Second-harmonic stabilization of a bulk photonic resonator

TL;DR

This work addresses long-term frequency drift in bulk photonic resonators by introducing second-harmonic stabilization, which uses energy conservation in SHG to map the absolute resonance to a measurable microwave signal $f_{\text{SH}}$. The key approach relies on the material- and dispersion-dependent mapping $f_{\text{SH}} = \nu_1 - \frac{1}{2}\nu_2$, with a calibrated scaling $\frac{df_{\text{SH}}}{d\nu_1} = \frac{1}{-48.7}$ that relates drift in the fundamental resonance $\nu_1$ to drift in $f_{\text{SH}}$. Characterization shows a narrow $f_{\text{SH}}$ spectrum and a consistent scaling with thermo-optic and dispersion properties, enabling drift inference with Hz/s precision and achieving about $1$–$3 \times 10^{-11}$ fractional stability at $\sim 10^3\ \text{s}$—a $\sim 10^3$ improvement over the free-running resonator. RAM and laser-lock electronics noise set the ultimate limits, pointing to RAM mitigation and in-situ scaling-factor calibration as routes to further enhance performance. Overall, SH stabilization offers a practical path to robust long-term stabilization of compact, ambient-condition frequency references for precision metrology.

Abstract

The resonant modes of optical cavities provide a powerful resource for laser-frequency stabilization, underpinning high-precision metrology and coherent signal generation. Photonic resonators in which the optical mode propagates through material offer a compact alternative to vacuum Fabry-Perot cavity systems, but their performance is limited by sensitivity of the material to the ambient environment. In this work, we explore second-harmonic (SH) stabilization, which exploits the interplay of a dispersive mode structure against the strict energy conservation of second-harmonic generation. Operationally, we use two, 1550 nm lasers to PDH-detect octave-spaced resonant modes of an ultra-high-Q photonic resonator with one laser frequency-doubled to 775 nm. Under SH stabilization, the microwave frequency offset between the 1550 nm lasers, which we refer to as the SH signal ($f_{SH}$) maps the absolute frequency of the 1550 nm laser to an electronic signal. We characterize this mapping through comparison of the absolute optical frequency inference provided by $f_{SH}$ to an out-of-loop optical measurement, and our results suggest $f_{SH}$ accurately proxies frequency drift. We evaluate the sensitivity and noise floor of this technique, considering contributions from laser locking and bulk material properties, and conclude that $f_{SH}$ is sufficiently sensitive to enhance long-term laser-frequency stability with respect to the resonator. These results demonstrate SH stabilization as a useful technique that infers absolute drift, thereby enabling the increased stability of future compact, precision frequency references.

Figures (3)

• Figure 1: (a) Experimental setup for SH stabilization. One laser at frequency $\nu_1$ directly locks to the dispersive resonator, and the other at frequency $\nu_2/2$ is first frequency-doubled using periodically poled lithium niobate (PPLN) to $\nu_2$ before locking to the resonator. An additional reference laser, $\nu_\text{ref}$, is used for out-of-loop characterization. The fused silica Fabry-Perot resonator is shown to the right. (b) Resonant mode structure diagram defining $f_{\text{SH}}~$ with modes highlighted around $\nu_1$ (red), $\nu_2/2$ (yellow), and $\nu_2$ (blue). (c) Demonstration of the correlation between changes in $f_{\text{SH}}~$ and changes in absolute resonant frequency. The green band shows resonant frequency fluctuations characterized with the external reference laser, and the black line shows fluctuations in $f_{\text{SH}}~$ scaled by a constant factor of 1/($-48.7$).
• Figure 2: (a) Top: spectrum of $f_{\text{SH}}$; bottom: frequency noise power spectral density (FN PSD) for $\nu_1$ (red), $\nu_2/2$ (yellow), and $f_{\text{SH}}~$ (magenta). Theoretical estimate of thermal noise is shown in dashed black. (b) System diagram for our experiment. Gray lines represent feedback loops including PDH locking and transmission lock-in detection. ILP: in-line polarizer, ISO: isolator, PM: phase modulator, CIRC: circulator, PD: photodetector, PPLN: periodically poled lithium niobate, PC: polarization control. (c) Thermal transient measurement of the scaling factor between $f_{\text{SH}}~$ and $\nu_1$, $df_\text{SH}/d\nu_1$. Linear fit with slope $1/(-48.7 \pm 0.1)$ is shown in dashed red, and residuals to the fit are histogrammed in the upper right inset.
• Figure 3: (a) Comparison of true optical deviation derived from external reference laser (green band) and scaled $f_{\text{SH}}~$ (black line). (b) Residual of truth signal and scaled $f_{\text{SH}}$. Dashed line shows linear fit for residual frequency drift. (c) Residuals for two longer data sets and their resulting linear drift fits. (d) Allan deviation for original optical signal shown in black. Allan deviations for the residual signals in panels b and c are plotted in their respective colors. An approximate power-law summary is include in dashed gray featuring 3 Hz/s linear drift and flicker noise that contributes $(-48.7)^2 \times 5\times10^3~\text{Hz}^2/\text{Hz}$ to the frequency noise PSD at 1 Hz offset.