Fig. 1. Overview of the modulator implementation and design.

a A illustration of the layer stack. Here, Al is aluminum, AlN is aluminum nitride, Mo is molybdenum, SiN is silicon nitride, SiO₂ is silica, and Si is silicon. The silica cladding above the waveguide is rendered transparent in the illustration so the waveguide is visible. b A false colored cross-section scanning electron microscope image of the layer stack illustrated in (a). c An optical mode profile with arrows indicating the electric field of the transverse electric (TE) mode is mostly $\widehat{x}$-directed. The z-component of the Poynting vector is shown as P_z. d Simulation of the relevant strain tensor components, S_xx and S_yy for the fundamental transducer acoustic mode. e An illustration of the design strategy. A total of C intersection points of the spiral waveguide with the acoustic wave, $\left\{x_n\right\}$, are optimized to maximize phase modulation and obey design rules such as the minimum bending radius, $r_{\min }$. f The field amplitude within a spiral with C = 38 modulated segments (the largest spiral experimentally measured later in this work) as a function of distance, s, along the waveguide normalized to the coherence length, L_coh. The modulated segment locations are colored in accordance with the acoustic field phase at each location. g. The acoustic field phase is compared to the optical phase-mismatch, revealing that the spirals are designed to counter the optical phase-mismatch through judicious selection of acoustic phase via placement of the spiral waveguides at locations $\left\{x_n\right\}$.