Maria Bayard Dühring - Solid Mechanics

6.4 Acousto-optical interaction in a Mach-Zehnder interferometer 41
Figure 6.5 Study of acousto-optical interaction in an optical waveguide. The color bars
show the refractive index change ∆n11/ √ P . The time averaged power flow in the x3direction
of the fundamental mode is indicated by the contour lines with an arbitrary
scale. (a): GaAs/AlGaAs sample. (b): SOI sample.
the optical mode is fully confined to the waveguide and its center is placed where
∆n11/ √ P is zero. The interaction is ∆neff,1 = 8.84 · 10 −6 W −1/2 , which is less than
for the GaAs/AlGaAs case. This shows that the geometry of the waveguide is important
for the acousto-optical interaction, and the two examples indicate that it is
efficient to have an aspect ratio of the waveguide with a bigger width and a lower
height such that the entire waveguide gets deformed as in the GaAs/AlGaAs case.
The waveguide of the SOI sample supports another first order mode as well, which
is polarized in the x2-direction. The interaction of this mode is less than the first
mode with ∆neff,2 = 5.15 · 10 −6 W −1/2 .
6.4.1 Parameter study of waveguide geometry
The acousto-optical model is now employed to improve the interaction in the SOI
sample by varying parameters in the geometry. First the height h of the waveguides
is studied and figure 6.6(a) shows the interaction ∆neff,ν as function of h for the two
first order modes that the waveguides support. An optimal height h = 0.19 µm of the
waveguides is found for the mode polarized in the x1-direction with ∆neff,1 = 1.61 ·
10 −5 W −1/2 , which is 1.8 times bigger than for the original height. In figure 6.7(a)
∆n11/ √ P is plotted for the optimal height together with the power flow of the
fundamental optical mode. As the waveguide has become thinner, the center of
the optical mode has moved closer to the surface and is overlapping better with
the change in refractive index compared to the original case seen in figure 6.5(b).
However, when the height is decreasing the optical wave will be less confined in
the waveguide and will be increasingly influenced by the SiO2 and the air. The air
will not contribute to an index difference in the two waveguides and the SiO2 will
have a negative influence on the difference, as the stress-optical constants related