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Amplitude and Phase of Tightly Focused Laser Beams in Turbid Media

Focal field amplitude for a 1 um thick slab (a,b) and a 150 um thick slab (c,d). The amplitudes in the focal plane (xy) are given in (a) and (c), whereas (b) and (d) depict the xz cross sections. The insets show the phase pattern with values 0 (blue) and pi (orange), and have the same dimensions as the amplitude plots.

Depth dependence of the focal volume. (a) Relative coherent and incoherent amplitude of the x-polarized light. Incoherent amplitude is determined from the transmission of the light propagating along theta=0. (b) Full width at half maximum (FWHM) of the focal amplitude along lateral (solid squares) and axial dimensions (solid circles). Medium thickness is expressed in units of lstar=100um.

A number of coherent imaging microscopy technologies are transforming biomedical research. These technologies utilize high intensities of highly focused light and detect signals that provide images of important cell and tissue constituents (such as collagen and elastin) which help understand tissue function and morphology (such as wound healing). Examples of nonlinear coherent techniques are second-harmonic generation (SHG), third-harmonic generation (THG) and coherent anti-Stokes Raman scattering microscopy (CARS).

Because these techniques can be used in thick tissue samples, understanding how tissue turbidity affects the focal volume is key to understanding the imaging properties of laser scanning optical microscopies. The dimensions of the focal volume, combined with the intensity of the electric field and its coherent properties largely defines imaging capabilities in terms of resolution and signal strength. To answer that need, we have developed a framework that combines Electric Field Monte Carlo simulations with diffraction theory to determine the amplitude and phase properties of electric fields propagating in turbid tissue. Rather than simulating the propagation of photons with a precisely defined location in space, we characterize waves by tracking the direction of the wave vector k and the path length traveled in between Mie scattering effects. We capture the effect of scattering into a single coherent transport function G(k,k') of the tissue medium. The function G(k,k') describes the amplitude and coherence loss of a set of incoming wave vectors k by converting it into a new set of wave vectors k' upon traversal of the medium. The coherence transport function is then inserted into the diffraction integral to combine the effects of diffraction and turbidity on the propagation of the focused electric field. Using this method, we are able to calculate the complete diffraction-limited focal field, and provide the first view of how the focal field is affected by turbidity.

"Amplitude and Phase of Tightly Focused Laser Beams in Turbid Media", C.K. Hayakawa, V. Venugopalan, V.V. Krishnamachari and E.O. Potma, Physical Review Letters, 103(043903), 2009.
For more information please contact Carole Hayakawa (hayakawa@uci.edu)