Comprehensive description of the electro-optic effects in strained silicon waveguides

Abstract

We present a novel and comprehensive analysis method that considers both plasma-dispersion effect and the strain-induced Pockels effect to faithfully describe the electro-optic effects taking place in a strained silicon waveguide under an applied voltage. The change of carrier distribution arising from the application of a voltage, leads to a redistribution of the electrostatic field which deeply affects the strain-induced Pockels effect. By simulating the strain gradients distribution inside the waveguide together with the free carrier concentration in silicon, we were able to describe that the effective index change due to Pockels effect in strained silicon waveguides and the applied voltage have a nonlinear relationship.

Fast linear electro-optic effect in a centrosymmetric semiconductor

“…The effective index change Δn eff P was described using the method employed in ref. 25 , which combined the perturbation theory for waveguides with the description of strain-induced χ (2) where the parameter N is given by…”

“…Then, an estimation of Γ coefficients could be performed by extending the model developed in ref. 25 to the microwave domain. The model hereafter consists the description of the S 21 electrical signal of the electro-optic responses measured,…”

“…It is wellknown that an electric field (induced by a voltage) applied into the Si waveguide automatically affects the carrier distribution, inducing a direct change in the effective index of the guided mode. However, these intrinsic changes in carrier distribution also modify the distribution of the electrical field inside the silicon waveguide, thereby significantly affecting the electro-optic efficiency induced by Pockels effect 25 . The carrier evolution under a bias voltage induces a screening effect, which makes the probing of the Pockels effect and a subsequent estimation of χ (2) coefficient in strained silicon waveguides vastly challenging.…”

Building blocks of silicon photonics

“…This allows classifying optical modulators in two main groups: (i) Electro-refraction modulators and (ii) Electro-absorption modulators, respectively. The most common physical effects exploited for optical modulation in photonics are Thermo-Optic (TO) [114], Pockels [115][116][117], Franz-Keldysh (FK) [118][119], Quantum confined Stark Effect (QCSE) [120][121][122][123][124][125][126][127], and Free-Carrier Plasma Dispersion effects .…”

“…5. This process is capable of generating the normally inhibited second-order susceptibility ((2) ≠ 0) and enables nonlinear phenomena like the Pockels effect [115][116][117][118]. The motivation is to develop strained silicon photonic devices for optical modulation: with a prospect for high-speed, low-loss, compact, low-power consumption, large optical bandwidth, and silicon compatible modulators.…”