Maria Bayard Dühring - Solid Mechanics

48 Chapter 6 Design of acousto-optical interaction [P3]-[P7]
increase in Δ eff,1 [%]
(b)
70
60
50
40
30
20
10
0
0 0.2 0.4 0.6 0.8 1
2r/w [−]
Figure 6.12 Study of the influence of an air hole below the waveguide with radius r. (a):
The color bar indicates ∆n11/ √ P and the time average power flow in the x3-direction is
shown by the contour lines with an arbitrary scale. (b): Increase in ∆neff,1 as function of
2r/w.
a simpler design change can be introduced. The optimization suggests that it as
an advantage to have an air hole underneath the output domain. To explore this
tendency further an air hole is introduced in the form of a half circle with the radius
r, see figure 6.12(a). The increase in ∆neff,1 as function of 2r/w, where w is the
width of the waveguide, is illustrated by figure 6.12(b). An optimum is obtained
around 2r/w = 0.8 where the interaction has increased with 65% compared to the
case without the air hole. When r is increasing two effects will influence the interaction.
First, the hole will trap the Rayleigh wave in the waveguide and introduce
additional strain concentrations that increase ∆n11/ √ P , see figure 6.12(a). As r
grows, strain is confined more and more to the waveguide above the hole until finally
the hole reaches a size, where the Rayleigh wave will be reflected instead. This
explains the sudden dip in the graph. The other effect is that the optical mode gets
more confined to the waveguide due to the refractive index contrast in the air. The
total increase in interaction is small compared to the increase obtained by topology
optimization, so the other air holes in the optimized design have an important influence
on the performance. To determine if the increased interaction is mainly due
to the strains around the hole or due to the better confinement of the optical wave,
the interaction ∆neff,1 is compared for the four cases seen in table 6.2. The value 1
Table 6.2 Increase in acousto-optical interaction ∆neff,1 compared to the original
GaAs/AlGaAs structure without the air hole. The original case corresponds to the value 1.
optical mode without hole optical mode with hole
strain without hole 1 1.03
strain with hole 3.29 1.65