Friday, November 30, 2012 4:00 p.m. in ETC 4.150
In the past decade there has been an increasing interest in the optics literature regarding the unique characteristics of focused, radially-polarized light beams. Of particular interest is the existence of a longitudinal component to the electric field in the focal region of the beam, of comparable amplitude to the radial component and yet with a smaller beamwidth [cf. Q. Zhan, Adv. Opt. Photon. 1, 1-57 (2009)]. In the linear approximation there exists a direct analogy between these light beams and radially-polarized shear wave beams in incompressible elastic media, and hence we may interpret the results found in the optics literature as applying to low-frequency shear waves propagating through tissue-like media. Unlike a plane shear wave, such a radially-polarized beam is predicted to generate a significant second harmonic when propagating nonlinearly through a tissue-like medium, and we present an analytic solution for the second harmonic generated by a focused, radially-polarized shear wave beam with Gaussian amplitude shading. Lastly we consider the possibility of generating radially-polarized beams in an elastic half-space using a piston source pushing on the bounding surface of the solid. Using an angular spectrum approach to model such a source, we demonstrate how the near-incompressibility of tissue-like media, and the Poisson effect that takes place directly below such a piston source, can be exploited to generate a radially-polarized shear wave beam.