Maria Bayard Dühring - Solid Mechanics

mode in the waveguide. The topology optimization approach is based on the piezoelectric model and the
objective function is the squared absolute value of the normal strain in the vertical direction. It vas shown
that the objective function could be increased more than 2 orders of magnitude by the optimization where
several smaller air holes were created in the design domain that initially consisted of solid material. The
effect of the air holes is to trap the SAW in the design domain close to the waveguide and to make strain
concentrations around the holes that extend into the waveguide. The increased strain concentration
in the waveguide changes the refractive index components such that the periodic difference in effective
refractive index for the fundamental guided mode, as the SAW passes the waveguide, is increased 10
times compared to the initial design. So the topology optimization approach is a promising method to
improve acousto-optical interaction.
Further work includes testing of other objective functions that depend both on the strain components
and the strain-optical constants such that the refractive index component in the horizontal direction
is optimized directly. Finally, the constraint, that the design variables are assigned to entire columns
starting at the surface, can be introduced in order to get designs that are easier to fabricate.
7. Acknowledgements
This work received support from the Eurohorcs/ESF European Young Investigator Award (EURYI,
www.esf.org/euryi) through the grant ”Synthesis and topology optimization of optomechanical systems”
and from the Danish Center for Scientific Computing (DCSC). Also support from the EU Network of
Excellence ePIXnet is gratefully acknowledged. The author is thankful to Ole Sigmund and Jakob S.
Jensen from the Department of Mechanical Engineering, Technical University of Denmark, for helpful
discussions related to the presented work.
8. References
[1] R.M. White and F.W. Voltmer, Applied Physics Letters, 17, 314-316, 1965.
[2] K.-Y. Hashimoto, Surface acoustic wave devices in telecommunications, modeling and simulation,
Springer, Berlin, 2000.
[3] M.M. de Lima Jr. and P.V. Santos, Modulation of photonic structures by surface acoustic waves.
Reports on Progress in Physics, 68, 1639-1701, 2005.
[4] M.M. de Lima Jr., M. Beck, R. Hey and P.V. Santos, Compact Mach-Zehnder acousto-optic modulator,
Applied Physics Letters, 89, 121104, 2006.
[5] M. van der Poel, M. Beck, M.B. Dühring, M.M. de Lima, Jr., L.H. Frandsen, C. Peucheret, O.
Sigmund, U. Jahn, J.M. Hwam and P.V. Santos, proceedings of European Conference on Integrated
Optics and Technical Exhibition, Copenhagen, Denmark, April 25-27, 2007.
[6] M.B. Dühring and O. Sigmund, Improving the acousto-optical interaction in a Mach-Zehnder interferometer,
Journal of Applied Physics, in press, 2009.
[7] M.P. Bendsøe and O. Sigmund, Topology optimization, theory, methods and applications, Springer
Verlag Berlin, 2003, ISBN 3-540-42992-1.
[8] E. Wadbro and M. Berggren, Topology optimization of an acoustic horn, Computer Methods in
Applied Mechanics and Engineering 196, 420-436, 2006.
[9] G.H. Yoon, J.S. Jensen and O. Sigmund, Topology optimization of acoustic-structure interaction
problems using a mixed finite element formulation, International Journal for Numerical Methods
in Engineering 70, 1049-1075, 2007.
[10] J. Du and N. Olhoff, Minimization of sound radiation from vibrating bi-material structures using
topology optimization, Structural and Multidisciplinary Optimization, 33, 305-321, 2007.
[11] M.B. Dühring, J.S. Jensen and O. Sigmund, Acoustic design by topology optimization, Journal of
Sound and Vibration, 317, 557-575, 2008.
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