Maria Bayard Dühring - Solid Mechanics

6.4 Acousto-optical interaction in a Mach-Zehnder interferometer 43
Δn eff,ν [W −1/2 ]
(a)
x 10−4
1.2
1
0.8
0.6
0.4
0.2
mode 1
mode 2
mode 3
mode 4
0
0 0.5 1 1.5 2 2.5
width, w [μm]
normalized index n eff,ν /n org [−]
(b)
1.1
1
0.9
0.8
0.7
0.6
left waveguide
right waveguide
mode 1
mode 2
mode 3
mode 4
0 0.5 1 1.5 2 2.5
width, w [μm]
Figure 6.8 Results from a study of the waveguide width w for the optimal height h =
0.19 µm. (a): ∆neff,ν of the four lowest order modes as function of w. (b): Normalized
index neff,ν/norg as functions of w.
supports the two first order modes whereas the waveguide with the optimal height
only supports the mode polarized in the x1-direction. The interaction is smaller for
the mode polarized in the vertical direction.
A study of the width w of the waveguides with the height fixed to h = 0.19 µm
is seen in figure 6.8(a). ∆neff,ν is plotted for the first four modes, for which the
mode order increases with the mode number. ∆neff,ν increases with increasing w for
all four modes, but the interaction is biggest for the first order mode. When w is
increasing, the confined optical mode will also extend in the horizontal direction and
will experience more stresses as long as w is smaller than half a SAW wavelength.
The power flow for the first order mode is plotted in figure 6.7(b) for w = 2.30 µm
and it overlaps well with the change in effective refractive index. The limit for the
increase is in principle when w approaches half a SAW wavelength. However, before
that the mode in the right waveguide with the SAW trough will start to degenerate
into two modes, so the graph is therefore stopped here. The difference in index
reaches 1.14 · 10 −4 W −1/2 , which is more than 12 times bigger than for the original
waveguide geometry. When w increases the waveguides will start to support an
increasing number of modes, which is also seen on figure 6.8(b) where neff,i/norg
for the four lowest order modes in the two waveguides are shown as functions of
w. The waveguide is single-moded until w = 0.60 µm and the interaction is here
2.92·10 −5 W −1/2 , which is 3.3 times bigger than for the original waveguide geometry.
This study of the waveguide geometry shows that it is possible to improve the optical
modulation by changing the waveguide size such that the mode is moved closer to
the surface and extended in the width to experience more stresses. This was also
expected when comparing with the GaAs/AlGaAs case as seen in figure 6.5(a).
As the stresses from the Rayleigh wave have their maximum just below the surface,
an alternative to changing the waveguide size is to bury the original waveguides