliding window radius and incorporating a Gaussian kernel function to update the shift vector. The number of lock points on the left and right sides of the central point determines the scanning direction to search for the transmission signal quickly. The laser is intentionally interrupted 306 times within 10,000 s to evaluate the relocking performance. The median auto-locking time of the laser is improved from 16 s to 4 s. By beating with another ultra-stable laser system, the laser frequency instability is measured to be less than $2.1\times {10}^{-14}$ and the linewidth is 5 Hz. This work improves the adaptation and relocking ability of the ultra-stable laser in a complex environment.

Nonlinear effects in optical fiber frequency transfer have a significant impact on the precision of frequency transfer. We investigate the main nonlinear effects, including the Brillouin scattering and the Raman scattering, in optical fiber frequency transfer through theoretical and simulation calculations in detail. The calculation results show that the threshold powers of the Brillouin scattering and the Raman scattering decrease with the increase in the fiber length; however, the fiber length has little to no impact on the threshold powers when the fiber length is greater than 10 km. The threshold powers, including the Brillouin scattering and the Raman scattering, increase as the attenuation coefficient increases. Conversely, when it comes to the gain coefficients, the outcomes exhibit a reverse trend. When the linewidth ${\mathsf{\Delta }v}_{laser}$ of the laser source is from 1 Hz to 1 MHz, the linewidth ${\mathsf{\Delta }v}_{laser}$ does not affect the threshold powers of the Brillouin scattering. This study seeks to offer design guidance aimed at mitigating nonlinear effects in optical fiber frequency transfer. The calculated results hold considerable potential in guiding various applications reliant on Brillouin and Raman scattering properties, such as laser technology and optical fiber sensing.

Ultra-stable optical cavities (USOCs) as fragile precision instruments have many important applications in space. In order to protect them from being damaged during a rocket launch, we analyzed a USOC by means of finite element methodology. The shock acceleration limits that the USOC can withstand in different directions and under various conditions are given. To increase the shock acceleration limit, the midplane thickness and the fixed hole diameter should be selected to be as high as possible. It is worth noting that the launch direction of the USOC should be selected as the horizontal direction, for which the shock acceleration limit that the USOC can withstand is approximately two times that of the vertical direction. In this paper, results provide guidance for the design of USOCs for space applications, especially the design to prevent the damage caused by a shock. The method could then be applied to other space optical cavities, providing a tool to improve the effect of shock at high accelerations.

Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the performance of state-of-the-art ultra-narrow linewidth lasers, we derive an expression of the TN for a cylindrical spacer according to the fluctuation–dissipation theorem, which takes into account the front face area of the spacer. This estimation is more suitable for the TN of the cylindrical USC than the previous one. Meanwhile, we perform detailed studies of the influence of the four support pads on the TN in cylindrical USCs for the first time by numerical simulations. For a 400 mm long cylindrical USC with an ultra-low expansion spacer and fused silica substrates, the displacement noise contributed from the four support pads is roughly four times that of the substrates and the GaAs/AlGaAs crystalline coating. The results show that the four support pads are the primary TN contributors under some materials and geometries of USCs.