Maria Bayard Dühring - Solid Mechanics

More documents

Recommendations

Info

vi Contents 6 Design of acousto-optical interaction [P3]-[P7] 33 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.2 The acousto-optical model . . . . . . . . . . . . . . . . . . . . . . . . 35 6.3 Modeling surface acoustic waves . . . . . . . . . . . . . . . . . . . . . 37 6.4 Acousto-optical interaction in a Mach-Zehnder interferometer . . . . 37 6.4.1 Parameter study of waveguide geometry . . . . . . . . . . . . 41 6.4.2 Topology optimization . . . . . . . . . . . . . . . . . . . . . . 46 6.5 High aspect ratio electrodes . . . . . . . . . . . . . . . . . . . . . . . 49 6.5.1 Periodic structure . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.5.2 Finite structure and acousto-optical interaction . . . . . . . . 51 7 Concluding remarks 55 7.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 References 59
Chapter 1 Introduction 1.1 Aim of the thesis The study of elastic and optical waves has obtained great importance during the last century. Waves with different kinds of properties have been discovered, which combined with an intense research in materials and fabrication techniques have allowed for the fabrication of structures down to nano scale, resulting in a range of important applications from sonar, ultrasound scanning over lasers, optical fibers and integrated optics. The field of research is continuously expanding and opening up for new and promising applications. It has therefore become essential to simulate and understand wave propagation in order to design wave devices. The aim of this thesis is to study propagating elastic and optical waves, which are described on a time-harmonic form, and to optimize wave devices either by varying different geometry parameters or by topology optimization. The method of topology optimization is a gradient based optimization method that has proven efficient for optimizing static and dynamic problems in engineering and is here extended to three new wave propagation problems with increasing complexity. First acoustic waves that are propagating in air are studied and topology optimization is employed to design sound barriers such that the noise is reduced behind the barrier. Then optical waves are simulated in photonic-crystal fibers and the energy flow through the core is maximized by designing the cross section of the fiber by use of topology optimization. Finally, surface acoustic waves are simulated in piezoelectric materials and their interaction with optical waves in channel waveguides is investigated. This study is both based on a parametric investigation of the geometry as well as topology optimization in order to improve the acousto-optical interaction. The different wave problems are all governed by second order differential equations that can be discretized and solved in a similar way by the finite element program Comsol Multiphysics with Matlab. 1.2 Structure of the thesis This thesis is a common introduction to the work done during the Ph.D. study. It gives an overview of the results presented in the seven publications [P1]-[P7] together with a few additional results related to the three different wave propagation problems that are simulated and optimized by parameter studies and topology optimization. The three wave problems are connected to each other through the two introductory chapters 2 and 3. Chapter 2 is a general introduction to elastic and optical 1
Page 1: Optimization of acoustic, optical a
Page 4 and 5: Title of the thesis: Optimization o
Page 6 and 7: Resumé (in Danish) Forskningsomr˚
Page 8 and 9: Publications The following publicat
Page 12 and 13: 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 60 and 61:
50 Chapter 6 Design of acousto-opti
Page 62 and 63:
Page 64 and 65:
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
Page 99:
Publication [P2] Design of photonic
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
Page 108 and 109:
Figure 4: The geometry of the cente
Page 110 and 111:
performance will decrease and some
Page 112 and 113:
[23] J. Riishede and O. Sigmund, In
Page 115 and 116:
Surface acoustic wave driven light
Page 117 and 118:
IDT GaAs AlGaAs 0.10 0.05 0.00 Ampl
Page 119:
Publication [P4] Improving the acou
Page 122 and 123:
083529-2 M. B. Dühring and O. Sigm
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 131:
Publication [P5] Design of acousto-
Page 134 and 135:
Figure 1: The geometry used in the
Page 136 and 137:
where ˜pijkl are the rotated strai
Page 138 and 139:
where ∂Φ ∂w R 2,n − i ∂Φ
Page 140 and 141:
Figure 3: The distribution of the o
Page 142 and 143:
[12] J.S. Jensen and O. Sigmund, To
Page 145 and 146:
Energy storage and dispersion of su
Page 147 and 148:
093504-3 Dühring, Laude, and Kheli
Page 149 and 150:
093504-5 Dühring, Laude, and Kheli
Page 151:
Publication [P7] Improving surface
Page 154 and 155:
FIG. 1: The geometry of the acousto
Page 156 and 157:
finer mesh. For the coupled model i
Page 158 and 159:
FIG. 4: Results for the finite mode
Page 160 and 161:
FIG. 6: Results for the acousto-opt
Page 162:
Suzuki, A. Onoe, T. Adachi and K. F
show all

Maria Bayard Dühring - Solid Mechanics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?