Telecommunication technologies

Table 1 Material and geometrical properties used in the FEM simulations
Full size table
We used an unstructured triangular mesh for all the different domains. To obtain converged results, we used a 0.2 mm maximum mesh size in the piezoelectric material region, a 0.15 mm maximum mesh size in the cavity and a 1 mm mesh size in the PML region.
We solved the set of coupled equations both as an eigenmode problem and also as a frequency domain problem. In the first case, all the eigenmodes were obtained simultaneously. In the latter case, we scanned the frequency in fine steps and monitored the pressure maximum in the center of the cavity to obtain the sustained cavity resonance modes. Using both methods, we obtained the same resonance frequencies. The frequency domain analysis helps with the understanding of pressure profile changes when sweeping the frequency to move from one mode to the next.
To obtain optical waveguide modes, the pressure profile is first transformed into a refractive index modulation profile in the medium. The refractive index profile is used as the input to our finite difference mode analysis. We used a commercial-grade eigenmode solver (http://www.lumerical.com/tcad-products/mode/; Lumerical Inc.) to calculate the supported optical modes at a transverse cross-section of the sculpted optical waveguide. We used a non-uniform mesh structure with 30 nm mesh elements in the core of the waveguide and gradually increasing mesh elements along the radial direction to ensure the convergence of the results, while preventing numerical instability. The ultrasonically sculpted optical waveguides support several modes in the visible range of the spectrum. A selection of the supported modes is shown in Fig. 1d–g at λ = 650 nm.