Modeling the Generation and Propagation of Radially-Polarized Shear Waves in Tissue-Like Media

date November 30, 2012
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Friday, November 30, 2012 4:00 p.m. in ETC 4.150

Kyle S. Spratt
Applied Research Laboratories and Department of Mechanical Engineering
The University of Texas at Austin

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.