Influence of mechanical resonances on the linearity of adiabatic frequency conversion in whispering gallery resonators

TL;DR

This work investigates how mechanical resonances in lithium niobate whispering-gallery resonators affect the linearity of adiabatic frequency conversion driven by electro-optic effects. A frequency-dependent EO model, incorporating both true Pockels and piezoelectric-elasto-optic contributions, explains distortions when drive harmonics overlap a mechanical mode around $f_m \approx 10.5$ MHz, and experiments on a millimeter-scale LiNbO$_3$ WGR validate the theory. The key finding is that even harmonics two orders of magnitude smaller than the fundamental can induce substantial nonlinearity in $Δν(t)$, revealing intrinsic limits to linear EO frequency control. The authors propose spectral strategies to preserve linearity—placing resonances between harmonics or shifting them to higher frequencies—and highlight implications for EO-tuned photonic systems, including FMCW LiDAR and laser self-injection locking.

Abstract

Adiabatic frequency conversion enables fast and efficient tuning of laser light by coupling it into an optical resonator whose eigenfrequency is varied on a timescale shorter than its photon lifetime. In this regime, the optical frequency follows the cavity resonance, allowing frequency shifts of several hundred gigahertz within sub-microsecond time - independent of optical power and without phase-matching constraints. While a linear dependence of the cavity resonance on a control parameter (e.g., applied voltage) suggests that arbitrary temporal signals could be linearly transferred to optical frequency changes, we show that this assumption fails near mechanical resonances of the resonator. Using a millimeter-sized lithium niobate whispering gallery resonator with a pronounced mechanical mode at 10.5 MHz, we observe strong deviations from linearity even when higher harmonics of the control signal coincide with this resonance. The experimental results are in excellent agreement with theoretical predictions. They demonstrate that mechanical resonances impose intrinsic limits on the linearity of adiabatic frequency conversion and other frequency control schemes based on the variation of the eigenfrequency of an optical cavity.

Figures (3)

• Figure 1: a Schematic illustration of the lithium niobate whispering gallery resonator (WGR) mounted on a post, without applied voltage. b The applied voltage $U(t)$ induces mechanical deformation via the piezoelectric effect. c Frequency response of the WGR to an applied voltage $r(f)$ showing a mechanical eigenmode near 10 MHz. d Signal flow model illustrating the effect of the voltage waveform $U(t)$ on the optical frequency shift $\Delta\nu(t)$ via the frequency-dependent electro-optic response. e Example voltage waveforms (left), their spectral components (center), and the resulting optical frequency shifts (right), showing the influence of resonance overlap on modulation linearity.
• Figure 2: a Photograph of the lithium niobate resonator mounted on a brass post. b Experimental setup for characterizing the piezoelectric response of the WGR. A laser emitting at 1560 nm is coupled into the resonator using a fiber polarization controller (FPC), a GRIN lens and a rutile prism. A vector network analyzer (VNA) applies a voltage to the electrodes. A photodiode (PD) detects the beat signal, which is recorded by the VNA. c Frequency dependent normalized electro-optic response $S_{21}$ of the WGR with a pronounced mechanical eigenmode near 10.5 MHz. Inset: Simulated mechanical deformation pattern corresponding to this eigenmode.
• Figure 3: a Experimental setup to investigate the influence of piezoelectric resonances on AFC in a lithium niobate WGR. The resonator is driven by an arbitrary waveform generator (AWG), and the signal is analyzed using an electrical spectrum analyzer (ESA). b Frequency spectra of the applied voltage signals (left) and the corresponding optical frequency shifts $\Delta\nu(t)$ (right) for five different drive frequencies: 4.3, 3.5, 2.1, 1.5, and 1.17 MHz. The blue-shaded region marks the mechanical resonance around 10.5 MHz. The white dashed lines indicate the expected behavior for linear adiabatic frequency conversion.