UC San Diego

Silicon is the primary candidate for the advancement of integrated photonics due to its prevalence within the electronics industry. One of the material’s most notable shortcomings, however, is its centrosymmetry, which causes it to lack a second-order nonlinear susceptibility, disallowing electro-optic modulation based on the Pockels effect [1]. To circumvent this complication, research efforts involving electro-optic modulation in silicon waveguides have instead exploited the free-carrier plasma dispersion effect, in which a change in the concentration of holes and electrons, generated by an electrical current, leads to deviations in both the real and imaginary parts of a semiconductor’s index of refraction [2-4]. Additionally, some work over the past decade has been devoted to exploring the strain-induced second-order nonlinear susceptibility in silicon [5-10]. By deforming silicon’s diamond lattice in an asymmetric way, it is possible to remove the material’s centrosymmetry, thereby generating a second-order nonlinearity within the material [5]. In recent works, values as high as 330 pm/V have been reported for the χ(2) coefficient in strained silicon waveguides [6].

Recently, however, it has been found that strained silicon’s electro-optic effect is roughly quadratic in nature, rather than linear, as would be expected for the Pockels effect [7]. Furthermore, many demonstrations of strained silicon’s nonlinear properties have incorrectly assumed that the electric field, used to control silicon's index of refraction, penetrates strongly into the semiconductor waveguide itself [6-10], and this is known to have led to inaccurately reported nonlinear coefficients. Instead, the observed behavior in strained silicon waveguides is now thought to be due to the capacitively-induced free-carrier effect, which has already been used to demonstrate high-bandwidth modulation [11-16]. Similarly, the wavemixing observed in the literature for strained silicon waveguides has been attributed largely to electric field-induced second-harmonic generation [17].