Abstract

Silicon has a centrosymmetric crystalline structure that leads to a null second order nonlinear χ⁽²⁾ coefficient. On the other hand, χ⁽²⁾ effects are highly sought in Si to develop low power and fast electro-optic modulators. Recently, it has been reported that by stressing a Si waveguide with a silicon nitride over-layer, a sizeable χ⁽²⁾ is induced. In [1] Second Harmonic Generation (SHG) measurements were reported in large area strained Si waveguides. However, the SHG data were affected by different contributions caused by the interfaces, the free carrier induced internal electric fields, the inhomogeneous strain and the uncontrolled modal structure of the waveguides. Here, we present SHG in Silicon On Insulator (SOI) strained Si waveguides, designed by a nonlinear propagation model. The design maximizes the SHG efficiency by a detailed simulation of the waveguide modal structure to achieve proper phase matching: n_eff(λp) = n_eff(λp/2), (n_eff is the effective refractive index and λp is the pump wavelength). Since the refractive index is dispersive, this condition is never satisfied for the same optical mode. However, the phase matching condition can be satisfied by different optical modes (modal phase matching). The cross section of the resulting waveguides is sketched in Fig.1(a). These are SOI waveguides with different widths around 2 μm, an height of 250 nm and a 140-nm-thick overlayer of silicon nitride, which induces a tensile stress of +1.25 GPa in Si. Waveguides of different widths have been measured for different pump powers, polarizations and wavelengths. The laser source was a ∼100 fs tunable laser operating at 1 kHz repetition rate. The temporal width of the laser pulses was tailored to about 13 ps, by means of a pulse shaper, in order to avoid walk-off effects within the waveguide. The operating wavelengths were (2.4 : 2.6) μm, to eliminate two photon absorption. A SPAD InGaAs detector, externally triggered by the pump laser led to a lowest detectable power of P ~ 0.01 fW. The experimental results are reported in Fig.1(b). The SHG generated power scales with the square of the pump power, as expected. The optical modes involved in this process are: TE1 for the pump and TM5 for SHG. No interface charge effects were observed and, therefore, we isolated in the measurements the effects of strain. We estimate a low value for the strain induced second order nonlinearity of χ⁽²⁾ = (0.304 ± 0.025) pm/V, which is actually an underestimation due to experimental issues. This value fits with other high frequency observations of the electro-optic effect in strained silicon [2].

© 2017 IEEE