The unique linear and massless band structure of graphene, in a purely two-dimensional 2 Sub-wavelength nanostructures in monolithic material platforms have witnessed rapid advances towards chip-scale optoelectronic modulators [13][14][15][16], photoreceivers [17][18], and high-bitrate signal processing architectures [19][20]. Coupled with ultrafast nonlinearities as a new parameter space for optical physics [21], breakthroughs such as resonant four-wave mixing [22] and parametric femtosecond pulse characterization [23][24] nonlinearities [33]. In this Letter we demonstrate the exceptionally high third-order nonlinear response of graphene with a wavelength-scale localized photonic crystal cavity, enabling ultralow power optical bistable switching, self-induced regenerative oscillations, and coherent four-wave mixing at femtojoule cavity energies on the semiconductor chip platform. The structure examined is a hybrid graphene-silicon cavity (as illustrated in Figure 1), achieved by rigorous transfer of monolayer large-area graphene sheet onto air-bridged silicon photonic crystal nanomembranes with minimal linear absorption and optimized optical input/output coupling. This optoelectronics demonstration is complemented with recent examinations of large-area [34][35] graphene field-effect transistors and analog circuit designs [36] for potential large-scale silicon integration. Figure 1 illustrates the graphene-cladded photonic crystal nanomembranes investigated. The optical nanocavity is a point-defect photonic crystal L3 cavity (with three missing holes) [35-36], with nearest holes at the cavity edges tuned by 0.15a (where a is the photonic crystal lattice 3 constant). The L3 cavity is side coupled to a photonic crystal line defect waveguide for optical transmission measurements. Chemical vapor deposition (CVD) grown graphene is wet-transferred onto the silicon nanomembrane [39][40] (see Methods; and Supplementary Information, Section S1), with the graphene heavily p-doped, on a large sheet without requiring precise alignment. As shown in Figure 1b, the single layer graphene is identified by Raman spectroscopy via the full-width half-maximum of the G and 2D band peaks (34.9 cm -1 and 49.6 cm -1 respectively) and the G-to-2D peak intensity ratio of ~ 1 to 1.5. The G band lineshape is a single and symmetrical Lorentzian indicating good uniformity graphene [41]. Heavily doped graphene is specifically prepared to achieve optical transparency in the infrared with negligible linear losses, as the Fermi level is below the one-photon interband optical transition threshold Transverse-electric (TE) polarization laser light is launched onto the optical cavity and evanescently coupled to the monolayer graphene. As shown in Figure 1d, the cavity transmission spectra, performed with tunable continuous-wave laser sources at 0.6 mW, shows a consistent and large resonance red-shift of 1.2 nm/mW, approximately 4× larger than that of our near-identical control cavity without graphene (more measurements detailed in the Suppleme...

We report first observations of deterministic phase- and resonance-controlled all-optical electromagnetically induced transparency in multiple coupled photonic crystal cavities. The full-range tuning of coherently coupled cavity-cavity phase and resonances allow observations of transparency resonance in dark states with lifetimes longer than incoherently summed individual cavities. Supported by theoretical analyses, our multipump beam approach allows arbitrary control in two and three coupled cavities, while the standing-wave wavelength-scale photon localization allows direct scalability for chip-scale optical pulse trapping and coupled-cavity QED.

Optical frequency combs, which emit pulses of light at discrete, equally spaced frequencies, are cornerstones of modern-day frequency metrology, precision spectroscopy, astronomical observations, ultrafast optics and quantum information. Chip-scale frequency combs, based on the Kerr and Raman nonlinearities in monolithic microresonators with ultrahigh quality factors, have recently led to progress in optical clockwork and observations of temporal cavity solitons. But the chromatic dispersion within a laser cavity, which determines the comb formation, is usually difficult to tune with an electric field, whether in microcavities or fibre cavities. Such electrically dynamic control could bridge optical frequency combs and optoelectronics, enabling diverse comb outputs in one resonator with fast and convenient tunability. Arising from its exceptional Fermi-Dirac tunability and ultrafast carrier mobility, graphene has a complex optical dispersion determined by its optical conductivity, which can be tuned through a gate voltage. This has brought about optoelectronic advances such as modulators, photodetectors and controllable plasmonics. Here we demonstrate the gated intracavity tunability of graphene-based optical frequency combs, by coupling the gate-tunable optical conductivity to a silicon nitride photonic microresonator, thus modulating its second- and higher-order chromatic dispersions by altering the Fermi level. Preserving cavity quality factors up to 10 in the graphene-based comb, we implement a dual-layer ion-gel-gated transistor to tune the Fermi level of graphene across the range 0.45-0.65 electronvolts, under single-volt-level control. We use this to produce charge-tunable primary comb lines from 2.3 terahertz to 7.2 terahertz, coherent Kerr frequency combs, controllable Cherenkov radiation and controllable soliton states, all in a single microcavity. We further demonstrate voltage-tunable transitions from periodic soliton crystals to crystals with defects, mapped by our ultrafast second-harmonic optical autocorrelation. This heterogeneous graphene microcavity, which combines single-atomic-layer nanoscience and ultrafast optoelectronics, will help to improve our understanding of dynamical frequency combs and ultrafast optics.