Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides

Transient Second-Order Nonlinear Media: Breaking the Spatial Symmetry in the Time Domain via Hot-Electron Transfer

Second-order optical effects are essential to the active control of light and the generation of new spectral components. The inversion symmetry, however, prevents achieving a bulk χ^{(2)} response, limiting the portfolio of the second-order nonlinear materials. Here, we demonstrate subpicosecond conversion of a statically passive dielectric to a transient second-order nonlinear medium upon the ultrafast transfer of hot electrons. Induced by an optical switching signal, the amorphous dielectric with vanishing intrinsic χ^{(2)} develops dynamically tunable second-order nonlinear responses. By taking the second-harmonic generation as an example, we show that breaking the inversion symmetry through hot-electron dynamics can be leveraged to address the critical need for all-optical control of second-order nonlinearities in nanophotonics. Our approach can be generically adopted in a variety of material and device platforms, offering a new class of complex nonlinear media with promising potentials for all-optical information processing.

Enhancing Pockels effect in strained silicon waveguides

The magnitude and origin of the electro-optic measurements in strained silicon devices has been lately the object of a great controversy. Furthermore, recent works underline the importance of the masking effect of free carriers in strained waveguides and the low interaction between the mode and the highly strained areas. In the present work, the use of a p-i-n junction and an asymmetric cladding is proposed to eliminate the unwanted carrier influence and improve the electro-optical modulation response. The proposed configuration enhances the effective refractive index due to the strain-induced Pockels effect in more than two orders of magnitude with respect to the usual configuration.

Phase tuning by length contraction

Typical integrated optical phase tuners alter the effective index. In this paper, we explore tuning by geometric deformation. We show that tuning efficiency, Vπ L, improves as the device size shrinks down to the optimal bend radius, contrary to conventional index-shift based approaches where Vπ L remains constant. We demonstrate that this approach is capable of ultra-low power tuning across a full FSR in a low-confinement silicon nitride based ring resonator of 580 μm radius. We demonstrate record performance with V_FSR = 16 V, Vπ L = 3.6 V dB, Vπ Lα = 1.1 V dB, tuning current below 10 nA, and unattenuated tuning response up to 1 MHz. We also present optimized designs for high confinement silicon nitride and silicon based platforms with radius down to 80 μm and 45 μm, respectively, with performance well beyond current state-of-the-art. Applications include narrow-linewidth tunable diode lasers for spectroscopy and non-linear optics, optical phased array beamforming networks for RF antennas and LIDAR, and optical filters for WDM telecommunication links.

On the influence of interface charging dynamics and stressing conditions in strained silicon devices

The performance of strained silicon devices based on the deposition of a top silicon nitride layer with high stress have been thoroughly analyzed by means of simulations and experimental results. Results clearly indicate that the electro-optic static response is basically governed by carrier effects. A first evidence is the appearance of a variable optical absorption with the applied voltage that should not occur in case of having a purely electro-optic Pockels effect. However, hysteresis and saturation effects are also observed. We demonstrate that such effects are mainly due to the carrier trapping dynamics at the interface between the silicon and the silicon nitride and their influence on the silicon nitride charge. This theory is further confirmed by analyzing identical devices but with the silicon nitride cladding layer optimized to have intrinsic stresses of opposite sign and magnitude. The latter is achieved by a post annealing process which produces a defect healing and consequently a reduction of the silicon nitride charge. Raman measurements are also carried out to confirm the obtained results.

Investigation of Electric Field Induced Mixing in Silicon Micro Ring Resonators

In this paper we present a detailed theoretical investigation of the electric field induced mixing effect, in which the up and down frequency-conversion processes are obtained by inducing an effective second order susceptibility via the periodic spatial distribution of reversed biased p-i-n junctions. The possibility of realizing a frequency generation process within an integrated microring resonator is demonstrated here, by simulations, in the silicon on insulator platform. Furthermore, general physical features have been investigated by means of a comparative analysis of the frequency generation performance as a function of the input pump power, the linear and nonlinear losses, and the coupling factors. A conversion efficiency of 627.5 %/W has been obtained for the second harmonic generation process. Therefore, an improvement of 4 to 50 times with respect to the straight waveguides is achieved, depending on the cavity ring radius. Finally, for the up/down conversion, from telecom idler to mid-IR and from Mid-IR to telecom signal, respectively, an efficiency of 85.9%/W and 454.4 %/W has been obtained in the silicon microring resonator, respectively.

Investigation of mid-infrared second harmonic generation in strained germanium waveguides

In this paper we present a detailed theoretical investigation of second harmonic generation in strained germanium waveguides operating at the mid infrared pump wavelength of 4 μm. The effective second order susceptibility has been estimated through a multiphysics approach considering the residual stress of the SiN_x cladding film. Furthermore, general physical features have been investigated by means of a comparative analysis of SHG performance as a function of input pump power, linear and nonlinear phase mismatching, effective recombination carrier lifetime, and temperature, taking into account both continuous and pulsed regimes. Finally, periodically poled germanium devices have been explored with the aim to improve the SHG efficiency. In the same operative conditions, efficiencies of 0.6% and 0.0018% have been obtained in poled and not-poled waveguides, respectively.

Effect of dielectric claddings on the electro-optic behavior of silicon waveguides

We fabricate silicon waveguides in silicon-on-insulator (SOI) wafers clad with either silicon dioxide, silicon nitride, or aluminum oxide and, by measuring their electro-optic behavior, we characterize the capacitively induced free-carrier effect. By comparing our results with simulations, we confirm that the observed voltage dependences of the transmission spectra are due to changes in the concentrations of holes and electrons within the semiconductor waveguides and show how strongly these effects depend on the cladding material that comes into contact with the waveguide. Waveguide loss is additionally found to have a high sensitivity to the applied voltage, suggesting that these effects may find use in applications that require low- or high-loss propagation. These phenomena, which are present in all semiconductor waveguides, may be incorporated into more complex waveguide designs in the future to create high-efficiency electro-optic modulators and wavemixers.

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

The observation of the electro-optic effect in strained silicon waveguides has been considered a direct manifestation of an induced χ(2) nonlinearity in the material. In this work, we perform high-frequency measurements on strained silicon racetrack resonators. Strain is controlled by a mechanical deformation of the waveguide. It is shown that any optical modulation vanishes, independent of the applied strain, when the applied voltage varies much faster than the carrier effective lifetime and that the DC modulation is also largely independent of the applied strain. This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free-carrier effects, our results set an upper limit of (8±3) pm/V to the induced high-speed effective χeff,zzz(2) tensor element at an applied stress of -0.5 GPa. This upper limit is about 1 order of magnitude lower than previously reported values for static electro-optic measurements.

Modeling of strain-induced Pockels effect in Silicon

We propose a theoretical model to describe the strain-induced linear electro-optic (Pockels) effect in centro-symmetric crystals. The general formulation is presented and the specific case of the strained silicon is investigated in detail because of its attractive properties for integrated optics. The outcome of this analysis is a linear relation between the second order susceptibility tensor and the strain gradient tensor, depending generically on fifteen coefficients. The proposed model greatly simplifies the description of the electro-optic effect in strained silicon waveguides, providing a powerful and effective tool for design and optimization of optical devices.

CMOS-compatible optical switching concept based on strain-induced refractive-index tuning

In this paper we present a planar lightwave switching mechanism based on large refractive index variations induced by electrically-driven strain control in a CMOS-compatible photonic platform. Feasibility of the proposed concept, having general validity, is numerically analyzed in a specific case-study given by a Mach-Zehnder Interferometer with Ge waveguides topped by a piezoelectric stressor. The stressor can be operated in order to dynamically tune the strain into the two interferometric arms. The strain modifies the Ge band structure and can induce refractive index variations up to 0.05. We demonstrate that this approach can enable ultra-compact devices featuring low loss propagation for light wavelengths below the waveguide band gap energy, high extinction ratios (>30 dB) and low intrinsic insertion losses (2 dB). The operation wavelength can be extended in the whole FIR spectrum by using SiGe(Sn) alloy waveguides.

On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities

Microresonator-based frequency comb generation at or near visible wavelengths would enable applications in precise optical clocks, frequency metrology, and biomedical imaging. Comb generation in the visible has been limited by strong material dispersion and loss at short wavelengths, and only very narrowband comb generation has reached below 800 nm. We use the second-order optical nonlinearity in an integrated high-Q silicon nitride ring resonator cavity to convert a near-infrared frequency comb into the visible range. We simultaneously demonstrate parametric frequency comb generation in the near-infrared, second-harmonic generation, and sum-frequency generation. We measure 17 comb lines converted to visible wavelengths extending to 765 nm.

Wavelength dependence of Pockels effect in strained silicon waveguides

We investigate the influence of the wavelength, within the 1.3μm-1.63μm range, on the second-order optical nonlinearity in silicon waveguides strained by a silicon nitride (Si₃N ₄) overlayer. The effective second-order optical susceptibility χxxy(2)¯ evolutions have been determined for 3 different waveguide widths 385 nm, 435 nm and 465 nm and it showed higher values for longer wavelengths and narrower waveguides. For wWG = 385 nm and λ = 1630 nm, we demonstrated χxxy(2)¯ as high as 336 ± 30 pm/V. An explanation based on the strain distribution within the waveguide and its overlap with optical mode is then given to justify the obtained results.

Tensor of the second-order nonlinear susceptibility in asymmetrically strained silicon waveguides: analysis and experimental validation

We theoretically consider the existence of multiple nonzero components of the second-order nonlinear susceptibility tensor, χ(2), generated via strain-induced symmetry breaking in crystalline silicon. We determine that, in addition to the previously reported χ(xxy)(2) component, the χ(yyy)(2) component also becomes nonzero based on the remaining symmetry present in the strained material. In order to characterize these two nonlinearities, we fabricate Fabry-Perot waveguide resonators on 250 nm thick silicon-on-insulator wafers clad with 180 nm of compressively stressed (-1.275  GPa) silicon nitride. We measure the shifts in these devices' modal effective indices in response to several bias electric fields and calculate the χ(eff,xxy)(2) and χ(eff,yyy)(2) nonlinear susceptibility tensor elements induced by the breaking of the guiding material's inversion symmetry. Through the incorporation of finite element simulations encompassing the theoretical distribution of strain, the applied bias field, and the optical modes supported by the waveguide geometry, we extract two phenomenological scaling coefficients which relate the induced optical nonlinearities to the local strain gradient.

Electro-optic light modulation and THz generation in locally plasma-activated silicon nanophotonic devices

Silicon is not an electro-optic material by itself but the required second-order optical nonlinearity can be induced by breaking the inversion symmetry of the crystal lattice. Recently, an attractive approach has been demonstrated based on a surface-activation in a CMOS-compatible HBr dry etching process. In this work, we further investigate and quantify the second-order nonlinearity induced by this process. Using THz near-field probing we demonstrate that this simple and versatile process can be applied to locally equip silicon nanophotonic chips with micro-scale areas of electro-optic activity. The realization of a first fully integrated Mach-Zehnder modulator device - based on this process - is applied to quantify the nonlinearity to an effective χ((2)) of 9 ± 1 pm/V. Analysis of the thermal stability of the induced nonlinearity reveals post-processing limitations and paths for further efficiency improvements.