Improving the acousto-optical interaction in a Mach-Zehnder interferometer

A method for modeling the interaction of the mechanical field from a surface acoustic wave and the optical field in the waveguides of a Mach-Zehnder interferometer is presented. The surface acoustic wave is generated by an interdigital transducer using a linear elastic plane model of a piezoelectric, inhomogeneous material, and reflections from the boundaries are avoided by applying perfectly matched layers. The optical modes in the waveguides are modeled by time-harmonic wave equations for the magnetic field. The two models are coupled using stress-optical relations and the change in effective refractive index introduced in the Mach-Zehnder interferometer arms by the stresses from the surface acoustic wave is calculated. It is then shown that the effective refractive index of the fundamental optical mode increases at a surface acoustic wave crest and decreases at a trough. The height and the width of the waveguides are varied for a silicon on insulator sample, and it is shown that the difference in effective refractive index between the waveguides can be increased 12 times for the right choice of waveguide size such that the optical modulation is improved. The difference is four times bigger if the waveguides are kept single moded. It is furthermore shown that the difference increases more than ten times when the waveguides are buried below the surface, where the mechanical stresses have their maximum, and in the case where two interdigital transducers are used the difference is increased 1.5 times.