Surface acoustic waves for acousto-optic modulation in buried silicon nitride waveguides

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).