Determination of the mode shapes of energy trapping resonators using X-ray topography

This paper considers the determination of the mode shapes using x-ray topography and the application of this method to resonant piezoelectric devices made of various materials (Quartz, LGS, Lithium tantalate). The basis of the method is recalled briefly and its application to thickness mode resonators or filters is particularly considered. A comparison of the observed mode shapes with those computed using the “essentially thickness mode” theory of H. F. Tiersten indicates that this theory give very good results concerning the modes shapes and the properties of the thickness mode devices even when materials presenting large coupling coefficients are used.