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Point source in a phononic grating - stop bands give rise to phonon-focusing caustics

Video abstract for the article 'Point source in a phononic grating: stop bands give rise to phonon-focusing caustics' by Istvan A Veres, Dieter M Profunser, Alex A Maznev, Arthur G Every, Osamu Matsuda and Oliver B Wright (Istvan A Veres et al 2012 New J. Phys. 14 123015). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/14/12/123015/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. If you put a point source of waves in a flat grating, which way will the waves go? Surprisingly, this question has not been considered until now. For sound waves, such structures are 'phononic crystals', whose acoustic properties are engineered to vary periodically in space. Main results. We fire blue laser light pulses repetitively to thermoelastically excite high-pitched sound ripples, which are detected over a sub-millimetre area by infrared pulses. Our grating has microscopic copper and silica strips on a silicon slab, and is gold-coated. At low acoustic frequencies we see roughly circular ripples because the sound wavelength, about 10 microns, is much larger than the width of the grating bars. But at high frequencies, we see an unusual X-shaped pattern. Wave phenomena are usually discussed in k-space and in group-velocity space (see figure). From numerical simulations, as well as from an analytical approach, at low frequencies we get rounded shapes in both spaces, implying circular ripples. As the frequency increases we hit a band gap in the horizontal direction, a direction waves can't travel, visible through the opening of the circles in k-space. This makes two circles in group velocity space, producing the X-shaped pattern or caustics. Wider implications. So a point-wave source in a grating produces caustics related to the band gap. This effect should also be seen in a variety of spatially-periodic structures, and is not just confined to sound. It should be seen in optics, with water waves, or even with matter waves.