Page 10 - Jan2013

ic crystals.15 It is known that such crystals exhibit very inter- esting filtering properties of interest in electronics and in seismology. Negative refraction for instance is found within this framework. Recently potential applications have been envisaged in which transformation of external bulk waves into phononic crystal propagation modes are considered. Although more complex than a corrugated surface, certain physical phenomena such as conversion into Scholte- Stoneley waves have been found already. Therefore one might expect continued interest in the diffraction phenomena at least for one more decade.
In what follows, a brief overview of a number of selected phenomena studied in the recent past with concise explana- tion and historical context will be presented.
Ultrasonic diffraction on periodic micro-structures
When ultrasound impinges a periodically corrugated material, it either scatters as it would on a regular surface, or it diffracts like light diffracts on a compact disk. Figure 1 shows an optical image of the cross section of a corrugated brass sample.
When frequencies are used resulting in wavelengths of the order of magnitude of the periodicity of the structure, it would diffract. However, as in Fig. 2, when a scan is made of such a sample at frequencies high enough to avoid diffraction, results are obtained showing good images of the corrugation.
If incident sound having a wavelength of the same order of magnitude as the corrugation periodicity is used, inter- esting diffraction effects occur. One such effect is the appearance of Wood anomalies in diffraction spectra of sound impinging the corrugated surface at normal inci- dence. In the 1980’s and the 1990’s such anomaly frequen- cies were used to generate Scholte-Stoneley waves on solids immersed in water.
In Fig. 3 experimental zero order reflection spectra are depicted, obtained using normally incident longitudinal waves impinging, from the waterside, a solid-water periodi- cally corrugated surface.
In this framework one can seek optimization of surfaces to enhance surface wave stimulation.18 Other anomalies also exist and they are, of course, not limited to normal incident sound. As a natural consequence, corrugated surfaces can be used to polarize ultrasonic waves.19,20 They can also be used as sophisticated filters for complex frequencies (transient sig- nals)21,22 or to direct sound in particular directions in 3- dimensional space23 when using 2-dimensional (doubly) cor- rugated surfaces.
Before we move on to a very interesting physical phenom- enon it is important to mention that diffraction effects can also be exploited in air-coupled applications. A recent example is the measurement of the thickness of cylinders in a dry envi- ronment. Indeed Bragg scattering of sound on periodically stacked cylinders reveals, with high accuracy,24 the cylinder diameter and is a rather easy technique to apply in industries such as steal-cord fabrication or even the pasta industry.
Perhaps a much more exciting phenomenon from a physical acoustics point of view is the backward displacement of beams when reflected off of a periodic structure. Breazeale
Fig. 1. Optical side view of a corrugated brass sample; Λ = 515 μm, h = 238 μm.16
Fig. 3. Experimental normal reflection spectrum into water for a brass – water interface, Λ = 25 μm =, h = 66 μm. These results have been extracted from17 as a representative example of the research undertaken on this subject in the 1980’s. The labels STn are added to show where anomalies appear that are related to the gener- ation of Scholte-Stoneley waves.
and Torbett1 performed experiments in the 1970’s to deter- mine whether there was an acoustic analogue of the optical Goos-Hänchen effect.
The Goos-Hänchen effect2 predicts that light incident near the critical angle on a dielectric interface from an opti- cally denser medium has a reflected beam that is laterally shifted from the position predicted by geometrical optics. The incident light beam transfers a portion of its energy into the optically rarer medium and excites an electromag- netic field that travels longitudinally for a certain distance along the interface. This energy is leaked back into the denser medium and interferes with the specularly reflected beam. This interference results in a reflected beam which exhibits a lateral displacement that appears as a forward beam shift. More complex structures such as multilayered media and periodically corrugated configurations of the
Fig. 2. An ultrasonic image of the sample presented in Fig. 1, based on a C-scan technique in which (in this example) the difference between the maximum ampli- tude of the plateau reflection and that of the valley reflection is represented by a color.16
Diffraction by Periodic Structures 9