Maria Bayard Dühring - Solid Mechanics

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54 Chapter 6 Design of acousto-optical interaction [P3]-[P7] because changes in n11/ √ P with the same sign surrounds the mode. ∆n11/ √ P for the case with thin electrodes changes sign into the substrate, and therefore a part of the optical mode is overlapping an area where the change in refractive index is zero. It has thus been proved that the acousto-optical interaction can be increased by the new types of surface acoustic waves generated by HAR electrodes. The problem could be investigated further by a parameter study in order to find the optimal position and size of the waveguide compared to the electrode size. Topology optimization could be applied to the problem to find other and more efficient shapes for the electrodes.
Chapter 7 Concluding remarks The work presented in this Ph.D. thesis is a contribution to the continuously growing research field of optimization of elastic and optical wave propagation. Three different types of wave devices have been simulated and their performances have been improved either by topology optimization or parameter studies of the geometry. The first problem treated structures for sound reduction, the other was concerned with the energy flow of optical waves in holey fibers, and finally the interaction between surface acoustic waves and optical waves in waveguides was studied. By investigating the waves propagating in the optimized structures, an increased understanding of their physical behavior and the function of the devices were obtained. The acquired knowledge could be employed to fabricate devices with improved efficiency. It is explained, that even though the three investigated problems describe very different physical phenomena, they can all be described in a similar way by second order differential equations. The time dependency is eliminated as a harmonic time variation can be assumed, and this simplifies the implementation, solving and optimization. The high-level programming language Comsol Multiphysics was found suitable for simulating the studied two-dimensional problems by the finite element method. The implementation time can be reduced with this software, because the differential equations are either predefined or can be specified in a straightforward manner and the discretization, meshing and solving are automated. The code can be extended with Matlab scripting such that studies of geometry parameters and the call to the MMA optimization-algorithm can be performed. The program is however not suited for solving bigger 3D problems due to high memory usage. The method of topology optimization has successfully been applied to the three types of wave problems. They are defined in a similar way and it was shown that a generic formulation of the optimization problem was suitable for all the wave problems with similar expressions for the objective functions and the interpolation functions. By applying continuation methods and a close-type Heaviside morphologyfilter, well defined designs with vanishing gray transition zones at the interfaces between air and solid material were in general obtained. The optimized designs guide and control the propagating waves such that objective function is optimized, and they indicate how much the performance can be increased with unrestricted design freedom. It is therefore concluded that the presented topology optimization method works well for the three wave propagating problems. However, the optimization problems are in general sensitive to factors as the initial guess, move limit, tolerance, filter size and continuation method. So even though essentially the same formulation of the topology optimization can be employed for the considered problems, many different factors must be varied and tested in order to get suitable 55
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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
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2 Chapter 1 Introduction waves. The
Page 14 and 15: 4 Chapter 2 Time-harmonic propagati
Page 20 and 21: 10 Chapter 2 Time-harmonic propagat
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
Page 66 and 67: 56 Chapter 7 Concluding remarks des
Page 68 and 69: 58 Chapter 7 Concluding remarks
Page 70 and 71: 60 References [14] E. Yablonovitch,
Page 72 and 73: 62 References [42] A. A. Larsen, B.
Page 74 and 75: 64 References [67] K. Svanberg, “
Page 77: Publication [P1] Acoustic design by
Page 80 and 81: 558 In Ref. [3] it is studied how t
Page 82 and 83: 560 2.2. Design variables and mater
Page 84 and 85: 562 When the mesh size is decreased
Page 86 and 87: 564 objective function, Φ [dB] 130
Page 88 and 89: 566 ARTICLE IN PRESS Fig. 6. The di
Page 90 and 91: 568 ~kðxÞ 1 ¼ k1 ARTICLE IN PRES
Page 92 and 93: 570 ARTICLE IN PRESS M.B. Dühring
Page 94 and 95: 572 ARTICLE IN PRESS M.B. Dühring
Page 96 and 97: 574 frequency or the frequency inte
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Page 102 and 103: photonic-crystal fibers used for me
Page 104 and 105: 2.2 Design variables and material i
Page 106 and 107: two air holes, is Λ = 3.1 µm, the
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Page 112 and 113: [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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