Silicon photonics meets the electronics requirement of increased speed and bandwidth with on-chip optical networks. All-optical data management requires nonlinear silicon photonics. In silicon only third-order optical nonlinearities are present owing to its crystalline inversion symmetry. Introducing a second-order nonlinearity into silicon photonics by proper material engineering would be highly desirable. It would enable devices for wideband wavelength conversion operating at relatively low optical powers. Here we show that a sizeable second-order nonlinearity at optical wavelengths is induced in a silicon waveguide by using a stressing silicon nitride overlayer. We carried out second-harmonic-generation experiments and first-principle calculations, which both yield large values of strain-induced bulk second-order nonlinear susceptibility, up to 40 pm V −1 at 2,300 nm. We envisage that nonlinear strained silicon could provide a competing platform for a new class of integrated light sources spanning the near-to mid-infrared spectrum from 1.2 to 10 µm. When a crystal possesses a significant second-order nonlinear optical susceptibility, χ (2) , it can produce a wide variety of wavelengths from an optical pump 1 . In fact, a second-order crystal generates shorter wavelengths by second-harmonic generation or longer wavelengths by spontaneous parametric down-conversion of a single pump beam. Such a crystal can also nonlinearly mix two different beams, thus generating other wavelengths by sum-frequency or difference-frequency generation. These possibilities are much more intriguing whenever the crystal can be used in integrated optical circuits because, on the one hand, light confinement reduces the average optical power needed to trigger nonlinear processes and, on the other hand, relatively long effective interaction lengths can be exploited.Si photonics has demonstrated the integration of multiple optical functionalities with microelectronic devices 2,3 . On the basis of the third-or higher-order nonlinearities of Si (ref. 4), functions such as amplification and lasing, wavelength conversion and optical processing have all been demonstrated in recent years 5 . However, third-order refractive nonlinearities require relatively high optical powers, and compete with nonlinear-loss mechanisms such as two-photon absorption and two-photon induced freecarrier absorption. Yet, the second-order term of the nonlinear susceptibility tensor cannot be exploited in Si simply because χ (2) vanishes in the dipole approximation owing to the crystal centrosymmetry: the residual χ (2) , which is due to higher-multipole processes, is too weak to be exploited in optical devices 6 .Second-harmonic generation (SHG) was observed in reflection from Si surfaces 7-11 or in diffusion from Si photonic crystal nanocavities 12 . This indicates that the reduction of the Si symmetry may indeed induce a significant χ (2) . In these cases, the Si symmetry was broken by the presence of a surface. Several groups have pointed out that the surface cont...

IntroductionCVD synthesis of graphene on catalytically-active substrates has emerged as the most promising approach for large-area production of graphene [1] . The self-limiting nature of CVD growth on metals such as copper (Cu) and platinum allows synthesis of large-scale homogeneous films of monolayer graphene. However, electrical characterization of polycrystalline samples of CVD graphene reveals that the presence of grain boundaries causes significant degradation of the electric performance, compared to pristine material obtained by mechanical exfoliation of flakes [2] . As demonstrated initially by Petrone et al [3] , samples fabricated using single-crystals of CVD graphene can have electrical performance comparable to that of exfoliated flakes [4] . Furthermore, recent reports have shown that by fully encapsulating CVD graphene with suitable materials such as hexagonal boron nitride (h-BN), low-temperature charge carrier mobility above 300 000 cm 2 / V s [5] or even 3 000 000 cm 2 / V s [6] can be achieved.Over the last few years the synthesis of large-crystal graphene has attracted a huge scientific interest, with significant advances in the achievable crystal size [7][8][9][10] . Recent work has reported single-crystals of graphene measuring 1 cm [10] and, using copper/nickel alloy as the growth substrate, even 4 cm [11] . Inevitably, these approaches still produce randomlydistributed crystals of graphene, which limits their applicability to scaled production of graphene devices. Furthermore, the commonly-used transfer methods either allow scalability while introducing significant performance degradation, or are limited to transferring areas of several tens of µm 2 [5] .For many applications the size of individual graphene devices is limited to tens or hundreds of microns, easily achievable by the current methods of single-crystal synthesis, however, ran-dom spatial distribution of graphene crystals in such samples makes polycrystalline graphene preferable for wafer-scale integration. This issue could be mitigated by selectively predetermining the nucleation sites for graphene crystals according to the target architecture, which could allow the fabrication of large and complex circuits utilising completely monocrystalline graphene. Patterned growth using polymer-based nucleation seeds was first reported by Wu et al [12] , however, only high-density arrays of 10-20 µm crystals were demonstrated. Arrays of similar dimensions were recently presented by Song et al, using poly(methyl methacrylate) (PMMA) seeds to nucleate graphene on top of CVD-grown h-BN [13] .In this work we present a method to selectively pattern the Cu growth substrate using chromium (Cr) nucleation seeds, which allows deterministic nucleation of large-crystal graphene, measuring several hundred microns. The nucleation density is highly-controlled by the combined use of natively oxidised Cu foils, non-reducing annealing and sample enclosure [14] , and measuring as low as 10 crystals per mm 2 . We also demonstrate a clean semi-dry tran...

The ability to feed energy into a system, or -equivalently -to drive that system with an external input is a fundamental aspect of light-matter interaction. The key concept in many photonic applications is the "critical coupling" condition [1,2]: at criticality, all the energy fed to the system via an input channel is dissipated within the system itself. Although this idea was crucial to enhance the efficiency of many devices, it was never considered in the context of systems operating in a non-perturbative regime. In this so-called strong coupling regime, the matter and light degrees of freedom are in fact mixed into dressed states, leading to new eigenstates called polaritons [3-10].Here we demonstrate that the strong coupling regime and the critical coupling condition can indeed coexist; in this situation, which we term strong critical coupling, all the incoming energy is converted into polaritons. A semiclassical theory -equivalently applicable to acoustics or mechanics -reveals that the strong critical coupling corresponds to a special curve in the phase diagram of the coupled light-matter oscillators. In the more general case of a system radiating via two scattering ports, the phenomenology displayed is that of coherent perfect absorption (CPA) [11,12], which is then naturally understood and described in the framework of critical coupling. Most importantly, we experimentally verify polaritonic CPA in a semiconductor-based intersubband-polariton photonic-crystal membrane resonator.This result opens new avenues in the exploration of polariton physics, making it possible to control the pumping efficiency of a system almost independently of its Rabi energy, i.e., of the energy exchange rate between the electromagnetic field and the material transition.

We report the observation of second-harmonic generation (SHG) in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapor deposition (LPCVD). Quasi-rectangular waveguides with a large cross section were used, with a height of 1 µm and various different widths, from 0.6 to 1.2 µm, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide depending on the waveguide cross section. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10 −4 to 10 −2 s −1 , with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up (observed delay and growth), the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogal-vanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 × 1 µm 2 cross section and 36 mm length, corresponding to 53 µW at 532 nm with 13 mW of IR input coupled into the waveguide. The according χ (2)-susceptibility amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.