Maria Bayard Dühring - Solid Mechanics

34 Chapter 6 Design of acousto-optical interaction [P3]-[P7]
the electrodes increases the SAW properties change significantly, and in [82, 81, 83]
numerical and experimental results show a multi-mode SAW propagation and a tenfold
slowing of the phase velocity. The high aspect ratio (HAR) electrodes measured
in the experiments are seen in figure 6.1(b) and 6.1(c).
Recently, a Rayleigh wave generated by thin electrodes has been employed to
create an optical switch by modulation of optical waves in the two waveguide arms
of a Mach-Zehnder interferometer (MZI). A MZI is an optical device consisting of a
waveguide that is split into two waveguide arms and after a distance the arms are
joined again as illustrated by figure 6.2(a). By sending a Rayleigh wave perpendicular
towards the waveguide arms a periodic modulation of the light is obtained.
The distance between the waveguide arms is an unequal number of half Rayleigh
wavelengths such that when a Rayleigh wave node is present at each waveguide the
output light will not change. When a wave crest is located at one waveguide a
trough will appear at the other waveguide, and the applied stresses with opposite
sign will introduce a refractive index difference in the arms that causes an opposite
phase change in them. By constructive and destructive interference the light
will be turned on and off periodically with a multiple of the SAW frequency depending
on the static phase difference in the two arms, which can be introduced
by a length difference between them. Experimental results are reported in [23] and
[P3]. For straight electrode fingers a 40% relative modulation was obtained for a
GaAs/AlGaAs sample, but only a 0-8% relative modulation was found for a silicon
on insulator (SOI) sample.
In this chapter a numerical model is presented in order to study the acoustooptical
interaction in a MZI and explain the difference in the experimental results.
To model the SAW propagation and the optical modes in the waveguides, it is sufficient
to consider a 2D model of a cross-section through the two waveguides and the
geometry is seen on figure 6.2(b). Perfectly matched layers (PML) are employed at
the domain borders to prevent reflections of the mechanical and electrical disturbances
from the SAW. PMLs were introduced for time-harmonic elastic problems in
(a)
(b)
Figure 6.2 Light modulation in a Mach-Zehnder interferometer. (a): 3D geometry of
a MZI with a propagating surface acoustic wave (M. van der Poel [P3]). (b): The 2D
cross-section through the waveguide arms of the MZI that is used in the simulations.