Probing 10 μK stability and residual drifts in the cross-polarized dual-mode stabilization of single-crystal ultrahigh-Q optical resonators (1901.01463v1)

Abstract: The thermal stability of monolithic optical microresonators is essential for many mesoscopic photonic applications such as ultrastable laser oscillators, photonic microwave clocks, and precision navigation and sensing. Their fundamental performance is largely bounded by thermal instability. Sensitive thermal monitoring can be achieved by utilizing cross-polarized dual-mode beat frequency metrology, determined by the polarization-dependent thermorefractivity of a single-crystal microresonator, wherein the heterodyne radio-frequency beat pins down the optical mode volume temperature for precision stabilization. Here, we investigate the correlation between the dual-mode beat frequency and the resonator temperature with time and the associated spectral noise of the dual-mode beat frequency in a single-crystal ultrahigh-Q MgF2 resonator to illustrate that dual-mode frequency metrology can potentially be utilized for resonator temperature stabilization reaching the fundamental thermal noise limit in a realistic system. We show a resonator long-term temperature stability of 8.53 {\mu}K after stabilization and unveil various sources that hinder the stability from reaching sub-{\mu}K in the current system, an important step towards compact precision navigation, sensing and frequency reference architectures.

• The paper presents an innovative approach to temperature stabilization in MgF₂ optical resonators using a cross-polarized dual-mode technique that achieves 8.53 μK stability.
• It employs dual continuous-wave lasers locked to TE and TM modes to generate a beat frequency metric, reaching 14.55 kHz frequency instability at 1000 s integration.
• Finite element modeling confirms minimal refractive index modifications, underscoring the method’s potential for high-precision photonic applications.

Assessment of Cross-Polarized Dual-Mode Temperature Stabilization in Ultra-High-Q Optical Resonators

The manuscript authored by Lim et al. explores an advanced approach to temperature stabilization in ultrahigh-Q optical microresonators, utilizing a cross-polarized dual-mode technique. Specifically, the paper investigates the stability and residual drifts in the temperature stabilization of a magnesium fluoride (MgF₂) resonator, which holds significant implications for high-precision photonic applications such as stable laser oscillators and microwave clocks.

This research builds upon the foundation that solid-state microresonators with high quality factors (Q) can be formidable candidates for maintaining high spectral purity in optical systems. However, their performance is generally hindered by thermal noise, making the stabilization of their temperature an inevitable stride for enhanced precision. The dual-mode beat frequency metrology capitalizes on the polarization-dependent thermorefractivity of the MgF₂ resonator to pin down the optical mode volume temperature, which is a critical component for the precision stabilization of the resonator.

In their experimental setup, the authors utilize two continuous wave lasers that are locked to transverse magnetic (TM) and transverse electric (TE) modes in the resonator. The cross-polarized dual-mode beat frequency created by the interaction of these modes is used as a metric for temperature stabilization. The results demonstrate that the long-term temperature stability of the resonator can reach 8.53 µK after stabilization, with an enhancement factor of 51.78× in long-term frequency instability measured at 14.55 kHz at 1000 seconds of integration time.

The paper uniquely addresses the theoretical model of dual-mode temperature stabilization and integrates FEM modeling to evaluate the effect of waveguide modal interactions on the stabilization process. The FEM simulations reveal minimal refractive index modifications due to the modal area expansions, emphasizing that deviations from theoretical predictions are not significant. The coupling between the resonator volume temperature and the mode volume temperature is one of the crucial aspects explored, finding that with increasing integration time, the correlation approaches the theoretically estimated values, attributed to the equilibrating effect of heat diffusion.

A significant portion of the analysis focuses on dissociating the sources of temperature instability, such as atmospheric variances affecting TEC control, and the intensity fluctuations of coupled laser power. By modulating the TE laser intensity through an acousto-optic modulator and examining its impact on resonator frequency, the contribution of relative intensity noise (RIN) to temperature instabilities is scrutinized.

From a theoretical perspective, achieving sub-µK temperature stabilization could substantially reduce the phase noise, thus enhancing the precision of resonator-based optical systems. Practically, this research advances the utility of optical resonators in fields demanding high precision, such as time-frequency metrology, navigation, and telecommunications. However, challenges remain, particularly concerning the noise floor introduced by the reference radio-frequency clock, which could limit the ultimate stability attainable in this system.

Future work might look toward improving thermal isolation methods and exploring alternative stabilizing schemes to mitigate low-frequency noise impacts. As AI and quantum technologies edge forward, these advancements in resonator stability present a pivotal step toward the development of compact, high-performance frequency references critical for next-generation technological applications.