Maria Bayard Dühring - Solid Mechanics

6.4 Acousto-optical interaction in a Mach-Zehnder interferometer 39
Table 6.1 Refractive index and stress-optical constants from [86].
Material n0 C11, C22, C33 C12, C13, C23 C44, C55, C66
[-] [10 −12 Pa −1 ] [10 −12 Pa −1 ] [10 −12 Pa −1 ]
Si 3.42 -11.35 3.65 -12.82
as seen in table III in that paper. The correct material constants are here given
in table 6.1. The inclusion of C44, C55 and C66 does not have any influence on
the general conclusions of paper [P4], but the actual values of the interaction have
increased. The graphs and results, where the influence of the three components is
taken into account, are presented in the following.
When the MZI is designed for acousto-optical interaction the propagation of the
Rayleigh wave has to be considered and adjusted. First it is important to be aware
that a part of the wave is reflected each time the geometry or the material, that the
wave passes through, change. An example is shown in [P3] where the transmission
of the Rayleigh wave that passes the two waveguides is measured as function of the
etching depth of the material around the waveguides. The transmission decreases
drastically after a certain etching depth because the wave is reflected and lost to
the bulk material. So in order to get a significant transmission of the Rayleigh
wave the changes in geometry and materials must be limited. In the SOI sample an
extra change in geometry and material is introduced compared to the GaAs/AlGaAs
sample, as the wave has to be generated in a ZnO layer. In addition to the reflections
of the Rayleigh wave, its wavelength will also change when the materials are varying
along the propagation direction. In the GaAs case this is not a problem as the two
materials are so similar that the wavelength is the same through the device. In the
SOI case the materials used are not similar and when the wave leaves the ZnO layer
the wavelength increases from 5.6 to 7.3 µm. This is a significant reason why the
SOI device does not work well, and the distance between the waveguides must be
adjusted according to this change in wavelength.
After the Rayleigh wave has been adjusted to the geometry and the materials,
the optical properties and the interaction must be considered. First it is verified that
the biggest difference in effective refractive index for the fundamental mode ∆neff,1
appears when one waveguide is influenced by a Rayleigh wave crest and the other
is influenced by a trough. The increase of the refractive index (neff,1 − nno)/ √ P for
the SOI case is calculated in the two waveguides for a complete SAW phase passing
through the waveguides. nno is the effective refractive index of the fundamental
optical mode when no mechanical stresses are applied. The results are plotted in
figure 6.4(a) where φsaw = 0 corresponds to a crest in the left waveguide and a
trough in the right. It is seen that the biggest difference in ∆neff,1 is found where
a wave crest and a trough is at the waveguides, respectively. This is clarified by
plotting the von Mises stress in the sample, see figure 6.4(b). At the surface the
von Mises stress is zero at the Rayleigh wave nodes and the biggest values are found