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We theoretically investigate the use of Rayleigh surface acoustic waves (SAWs) for refractive index modulation in optical waveguides consisting of amorphous dielectrics. Considering low-loss Si$_3$N$_4$ waveguides with a standard core cross section of 4.4$\times$0.03 $\mu$m$^2$ size, buried 8 $\mu$m deep in a SiO$_2$ cladding we compare surface acoustic wave generation in various different geometries via a piezo-active, lead zirconate titanate film placed on top of the surface and driven via an interdigitized transducer (IDT). Using numerical solutions of the acoustic and optical wave equations, we determine the strain distribution of the SAW under resonant excitation. From the overlap of the acoustic strain field with the optical mode field we calculate and maximize the attainable amplitude of index modulation in the waveguide. For the example of a near-infrared wavelength of 840 nm, a maximum shift in relative effective refractive index of 0.7x10$^{-3}$ was obtained for TE polarized light, using an IDT period of 30 - 35 $\mu$m, a film thickness of 2.5 - 3.5 $\mu$m, and an IDT voltage of 10 V. For these parameters, the resonant frequency is in the range 70 - 85 MHz. The maximum shift increases to 1.2x10$^{-3}$, with a corresponding resonant frequency of 87 MHz, when the height of the cladding above the core is reduced to 3 $\mu$m. The relative index change is about 300-times higher than in previous work based on non-resonant proximity piezo-actuation, and the modulation frequency is about 200-times higher. Exploiting the maximum relative index change of 1.2$\times$10$^{-3}$ in a low-loss balanced Mach-Zehnder modulator should allow full-contrast modulation in devices as short as 120 $\mu$m (half-wave voltage length product = 0.24 Vcm)., Comment: 19 pages, 8 figures

We report the observation of second-harmonic generation in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapour deposition. Quasi-rectangular waveguides with a large cross section were used, with a height of 1 {\mu}m and various different widths, from 0.6 to 1.2 {\mu}m, 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. 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, 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 photogalvanic 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 x 1 {\mu}m$^2$ cross section and 36 mm length, corresponding to 53 {\mu}W at 532 nm with 13 mW of IR input coupled into the waveguide. The according $\chi^{(2)}$ amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency., Comment: 20 pages, 10 figures