No abstract

Photonic synthesis of radiofrequency revived the quest for unrivalled microwave purity by its seducing ability to convey the benefits of the optics to the microwave world 1-11 . In this work, we perform a high-fidelity transfer of frequency stability between an optical reference and a microwave signal via a low-noise fiber-based frequency comb and cuttingedge photo-detection techniques. We demonstrate the generation of the purest microwave signal with a fractional frequency stability below 6.5 x 10 -16 at 1 s and a timing noise floor below 41 zs.Hz -1/2 (phase noise below -173 dBc.Hz -1 for a 12 GHz carrier). This outclasses existing sources and promises a new era for state-of-the-art microwave generation. The characterization is achieved through a heterodyne cross-correlation

The synthesis of ultralow-noise microwaves is of both scientific and technological relevance for timing, metrology, communications and radio-astronomy.Today, the lowest reported phase noise signals are obtained via optical frequency-division using mode-locked laser frequency combs. Nonetheless, this technique ideally requires high repetition rates and tight comb stabilisation. Here, a soliton microcomb with a 14 GHz repetition rate is generated with an ultra-stable pump laser and used to derive an ultralow-noise microwave reference signal, with an absolute phase noise level below −60 dBc/Hz at 1 Hz offset frequency and −135 dBc/Hz at 10 kHz. This is achieved using a transfer oscillator approach, where the free-running microcomb noise (which is carefully studied and minimised) is cancelled via a combination of electronic division and mixing. Although this proofof-principle uses an auxiliary comb for detecting the microcomb's offset frequency, we highlight the prospects of this method with future selfreferenced integrated microcombs and electrooptic combs, that would allow for ultralow-noise microwave and sub-terahertz signal generators.

Dual-comb interferometry utilizes two optical frequency combs to map the optical field's spectrum to a radio-frequency signal without using moving parts, allowing improved speed and accuracy. However, the method is compounded by the complexity and demanding stability associated with operating multiple laser frequency combs. To overcome these challenges, we demonstrate simultaneous generation of multiple frequency combs from a single optical microresonator and a single continuous-wave laser. Similar to space-division multiplexing, we generate several dissipative Kerr soliton states -circulating solitonic pulses driven by a continuous-wave laser -in different spatial (or polarization) modes of a MgF 2 microresonator. Up to three distinct combs are produced simultaneously, featuring excellent mutual coherence and substantial repetition rate differences, useful for fast acquisition and efficient rejection of soliton intermodulation products. Dual-comb spectroscopy with amplitude and phase retrieval, as well as optical sampling of a breathing soliton, is realised with the free-running system. Compatibility with photonic-integrated resonators could enable the deployment of dual-and triple-combbased methods to applications where they remained impractical with current technology. IntroductionShortly after the inception of the optical frequency comb 2 , it was realised that combining two combs with slightly different repetition rates on a photodetector produces a radio-frequency (RF) interferogram that samples the optical response 3,4 , without any moving parts. Such dual-comb techniques have been demonstrated in both real-time 5,6 and mid-infrared 7 spectroscopy, distance measurements 8 , two-way time transfer 9 , coherent anti-Stokes Raman spectro-imaging 10 , as well as photonic analogue to digital conversion 11 . However, facing the complexity and cost associated with operating two laser frequency combs, novel methods are being actively explored with a view to reduce the system complexity and inherently improve the mutual coherence. For example, instead of phase locking two independent conventional * tobias.kippenberg@epfl.ch mode-locked lasers, both combs can be generated in the same laser cavity 12 , via repetition rate switching of a single comb 13 , or spectrally broadened in the same fibre in opposite propagation directions 14 . As the noise sources are common mode, the relative coherence between the combs is significantly improved, allowing for longer coherent averaging 4 .Recent advances in the field of high-quality-factor microresonators pumped with a continuous wave (CW) laser have led to the discovery of 'Kerr' frequency combs 15 (also termed 'microcombs') that arise due to nonlinear wave mixing mediated by the optical Kerr effect.One particular state of such combs corresponds to the formation of dissipative Kerr solitons 16 (DKSs) -self-localised pulses of light circulating in the resonators arising from the double balance between loss and parametric gain and between dispersion and nonlinearity 17,18 . The ...

Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibres to mode-locked lasers, they provide insights into the fundamental interactions between solitons and the underlying dynamics of the nonlinear systems. Here, we enter the multistability regime of a Kerr microresonator to generate superpositions of distinct soliton states that are pumped at the same optical resonance, and report the discovery of heteronuclear dissipative Kerr soliton molecules. Ultrafast electrooptical sampling reveals the tightly shortrange bound nature of such soliton molecules, despite comprising cavity solitons of dissimilar amplitudes, durations and carrier frequencies. Besides the significance they hold in resolving soliton dynamics in complex nonlinear systems, such heteronuclear soliton molecules yield coherent frequency combs whose unusual mode structure may find applications in metrology and spectroscopy.