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...

A study is made of frequency-comb generation described by the driven and damped nonlinear Schrödinger equation on a finite interval. It is shown that frequency-comb generation can be interpreted as a modulational instability of the continuous-wave pump mode, and a linear stability analysis, taking into account the cavity boundary conditions, is performed. Further, a truncated three-wave model is derived, which allows one to gain additional insight into the dynamical behavior of the comb generation. This formalism describes the pump mode and the most unstable sideband and is found to connect the coupled mode theory with the conventional theory of modulational instability. An in-depth analysis is done of the nonlinear three-wave model. It is demonstrated that stable frequency-comb states can be interpreted as attractive fixed points of a dynamical system. The possibility of soft and hard excitation states in both the normal and the anomalous dispersion regime is discussed. Investigations are made of bistable comb states and the dependence of the final state on the way the comb has been generated. The analytical predictions are verified by means of direct comparison with numerical simulations of the full equation and the agreement is discussed.

We provide a perspective overview of the emerging field of nonlinear optics in multimode optical fibers. These fibers enable new methods for the ultrafast light-activated control of temporal, spatial, and spectral degrees of freedom of intense, pulsed beams of light, for a range of different technological applications.

a b s t r a c tIt is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently simulated using standard algorithms, resulting in orders of magnitude improvements in the computation time.