Maria Bayard Dühring - Solid Mechanics
Maria Bayard Dühring - Solid Mechanics
Maria Bayard Dühring - Solid Mechanics
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52 Chapter 6 Design of acousto-optical interaction [P3]-[P7]<br />
Table 6.3 Half of the phase velocity vp and the energy fraction Emech,elec/Emech,tot for<br />
the periodic and finite structure for the six modes and h/2p = 1.<br />
Mode number 1 2 3 4 5 6<br />
Mode type SH1 VP1 SH2 VP2 SH3 VP3<br />
phase velocity periodic device 337 523 1004 1512 1641 2273<br />
vp [ms −1 ] finite device 337 523 1004 1510 1639 2275<br />
Emech,elec/Emech,tot periodic device 90.5 81.7 88.8 76.4 83.1 41.7<br />
[%] finite device 90.3 81.5 88.5 75.5 82.1 45.0<br />
mechanical energy fraction Emech,elec/Emech,tot are in fine agreement for the periodic<br />
and the finite model as seen from table 6.3 where the results are listed for h/2p = 1.<br />
The small deviations in the values are due to energy loss to the bulk material because<br />
of the limited number of electrodes in the finite structure.<br />
In order to study acousto-optical interaction, a buried channel waveguide is introduced<br />
below one of the electrodes in the waveguide area indicated in figure 6.15.<br />
The waveguide is supposed to be created by annealed proton exchange, which will<br />
introduce a refractive index variation that can confine optical modes. The eigenvalue<br />
problem for the optical modes is solved in the optical area. The waveguide is<br />
multi-moded and the two first order modes are considered here. The one polarized in<br />
the x1-direction is denoted optical mode 1 and the one polarized in the x2-direction<br />
is denoted optical mode 2. The acousto-optical interaction ∆neff,ν is calculated for<br />
the two optical modes both for the six acoustic modes with h/2p = 1 and for the<br />
Rayleigh wave excited by thin electrodes with h/2p = 0.01. The results are given in<br />
table 6.4. The SH modes interact most efficiently with optical mode 1 and the VP<br />
modes interact best with optical mode 2. The acousto-optical interaction decreases<br />
with increasing mode number within the two different categories of acoustic modes.<br />
The six acoustic modes with high aspect ratio electrodes interact better in general<br />
Table 6.4 The difference in effective refractive index for the two first order optical modes<br />
influenced by the six acoustic modes with h/2p = 1 as well as by the thin electrodes with<br />
h/2p = 0.01.<br />
∆neff,1 [W −1/2 ] ∆neff,2 [W −1/2 ]<br />
mode 1 (SH1) 1.55 · 10 −3 8.97 · 10 −4<br />
mode 3 (SH2) 9.08 · 10 −5 6.62 · 10 −5<br />
mode 5 (SH3) 3.08 · 10 −6 2.50 · 10 −6<br />
mode 2 (VP1) 7.35 · 10 −5 7.21 · 10 −4<br />
mode 4 (VP2) 1.18 · 10 −5 6.35 · 10 −5<br />
mode 6 (VP3) 6.49 · 10 −6 1.38 · 10 −5<br />
thin electrodes 2.51 · 10 −6 1.71 · 10 −6