Maria Bayard Dühring - Solid Mechanics

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52 Chapter 6 Design of acousto-optical interaction [P3]-[P7] Table 6.3 Half of the phase velocity vp and the energy fraction Emech,elec/Emech,tot for the periodic and finite structure for the six modes and h/2p = 1. Mode number 1 2 3 4 5 6 Mode type SH1 VP1 SH2 VP2 SH3 VP3 phase velocity periodic device 337 523 1004 1512 1641 2273 vp [ms −1 ] finite device 337 523 1004 1510 1639 2275 Emech,elec/Emech,tot periodic device 90.5 81.7 88.8 76.4 83.1 41.7 [%] finite device 90.3 81.5 88.5 75.5 82.1 45.0 mechanical energy fraction Emech,elec/Emech,tot are in fine agreement for the periodic and the finite model as seen from table 6.3 where the results are listed for h/2p = 1. The small deviations in the values are due to energy loss to the bulk material because of the limited number of electrodes in the finite structure. In order to study acousto-optical interaction, a buried channel waveguide is introduced below one of the electrodes in the waveguide area indicated in figure 6.15. The waveguide is supposed to be created by annealed proton exchange, which will introduce a refractive index variation that can confine optical modes. The eigenvalue problem for the optical modes is solved in the optical area. The waveguide is multi-moded and the two first order modes are considered here. The one polarized in the x1-direction is denoted optical mode 1 and the one polarized in the x2-direction is denoted optical mode 2. The acousto-optical interaction ∆neff,ν is calculated for the two optical modes both for the six acoustic modes with h/2p = 1 and for the Rayleigh wave excited by thin electrodes with h/2p = 0.01. The results are given in table 6.4. The SH modes interact most efficiently with optical mode 1 and the VP modes interact best with optical mode 2. The acousto-optical interaction decreases with increasing mode number within the two different categories of acoustic modes. The six acoustic modes with high aspect ratio electrodes interact better in general Table 6.4 The difference in effective refractive index for the two first order optical modes influenced by the six acoustic modes with h/2p = 1 as well as by the thin electrodes with h/2p = 0.01. ∆neff,1 [W −1/2 ] ∆neff,2 [W −1/2 ] mode 1 (SH1) 1.55 · 10 −3 8.97 · 10 −4 mode 3 (SH2) 9.08 · 10 −5 6.62 · 10 −5 mode 5 (SH3) 3.08 · 10 −6 2.50 · 10 −6 mode 2 (VP1) 7.35 · 10 −5 7.21 · 10 −4 mode 4 (VP2) 1.18 · 10 −5 6.35 · 10 −5 mode 6 (VP3) 6.49 · 10 −6 1.38 · 10 −5 thin electrodes 2.51 · 10 −6 1.71 · 10 −6
6.5 High aspect ratio electrodes 53 compared to the acoustic mode for the conventional thin electrodes. The interaction is a result of how efficiently the acoustic mode is excited with the applied electrical power and how well the acoustic and optical mode shapes match each other. The acoustic modes of lower order are more efficiently excited by a certain amount of electrical power than the modes of higher order. This fact can be explained by considering the energy confinement to the electrodes in figure 6.14(b). At the energy limits for increasing aspect ratio the energy is concentrated in the electrodes and in the substrate just below where the electrodes are attached. Therefore the stress concentration around the waveguide will be big. As the lower order acoustic modes are closer to the energy limits for h/2p = 1 the values of the stresses will be bigger than for the higher order modes. As the structure with high aspect ratio electrodes is more compliant than the almost plane surface with the thin electrodes, more power has to be applied to the thin electrodes in order to get the same stresses. It can therefore be expected that the change in refractive index is biggest for the low order acoustic modes with high aspect ratio electrodes. The other issue is how well the acoustic modes overlap with the optical modes. The optical modes will mainly detect the changes in refractive index in their polarization direction. So for optical mode 1 it is the SAW induced changes of the refractive index in the x1-direction ∆n11 that are important. The optical mode 2 must overlap with ∆n22. The acoustic modes of the same polarization type all have a similar pattern of changes in refractive index in the different directions around the optical waveguide. As an example ∆n11/ √ P is plotted for SH1 in figure 6.16(a) with the power flow of optical mode 1 indicated with contour lines. The same is plotted for the case with the thin electrodes in figure 6.16(b). The change in the refractive index is bigger for SH1 than for the case with the thin electrodes. The SH1 mode overlaps best with the optical mode Figure 6.16 Results for the acousto-optical interaction. The color bars show ∆n11/ √ P and the time averaged power flow in the x3-direction of the optical mode 1 is indicated by the contour lines with an arbitrary scale. (a): Results for SH1 with h/2p = 1. (b): Results for the thin electrodes with h/2p = 0.01.
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Optimization of acoustic, optical a
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Title of the thesis: Optimization o
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Resumé (in Danish) Forskningsomr˚
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Publications The following publicat
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vi Contents 6 Design of acousto-opt
Page 12 and 13: 2 Chapter 1 Introduction waves. The
Page 14 and 15: 4 Chapter 2 Time-harmonic propagati
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Page 22 and 23: 12 Chapter 3 Topology optimization
Page 32 and 33: 22 Chapter 4 Design of sound barrie
Page 38 and 39: 28 Chapter 5 Design of photonic-cry
Page 44 and 45: 34 Chapter 6 Design of acousto-opti
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[23] J. Riishede and O. Sigmund, In
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Surface acoustic wave driven light
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IDT GaAs AlGaAs 0.10 0.05 0.00 Ampl
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Publication [P4] Improving the acou
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083529-2 M. B. Dühring and O. Sigm
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Publication [P5] Design of acousto-
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Figure 1: The geometry used in the
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where ˜pijkl are the rotated strai
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where ∂Φ ∂w R 2,n − i ∂Φ
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Figure 3: The distribution of the o
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[12] J.S. Jensen and O. Sigmund, To
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Energy storage and dispersion of su
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093504-3 Dühring, Laude, and Kheli
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093504-5 Dühring, Laude, and Kheli
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Publication [P7] Improving surface
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FIG. 1: The geometry of the acousto
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finer mesh. For the coupled model i
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FIG. 4: Results for the finite mode
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FIG. 6: Results for the acousto-opt
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Suzuki, A. Onoe, T. Adachi and K. F
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Maria Bayard Dühring - Solid Mechanics

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