Second‐Order Optical Nonlinearity in Silicon Waveguides: Inhomogeneous Stress and Interfaces

Abstract

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.

High-frequency electro-optic measurement of strained silicon racetrack resonators

“…We remark here that our results do not exclude the presence of a strain induced χ (2) in Silicon. Indeed, there exist proofs of Second Harmonic Generation (SHG) in strained Silicon that intrinsically can not have an explanation purely relying on free carrier [10,11,18]. These experiments revealed a χ (2) value of up to 40 pm/V for −1.2 GP a applied stress.…”

“…The linear relation between these two physical quantities is considered as the evidence of the observation of a Pockels effect. Unfortunately, a linear effective index variation of the optical mode of a waveguide can also be induced by free carriers [13,14] or by trap states and localized charges at the SiN x -Si interface [11,13]. A definitive proof of the strain induced non-linearity can be obtained by high frequency measurements in an interferometer structure since the Pockels effect and the free carrier dispersion are characterized by two different characteristic times.…”

“…Strain induced χ (2) could be instrumental to make ultrafast and energy efficient electro-optic modulators for the Silicon photonics platform which would replace present electro-optic modulators based on the plasma dispersion effect [6][7][8][9]. More generally, the presence of an appreciable χ(2) in Silicon would validate the Silicon-on-Insulator (SOI) platform as an alternative to Lithium Niobate for second order nonlinear optics [10,11]. In most of these works, the centro-symmetry of Silicon is broken by a stressing film of Silicon Nitride which induces strain in the underlying Silicon waveguide and enables a χ (2) = 0 -at least from a first principle point of view [12].…”

“…(2) in Silicon would validate the Silicon-on-Insulator (SOI) platform as an alternative to Lithium Niobate for second order nonlinear optics [10,11]. In most of these works, the centro-symmetry of Silicon is broken by a stressing film of Silicon Nitride which induces strain in the underlying Silicon waveguide and enables a χ (2) = 0 -at least from a first principle point of view [12].…”

“…With the exception of refs. [10,11], the Pockels effect was investigated by using an integrated imbalanced Mach-Zehnder interferometer in which one or both interferometer arms are driven by a DC or a low frequency (≈ kHz) AC electric field [1][2][3][4][5]. Then, an effective χ (2) mat value is extracted from the measured shift of the interference fringes by taking into account the system geometry and the magnitude of the applied static electric field.…”