Second harmonic generation in engineered silicon waveguides

In the last years, Silicon becomes one of the most important technological platform for integrated photonics technologies. Nonlinear silicon photonics is a desired upgrade of this thecnology as it gives the opportunity to directly process the signal on the chip by using the wide spectrum of nonlinear phenomena. To have access to high order nonlinearities a large optical pump power is needed. Second order nonlinear effects are desirable due to the reduction of the used power with respect to third order nonlinearities. Moreover, it allows to achieve interesting efforts, such as wavelength conversion and generation of quantum states. Here the problem is that silicon has a diamond crystalline structure. Therefore, silicon is a centrosymmetric material. For a geometrical point of view, this property is reflected in a symmetry of the polarization vector P(E) = -P(-E) . The polarization vector is related to the electric field by: P = P^0 + P^(2) + P^(3) +... From equation 2, it is possible to see that, in order to respect the centrosymmetry, chi^(2) =0. So, in the dipole approximation, second order nonlinearities are inhibited in Silicon. Many efforts have been spent to induce second order nonlinearities in Silicon. At first, strained silicon, in which the centrosymmetry of Silicon crystalline structure is broken by an inhomogeneous strain, seemed to be the most viable solution. In strained silicon waveguides, the inhomogeneous strain is applied by a stressing layer of different materials with a different lattice constant deposited on top of the waveguide [4]. The first experiment based on Silicon waveguides was performed in 2006 by Jacobsen et al. that measured a nonlinear coefficient chi^(2) = 15 pm/V with a SiN stressing layer via DC electro-optic effect. This work was followed by many others, reaching values for the strain-induced second order nonlinear coefficient chi^(2) up to 340 pm/V. Few works gave a different interpretation of the chi^(2). It was demonstrated that during the deposition of the stressing layer there is the formation of dangling bonds at the interface between the deposited layer and the silicon waveguide. These dandling bonds act as positive fix ions. The formation of this charges, indeed, determined an abundance of free-carriers in the core of the waveguide that, because of the free carrier dispersion, can affect the value of the effective measured nonlinear coefficient in the DC electro-optic effect. Azadeh et al. demonstrated for the firs time the crucial role of this phenomenon which overtakes the strain effect, also confirmed by Olivares et al. An upper limit of chi^(2) = 8 pm/V due to a strain effect was experimentally fixed. Other works investigated second order nonlinearities in Silicon looking at the Second Harmonic Generation (SHG). Cazzanelli et al. measured a value of chi^(2) = 40 pm 30 pm/V by SHG in multimodal waveguides using a pump wavelength above 2 um, without any phase matching mechanism. It was also demonstrated that stressing layers that induced the same value of strain but realized with different materials yield different SHG, making clear that not only strain but also charged defects play an important role in the generation of the SH signal. Indeed, it was demonstrated that charged defects can induce an electric DC field that interacts with the large chi^(3) of bulk silicon to give a dressed (effective) second order nonlinear coefficient chi^(2)_EFISH = 3 chi^(3) E_DC via electric-field-induced second harmonic (EFISH) generation. So in 2017 the effect of the strain on silicon waveguides was not clear. The aim of my PhD work is try to understand the origin of the dressed chi^(2) in silicon waveguide and propose a way to engineer and control it. In order to understand the origin of second order nonlinearities in silicon, an experiment that can separate the role of the strain and the role of the trapped charged defects at the interface between the silicon waveguide and the stressing layer in an unambiguously way was performed. The sample used was composed by a set of strip silicon waveguides 243 nm thick with a SiN stressing layer of 140 nm deposited on the top of the waveguide. The waveguides were engineered in order to have intermodal phase matching condition between the TM1 mode for the pump wavelength and TE3 mode for the generated SH wavelength. Different widths of the waveguide have been used in order to tune the phase-matching condition wavelength. To investigate the role of the strain, the sample was mounted on a sample holder equipped with a screw to deformed the waveguide. Rotating the screw, a vertical displacement Delta_H is induced in the center of the sample orthogonal to its main plain. This displacement acts as an external load that increase the strain in the silicon waveguide. SHG was measured for different values of the Delta_H displacement. Increasing the load in the sample there is a red-shift of peak. Indeed, increasing the strain in the sample a change in the effective index is induced, and a change in the phasematching condition is obtained. However, SH power is always the same, revealing that the value of chi^(2) is not increasing with the strain. To investigate the role of the trapped defect at the Si/SiN interface, following the idea of Piccoli et al., the sample was exposed to UV irradiation to induce a passivation (i.e. neutralization) of the defects. Then, SHG was measured and no generation can be detected. These results clarify that the main causes of the SH in silicon waveguide is not given by the strain but by the charge defect and an upper limit of chi^(2) at 0,05 pm/V for the strain induced second order nonlinear coefficient was experimentally fixed. This result is also supported by an earlier theoretical estimation given by Khurgin et al. in 2015. From these observations, the use of an applied electric field emerges as a way to induce a controlled effective chi^(2) in silicon waveguide suitable for technological application. The idea is based on the use of a controlled external E_DC field in order to obtain the desired value of chi^(2) where the electric field can be generated by placing lateral p-i-n junctions across the waveguide that can be reverse biased using metallic pads. In this way, chi^(2) can be enhanced increasing the applied bias and the only limitation is the breakdown field of silicon, that is known to be around V = 24 V. Timurdogan et al. demonstrated that it is also possible to use the periodicity of the p-i-n junctions to absorb the mismatch between the pump and the SH modes in order to obtain a quasi-phase matching condition. The sample used was a set of rib waveguides with different widths. Along the propagation direction of the waveguide p-i-n junctions have been grown. Since in the generation efficiency what matters is not the overall chi^(2) but the amplitude of its oscillations along the length of the waveguide, an interdigitated poling configuration was studied. In this configuration, regions of p-i-n junctions and regions of n-i-p junctions are periodically alternated. Second harmonic generation was observed in this poled waveguide and the SH signal increased quadratically with both the pump power and the applied bias, according with the theory. It was also demonstrated that a larger conversion efficiency is obtained using this poling configuration instead of the poling configuration proposed by Timurdogan in 2017. Also a modeling of the effect of the fabrication defects has been done. The pump P_p and the generated P_SH powers are related by P_SH = P_p^2|gamma^(2)|^2 L^2 S where S is the poling therm which describes what is happening along the length of the waveguide. S is a function of the geometry of the waveguide and of the periodicity of the p-i-n junctions: S=1/L^2 |int_0^L s(z) exp(i Delta beta z) dz|^2. During the fabrication, an unwanted variation of the geometrical parameters can be induced along the length of the waveguide both in the waveguide cross section and in the poling period. The effect of this two kind of variations has been studied. Moreover, the coherence length of the process has been also studied, in order to have a clear understanding of the EFISH process. the developed model was compared with the experimental data. It is possible to extract the effective Delta chi^(2) of the EFISH process with an interdigitated poling configuration, when 24 V are applied to the junctions: Delta chi^(2)_eff=78 pm 3 pm/V. Finally it was perform a study of microrings that can accomodate geometrical defects. Using a 4-bar symmetry of the chi^(2) tensor, a study of the conversion efficiency as a function of the different parameters of the microring has been performed. It was demonstrated that the most critical parameter is the thickness of the waveguide in the ring and it was shown a method to find a geometry that allows to have efficient conversion efficiency in a range of thickness of 16 nm around the nominal value. Moreover, this method is more general, since it is based only on the symmetry of the nonlinear tensor. Therefore, it can be easily applied to other materials.