Modelling and Analysis of Mechanical and Thermal Response of an Ultrastable, Dual-Axis, Cubic Cavity for Terrestrial and Space Applications

TL;DR

This work tackles the need for transportable optical clocks by analyzing a 7.5 cm dual-axis cubic cavity using finite-element methods to quantify mechanical and thermal stability under realistic mounting and thermal conditions. It demonstrates that bore radius principally governs length stability while other geometry and annular-ring parameters provide tunable control, and it shows that a multilayer thermal shield with radiative and mirror-absorption effects yields long thermal time constants; annular rings can tune the zero-crossing temperature toward room temperature. The results guide robust, compact cavity designs suitable for terrestrial and space environments, enabling reliable multi-wavelength stabilization for next-generation clocks in geodesy, VLBI, and deep-space navigation.

Abstract

Transportable all-optical atomic clocks represent the next-generation devices for precision time keeping, ushering a new era in encompassing a wide range of PNT (Positioning, Navigation and Timing) applications in the civil and strategic sectors. Their performance relies on ultra-stable, narrow-linewidth lasers, frequency stabilized to a compact portable optical cavity. Among various designs, the cubic spacer-based ultra-stable cavity is particularly well-suited for transportable applications due to its low sensitivity to vibrations, owing to its symmetric geometry and robust mounting structure. While longer cavities offer a lower fundamental thermal noise floor, one needs to strike a balance between transportability and size. In this aspect, the 7.5 cm dual-axis cubic cavity offers a lower fundamental thermal noise floor in comparison to smaller counterparts, while still retaining a reasonable SWaP (Size, Weight and Power) for terrestrial and aerial PNT applications. Its dual-axis design also enables multi-wavelength laser stabilization, making it a promising candidate for future transportable clock applications. This work presents a detailed study of the 7.5 cm dual-axis cubic cavity using FEM (Finite Element Method) to evaluate its mechanical and thermal stability. We analyze the impact of various geometric factors, mounting forces, and machining imperfections, while also modelling thermal effects such as conduction, radiation, and mirror heating within a vacuum chamber and thermally shielded environment. Our findings provide design insights for developing robust dual-axis optical reference cavities, advancing the deployment of portable atomic clocks for next-generation applications in PNT, geodesy, VLBI (Very Long Baseline Interferometry) and deep space missions.

Figures (16)

• Figure 1: Comparative study of 5 cm, 7.5 cm, and 10 cm dual-axis cubic cavities under supportive forces of (a) 50 N (for terrestrial applications) and (b) 500 N (for space applications).
• Figure 2: 7.5 cm dual-axis cubic cavity design in COMSOL.
• Figure 3: (a) Effect of cutout depth on the length stability ($\Delta L/L$). A 6th-order polynomial fit is applied to the data to determine the zero-crossing cutout depths and corresponding sensitivities. (b) Magnitude of axial displacement (in mm) along the x-direction due to deformation for the first zero-crossing cutout 12.97 mm when supporting forces are applied.
• Figure 4: Effect of supporting forces: (a) in the 1-10 N range, (b) in the 25-500 N range, and (c) on zero-crossing cutouts and sensitivity (The lines in this figure are provided for visual guidance only and do not represent the relationship between the data points).
• Figure 5: Effect of geometric parameters on the length stability of the cubic cavity: (a) Bore radius $b$, (b) Support radius $s_r$, (c) Mirror radius $m_r$, (d) Mirror thickness $m_t$, (e) Annular ring thickness $a_t$, and (f) Annular ring inner radius $a_{r2}$. Each parameter is systematically varied to assess its influence on the cavity’s fractional length change while keeping other parameters constant.