A Search and Discovery report in the September 2013 issue of Physics Today (page 14) describes interesting work by Chia Wei Hsu and colleagues on guided optical modes within the radiation continuum.1 Readers may be interested to know that surface states in the radiation continuum are well known in crystal acoustics. While surface acoustic waves (SAWs) are normally slower than bulk acoustic waves (see Physics Today, March 2002, page 42), crystal surfaces support so-called pseudo-SAWs, whose velocity exceeds the slow transverse bulk velocity.

Pseudo-SAWs are leaky because of their coupling to the radiation continuum of bulk modes, but in isolated propagation directions the coupling to bulk modes disappears and pure surface modes termed supersonic surface waves appear.2 Just as in optics, sometimes symmetry incompatibility is involved. For example, in a supersonic SAW found in the [110] direction on the basal plane of cubic crystals such as silicon and germanium, particles move in ellipses contained in the vertical (sagittal) plane, whereas the slow transverse wave is polarized in the horizontal direction orthogonal to that plane. As soon as the wavevector deviates from [110], symmetry incompatibility is lifted and the mode becomes leaky.

However, the same pseudo-SAW branch contains another isolated, pure-mode point in a totally inconspicuous direction.3 Such “secluded” surface-wave solutions within the radiation continuum that are unrelated to symmetry incompatibility are stable with respect to system perturbations such as a change in the orientation of the surface.4 Although the existence of supersonic SAWs on a bare substrate requires elastic anisotropy, we found a supersonic mode guided by a layer with a periodic mass loading on an isotropic substrate.5 The structure we considered was somewhat analogous to the photonic-crystal slab used by Hsu and colleagues, but with an important difference: In the acoustic case, there are two bulk modes, longitudinal and transverse; our guided mode was faster than the transverse but slower than the longitudinal. Whether a guided mode can be faster than any bulk wave is unclear, since it will require that the radiation into both bulk modes be canceled simultaneously.

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