A theoretical model that deals with SHG from crystallized type I collagen fiber formed by a bundle of fibrils is established. By introducing a density distribution function of dipoles within fibrils assembly into the dipole theory and combining with structural order (m,l) parameters revealed by quasi-phase-matching (QPM) theory, our established theoretical model comprehensively characterizes both biophysical features of collagen dipoles and the crystalline characteristics of collagen fiber. This new model quantitatively reveals the 3-D distribution of second-harmonic generation (SHG) emission angle (θ,φ) in accordance with the emission power. Results show that fibrils diameter d1 and structural order m, which describes the structural characteristics of collagen fiber along the incident light propagation direction has significant influence on backward/forward SHG emission. The decrease of fibrils diameter d1 induces an increase of the peak SHG emission angle θmax. As d1 decreases to a threshold value, in our case it is around d1 = 150 nm when (m,l) = (1,0), θmax > 90 deg, indicating that backward SHG emission appears. The SHG may have two symmetrical emission distribution lobes or may have only one or two unsymmetrical emission lobes with unequal emission power, depending on the functional area of (m,l) on d1.
In biological tissue, the relative strongly SHG (second-harmonic Generation) will be shown in the collagen and the
cell membrane with dye molecules under the irradiation of laser. The SHG has a broad prospect in detecting and imaging
of the biological tissue for its non-phototoxicity and non-photobleaching. In biological tissue, not only the SHG intensity
and emission angle will have more obvious change, but also the spectrum of the SHG will be subject to certain changes
when the temperature in the outside world and its structure got a obviously change. According to Kuzyk and Kruhlak's
dipole-free sum-over-states theory which gives a introduction for the nonlinear susceptibilities, the relationship between
hyperpolarizability of biological tissue, environment temperature and biological tissue's structure is shown in
mathematics. In the conditions of control the temperature in experiments, the biological tissue's structure shift can be
detected by analyze the SHG spectrum of biological. Also diverse biological tissues' differences in structure can be
demonstrated in the spectrum. The change of SHG spectrum for the same biological tissue with environment temperature
is discussed. Therefore, SHG spectroscopy analysis provides a new technology for the process of biological tissue
lesions. Beside, this research gives a theory results provided by environment temperature which give an explanation for
experiment result.
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