Keywords: surface acoustic waves, piezoelectric material, finite element analysis, perfectly matched layers, acousto-optic interaction.

This is a study of surface acoustic waves (SAW) generated by high aspect ratio (HAR) electrodes and their use for the design of integrated acousto-optical modulators. SAWs are extensively used in electromechanical filters and resonators for telecommunication [1] and a new application is modulation of optical waves [2]. In these applications SAWs are generated by interdigital transducers (IDTs) with limited electrode height such that the SAW mode properties are similar to the propagation on a free surface. In [3] it was shown by a finite element method/boundary element method algorithm that the SAW properties are significantly changed when HAR electrodes are used. Multimode SAW propagation was found and up to a ten-fold slowing of the SAW velocity was obtained. In [4] we introduced a periodic finite element model of a piezoelectric, anisotropic material to simulate the HAR electrodes. Perfectly matched layers (PML) were employed to absorb acoustic and electric disturbances propagating away from the surface [5]. With this model the mode shapes for the periodic structure could be plotted which showed that they all consisted of a combined vibration at the surface and in the electrode. This indicates that a part of the energy is trapped in the electrodes and therefore we here use the model to calculate the ratio of mechanical energy stored in the electrodes and observe that it increases with increasing electrode height. So the electrodes act as a mechanical resonator which slows down the SAW velocity.

This model is modified to examine the structure with a finite number of HAR electrodes by employing PLMs at the vertical borders. This shows that SAWs are generated and propagate out of the electrodes and a part of the energy is lost to bulk waves. An optical mode in a waveguide at the surface is then matched with the six acoustic modes. The strain is first calculated using the piezoelectric model which is then coupled to a model of the optical wave such that the change in effective refractive index (n_eff) is obtained. The change in n_eff is different for the six modes and for four of the modes the change is bigger than for the case with flat electrodes, as in a conventional IDT. This indicates that acousto-optical interaction can be improved when using SAWs generated by HAR electrodes.

1

K.-Y. Hashimoto, "Surface acoustic wave devices in telecommunications modeling and simulation", Springer, Berlin, 2000.

2

M.M. de Lima Jr., P.V. Santos, "Modulation of photonic structures by surface acoustic waves", Rep. Prog. Phys., 68, 1639-1701, 2005. doi:10.1088/0034-4885/68/7/R02

3

V. Laude, A. Khelif, T. Pastureaud, S. Ballandras, "Generally polarized acoustic waves trapped by high aspect ratio electrode gratings on piezoelectric substrates", J. Appl. Phys., 90, 5, 2492-2487, 2001. doi:10.1063/1.1394160

4

V. Laude, M.B. Dühring, H. Moubchir, N. Khelfaoui, A. Khelif, "Dispersion and polarization of surface waves trapped in high aspect ratio electrode arrays, IEEE Ultrason. Symp. Proc., paper 3E-3, New York, 2007.

5

M.B. Dühring, "Simulation and optimization of surface acoustic wave devices, Proceedings of 7th World Congress of Structural and Multidisciplinary Optimization, Seoul, Korea, COEX, 2007.

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