Diamond nonlinear photonics

Despite progress towards integrated diamond photonics1–4, studies of optical nonlinearities in diamond have been limited to Raman scattering in bulk samples5. Diamond nonlinear photonics, however, could enable efficient, in situ frequency conversion of single photons emitted by diamond’s colour centres6,7, as well as stable and high-power frequency microcombs8 operating at new wavelengths. Both of these applications depend crucially on efficient four-wave mixing processes enabled by diamond’s third-order nonlinearity. Here, we have realized a diamond nonlinear photonics platform by demonstrating optical parametric oscillation via four-wave mixing using single-crystal ultrahigh-quality-factor (13 10) diamond ring resonators operating at telecom wavelengths. Threshold powers as low as 20 mW are measured, and up to 20 new wavelengths are generated from a single-frequency pump laser. We also report the first measurement of the nonlinear refractive index due to the third-order nonlinearity in diamond at telecom wavelengths. Diamond, as an attractive platform for on-chip photonics1,9, combines the advantages of a high refractive index (n1⁄4 2.4) and low absorption losses within its large transmission window (from the ultraviolet to far-infrared). Diamond also offers excellent thermal properties (high thermal conductivity and low thermooptic coefficient), enabling high power handling capabilities10. In addition, a relatively high nonlinear refractive index11,12 (n21⁄4 1.3× 10 m W for visible wavelengths) and the lack of two-photon absorption (owing to its large bandgap of 5.5 eV) make diamond a promising candidate for integrated nonlinear optics over a wide wavelength range, spanning the visible and infrared. To date, on-chip nonlinear nanophotonic systems have been realized in various material platforms, including silica13, silicon14, Si3N4 (ref. 15) and III–V materials 16,17. Some of these materials have even been used to implement microresonator-based high-repetition-rate frequency combs (up to terahertz)8,15,18–20. The diamond nonlinear photonics platform that we demonstrate here could potentially extend the operating range of microcombs to new wavelengths, resulting in temperature-stabilized frequency combs over a wide wavelength range. Moreover, diamond offers the unique opportunity to combine nonlinear photonics with quantum optics: for instance, diamond nonlinearities could allow for frequency translation (to the telecom wavelength range for example7) and pulse shaping21,22 of single photons generated by its numerous colour centres, which often emit in the visible. These processes promise the coalescence of quantum information science with classical optical information-processing systems on the same chip. As a consequence of an inversion symmetry in its crystal lattice, diamond’s lowest-order non-zero nonlinear susceptibility12 is x . A third-order nonlinear parametric process where two pump photons at frequency vP are converted to two different photons at vþ and v2 (denoted signal and idler, respectively), such that energy conservation is satisfied by 2vp1⁄4 vþþ v2 , is called fourwave mixing (FWM). The FWM gain scales with the pump intensity, and the pump power requirement can be reduced by confining the light to nanowaveguides23. In addition to energy conservation, FWM in a waveguide also entails momentum conservation or phase-matching, which implies Dk1⁄4 2gPp2DkL≈ 0 (refs 23,24). Here, the second term DkL1⁄4 2kp2 kþ2 k2 is the phase mismatch due to the linear dispersion (kp, kþ and k2 are the pump, signal and idler wavenumbers, respectively), g1⁄4 2pvpn2/cAeff is the effective nonlinearity and Aeff the effective optical mode area. The term 2gPp arises from the nonlinear response to the strong pump, which imposes self-phase modulation (SPM) on itself and crossphase modulation (XPM) on the generated modes that is twice as large as the SPM18,25. This nonlinear phase shift needs to be compensated for by the linear dispersion, that is, DkL. 0. Consequently, the group velocity dispersion (GVD) of the optical mode needs to be anomalous around the pump wavelength23,24; that is, GVD1⁄42(l/c).dneff/dl. 0, where neff is the effective index of the waveguide mode, l is the wavelength and c is the speed of light in vacuum. The FWM efficiency can be drastically increased by using high-Q resonators14,26, where photons make multiple round-trips on resonance, resulting in the optical intensity being enhanced by a factor of the finesse. Optical parametric oscillation (OPO) is achieved when the round-trip FWM gain exceeds the loss in the resonator, a process analogous to a laser above threshold, and bright coherent light is generated at the signal and idler wavelengths. In our diamond ring resonators (Fig. 1), momentum is intrinsically conserved because the optical modes are angular momentum eigenstates27. In this case, anomalous dispersion is required to achieve energy conservation between the cavity modes m (with different angular momentum) that participate in the FWM process18. This implies that the frequency separation between adjacent modes of the ring resonator, |vm2 vm21| (or the free-spectral range, FSR), increases as a function of the mode number m. The resonator dispersion D2, given by the change in the FSR (vmþ1þ vm212 2vm), thus needs to be positive for modes around the pump wavelength18,28. The unequal frequency spacing of the resonator modes due to anomalous dispersion is compensated by nonlinear optical mode pulling, that is, a shift in the resonance frequencies caused by SPM and XPM due to the pump18,25. The intrinsic material dispersion of diamond is normal at telecom wavelengths. The net waveguide dispersion can be engineered to be anomalous through geometrical dispersion by appropriately designing the cross-sectional dimensions15,20,23,28. However, our fabrication technique (see Methods) relies on thin singlecrystal diamond (SCD) films, which are typically wedged, resulting in a thickness variation of at least 300 nm across a millimeter-sized sample9. This effect occurs as a result of the mechanical polishing process for thin diamond plates ( 20 mm thick) that are used to realize our diamond-on-insulator platform4. Accordingly, the ring resonator design has to be robust and the dispersion insensitive to