Light scattering and transmission of Gaussian (G) and Laguerre-Gaussian (LG) vortex beams with different orbital angular momentum (L) in various turbid media were investigated. Transmittance was measured with varied ratios of sample thickness (z) to scattering mean free path (l_s) of turbid media, z/l_s. In the ballistic region, the LG and G beams were found to have no significant difference on transmittance, while in the diffusive region, the LG beams showed a higher received signal than the G beams, and the LG beams with higher L values showed a higher received signal than those with lower L values. The transition points from ballistic to diffusive regions for different scattering media were determined. This newly observed transmittance difference of LG and G beams may be used for deep target detection in turbid media through LG beam imaging.

With the use of longer near-infrared (NIR) wavelengths, image quality can be increased due to less scattering (described by the inverse wavelength power dependence 1/λ(n) where n ≥ 1 ) and minimal absorption from water molecules. Longer NIR windows, known as the second (1100 nm to 1350 nm) and third (1600 to 1870 nm) NIR windows are utilized to penetrate more deeply into tissue media and produce high-quality images. An NIR supercontinuum (SC) laser light source, with wavelengths in the second and third NIR optical windows to image tissue provides ballistic imaging of tissue. The SC ballistic beam can penetrate depths of up to 10 mm through tissue.

Light transmission of Gaussian (G) and Laguerre-Gaussian (LG) vortex beams in mouse brain tissue is investigated. Transmittance is measured with different orbital angular momentums (OAM) at various tissue thicknesses. In both ballistic and diffusive regions, transmittances of G and LG beams show no significant difference. The transition point from ballistic to diffusive region for the mouse brain tissue is determined at about 480 µm. The observed transmittances of the G and LG beams show independence on OAM modes, which may be attributed to poorly understood interference effects from brain tissue.

We detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These tree-level four-point scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of q-analysis. We interpret the Coon amplitude as a q-deformation of the Veneziano amplitude for all q ≥ 0 and discover a new transcendental structure in its low-energy expansion. We show that there is no analogous q-deformation of the Virasoro amplitude.

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