Intraresonance frequency combs in Kerr microresonators

TL;DR

The paper addresses the dispersion-limited nature of conventional Kerr microresonator frequency combs by introducing intraresonance combs formed via dual-pumping a single resonance. The authors realize this in high-Q Kerr microresonators (Si3N4) using a dual-pump source and heterodyne readout, supported by qualitative theory and numerical modelling. They demonstrate up to eight intermediate lines between the pumps with an $(n+1)$-fold phase stability, show spontaneous phase multistability and seed-controlled switching, and map the regime landscape with respect to pump separation and detuning. The results point to a dispersion-relaxed, compact platform for engineered multifrequency optical resources with potential applications in microwave photonics, sensing, and quantum information, while offering insights connecting to breather Kerr comb dynamics.

Abstract

For more than 20 years, optical microresonators have served as the backbone of integrated nonlinear photonics, exploiting Kerr nonlinearity to generate octave-spanning frequency combs, enable quantum effects, and drive optical parametric oscillators. Since the inception of microresonator-based nonlinear optics, related studies have focused primarily on regimes in which photons with distinct resonant modes can interact. Although multiple comb lines can occupy a single resonance during the Kerr comb formation process, their mutual interactions have remained largely unexplored. Here we demonstrate a Kerr comb formation that is confined to a single resonance of a microresonator via dual-pumping. MHz-scale comb-line spacing reveals previously unobserved Kerr-comb dynamics, featuring parametrically driven phase multistability that can be observed directly in the temporal domain. Two laser pumps serve as phase-coupled references for heterodyne read-out, simplifying the measurements.

Figures (5)

• Figure 1: a: Experimental setup used to to generate multiple intraresonance subharmonics in a $\chi(3)$ microresonator. OSA, optical spectrum analyser; ESA, electrical spectrum analyser; OSC, oscilloscope; ISO, optical isolator; EDFA, erbium-doped fibre amplifier with an isolator; PD, photodetector; FPC, fibre polarisation controller; LO, local oscillator. See the Methods section for a detailed description of the setup. b: Spectrum of the LO-comb beat on the PD, recorded on the ESA, for multiple values of $n$. c: Spectrum of the comb self-beat on the PD, recorded on the ESA, for multiple values of $n$. d: Temporal intensity profile of the out-coupled field, recorded on the PD, for $n$ parametrically generated lines between pumps separated by $\Delta f=33~\mathrm{MHz}$. e: Optical spectrum of the out-coupled field recorded on the OSA. Inset: Heterodyne probing with the LO reveals the fine intraresonance DOPO structure. f: Oscillogram of the pump-resonance transmission versus the laser detuning from the cold resonance, showing the spike in DOPO power when both pumps are tuned to resonance.
• Figure 2: Quadrature-density (I/Q) diagrams of the PD electrical signal, recorded on an ESA for multiple values of $n$. The measurements are taken with pump modulation to toggle the system between above- and below-threshold operation and thereby reveal all possible phase realisations.
• Figure 3: Injection measurements obtained with pump modulation toggling the generation process on and off. a: Spontaneous symmetry breaking in the absence of external injection; each point marks the phase of an individual realisation. b: Evolution of the generation phase while the injection phase is varied. The time axis is rescaled to the injection phase. c: Quadrature phase diagram showing all possible phase states of the given regime as the injection phase is varied stepwise. Arrows indicate transitions from below- to above-threshold regimes.
• Figure 4: Simulation results regarding the intraresonance field of the microresonator under a bichromatic pumping process that is continuously tuned towards a cavity resonance. The pump-resonance detuning level is swept from -346MHz to 209MHz, and the scan is halted at 118.2µs. a: Spectrogram of the intracavity field during the detuning sweep. b: Phase bistability of the degenerate (DOPO) line at $\Delta f/2$ from each pump (green on a,d). The colours denote independent realizations. c: Fourfold phase stability of the line detuned by $\Delta f/4$ from the right pump (cyan in a,d). The colours denote independent realizations. d The intracavity emission spectrum observed at 134.7µs.
• Figure 5: a: Map of the state realizations as a function of the dual-pump frequency detuning level $\Delta f$ and the degree of pump resonance detuning from the cold resonance under equal pump powers. Each data point corresponds to a specific oscillation state. b: The time-frequency spectrogram of the photodetector signal as the dual-pump is red-detuned across the microresonator resonance. The observed sequence of intraresonance states is $n=3 \rightarrow 7 \rightarrow 3 \rightarrow 1$. The $n=7$ state arises from the four-wave mixing of the $n=3$ comb lines acting as pumps.