Attosecond-timing millimeter waves via Kerr optical frequency division

Abstract

Millimeter-wave oscillators underpin key applications in communication, spectroscopy, radar, and astronomy, yet their achievable spectral purity remains limited. Approaches that directly generate millimeter-wave carriers are fundamentally limited by quantum and thermal phase-noise processes. Here we show that these limits can be overcome by combining Kerr-induced optical frequency division in a chip-scale microresonator with a large-spacing dual-wavelength Brillouin laser. This 3.3 THz optical reference injection-locks a Kerr soliton microcomb, with a repetition rate that becomes a coherently divided 300 GHz carrier with phase noise below the quantum limit of a corresponding 300 GHz dual-wavelength Brillouin laser and far below the thermo-refractive noise of a microring resonator. Cross-correlation phase-noise measurements were developed to show that the resulting oscillator reaches a phase-noise floor of -152 dBc/Hz at 1 MHz offset, consistent with photodetection shot noise. Integration of the measured spectrum yields an RMS timing jitter of 135 as from 1 kHz to 1 MHz. These results establish optical frequency division as a generic method for generation of sub-terahertz carriers with coherence no longer constrained by direct-generation limits.

Figures (3)

• Figure 1: Kerr optical frequency division of a multi-terahertz optical reference to 300 GHz.(A) Conceptual architecture of the oscillator. A dual-wavelength Brillouin laser (DWBL) provides two mutually coherent optical tones, $\nu_p$ and $\nu_i$, separated by $\Delta\nu$ (opto-THz). These tones simultaneously pump and injection-lock a Kerr soliton microresonator, inducing optical frequency division such that the soliton repetition rate satisfies $f_{\mathrm{rep}}=\Delta\nu/N$. After spectral conditioning and dispersion compensation of the optical pulse train, photodetection converts the repetition rate directly into a millimeter-wave carrier. (B) Optical spectrum of the Kerr soliton comb after suppression of the pump and injection tones. The spectrum exhibits a smooth $\mathrm{sech}^2$ envelope characteristic of dissipative Kerr solitons. The injected optical tone $\nu_i$ overlaps the comb line at $\mu_0+N\cdot f_{\mathrm{rep}}$, dividing the optical reference. (C) Injection-locking dynamics of Kerr optical frequency division. As the detuning between the injected optical tone and the free-running comb mode is varied, the system transitions from free-running operation through frequency pulling into a robust injection-locked regime, where $f_{\mathrm{rep}}$ (blue) is pinned to $\Delta\nu/N$ and $\mu_{0}+N\cdot f_{\mathrm{rep}} = \nu_{i}$ over a wide detuning range.
• Figure 2: Noise scaling and timing-jitter performance enabled by Kerr optical frequency division.(A) Conceptual phase-noise scaling for Kerr OFD of dual-wavelength Brillouin lasers. Optical separations $\Delta\nu_{3.3\,\mathrm{THz}}$ (black) and $\Delta\nu_{300\,\mathrm{GHz}}$ (red) highlight that low-frequency noise from acoustic and temperature fluctuations scales quadratically with optical separation, while the Schawlow--Townes contribution is independent of $\Delta\nu$. Dividing $\Delta\nu_{3.3\,\mathrm{THz}}$ down to $f_{\mathrm{rep}}=300~\mathrm{GHz}$ suppresses the technical and quantum-limited phase noise by $20\log_{10}(N)$ until the photodetection noise floor is reached (blue). (b) Cross-correlation phase-noise measurement architecture. The 300 GHz millimeter-wave signal generated by Kerr optical frequency division ($f_{\rm rep}$) is downconverted using two independent photonic local oscillators at 300 GHz (LO$_1$ and LO$_2$). Each LO is generated by optical heterodyne beating on a uni-traveling-carrier photodiode, converting the optical-frequency difference signals into millimeter-wave electrical local oscillators. The Kerr OFD signal is mixed with each LO to produce intermediate-frequency signals ($f_{\rm if,1}$ and $f_{\rm if,2}$) that are independently amplified and digitized. RF and digital cross-correlation between the two channels suppresses uncorrelated detection noise, enabling measurement of the phase noise of the Kerr OFD signal. (C) Measured single-sideband phase-noise spectra at 300 GHz. The Kerr OFD signal (blue) exhibits substantially lower phase noise than both a free-running soliton (green) and directly generated 300 GHz DWBL signals (red), closely following the scaled noise of $\Delta\nu_{3.3\,\mathrm{THz}}$. (D) Integrated timing jitter derived from the measured phase-noise spectra. Kerr OFD yields a total jitter of 135 as (1 kHz--1 MHz), compared to 395 as for directly generated 300 GHz DWBL signals.
• Figure 3: Benchmarking timing-noise performance of a Kerr-induced optical frequency divider. Timing-noise power spectral density (PSD) of the Kerr OFD oscillator (blue) compared to other state-of-the-art oscillators. The Kerr OFD achieves timing noise of 18 zs/$\sqrt{\mathrm{Hz}}$, with PSD values falling well below the technical noise of conventional 300 GHz dual-wavelength Brillouin lasers and approaching the quantum-limited regime. The results are benchmarked against full OFD xie2017photonic (red), which represents the quietest microwave signals demonstrated to date, and externally-referenced microcomb oscillators kwon2022ultrastablekudelin2024photonicjin2025microresonatorji2025dispersivetetsumoto2021opticallykuse2022low (blue shaded band), which remain limited by servo bumps and photodetection shot noise. The Kerr OFD oscillator decisively surpasses all previous microcomb-based microwave and millimeter-wave demonstrations, achieving performance once reserved for full OFD but with radically reduced complexity.