The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, <δ>. A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.

Collagen (type I) fibers are readily visualized with second harmonic generation (SHG) microscopy though the molecular origin of the signal has not yet been elucidated. In this study, the molecular origin of SHG from type I collagen is investigated using the time-dependent coupled perturbed Hartree-Fock calculations of the hyperpolarizibilities of glycine, proline, and hydroxyproline. Two effective nonlinear dipoles are found to orient in-the-plane of the amino acids, with one of the dipoles aligning close to the pitch orientation in the triple-helix, which provides the dominant contribution to the SHG polarization properties. The calculated hyperpolarizability tensor element ratios for the collagen triple-helix models: [(Gly3)n]3, [(Gly-Pro2)n]3, and [(Gly-Pro-Hyp)n]3, are used to predict the second-order nonlinear susceptibility ratios, χ(zzz)(2)/χ(iiz)(2) and χ(zii)(2)/χ(iiz)(2) of collagen fibers. From SHG microscopy polarization in, polarization out (PIPO) measurements of type I collagen in human lung tissue, a theoretical method is used to extract the triple-helix orientation angle with respect to the collagen fiber. The study shows the dominant role of amino acid orientation in the triple-helix for determining the polarization properties of SHG and provides a method for determining the triple-helix orientation angle in the collagen fibers.

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy-momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.

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The generalized Born−Infeld electrodynamics with two parameters is investigated. In this model the propagation of a linearly polarized laser beam in the external transverse magnetic field is considered. It was shown that there is the effect of vacuum birefringence, and we evaluate induced ellipticity. The upper bounds on the combination of parameters introduced from the experimental data of BRST and PVLAS Collaborations were obtained. When two parameters are equal to each other, we arrive at Born−Infeld electrodynamics and the effect of vacuum birefringence vanishes. We find the canonical and symmetrical Belinfante energy-momentum tensors. The trace of the energy-momentum tensor is not zero and the dilatation symmetry is broken. The four-divergence of the dilatation current is equal to the trace of the Belinfante energy-momentum tensor and is proportional to the parameter (with the dimension of the field strength) of the model. The dual symmetry is also broken in the model considered.

With polarization dependent second harmonic generation (SHG) microscopy becoming a more popular method for investigating the structure of biological materials, there is a need to develop tools with which to understand and interpret the observed SHG properties. Quantum mechanical calculations of the hyperpolarizability tensor have become a popular method for understanding the SHG properties of biomolecules. Visualization of the full hyperpolarizability tensor, termed the unit sphere representation, has been developed to provide insight and intuition on the relationship between SHG properties and molecules. A single vector representation is also presented, which approximates the SHG properties of molecules for certain cases, where the anisotropy is negligible.

A new model of nonlinear electrodynamics with a dimensional parameter β coupled to gravity is considered. We show that an accelerated expansion of the universe takes place if the nonlinear electromagnetic field is the source of the gravitational field. A pure magnetic universe is investigated and the magnetic field drives the universe to accelerate. In this model, after the big bang, the universe undergoes inflation, and the accelerated expansion and then decelerates approaching Minkowski spacetime asymptotically. We demonstrate the causality of the model and a classical stability at the deceleration phase.

Polarization‐dependent second‐harmonic generation (P‐SHG) microscopy is used to characterize molecular nonlinear optical properties of collagen and determine a three‐dimensional (3D) orientation map of collagen fibers within a pig tendon. C6 symmetry is used to determine the nonlinear susceptibility tensor components ratios in the molecular frame of reference χzzz2/χzxx2 and χxyz2/χzxx2, where the latter is a newly extracted parameter from the P‐SHG images and is related to the chiral structure of collagen. The χxyz2/χzxx2 is observed for collagen fibers tilted out of the image plane, and can have positive or negative values, revealing the relative polarity of collagen fibers within the tissue. The P‐SHG imaging was performed using a linear polarization‐in polarization‐out (PIPO) method on thin sections of pig tendon cut at different angles. The nonlinear chiral properties of collagen can be used to construct the 3D organization of collagen in the tissue and determine the orientation‐independent molecular susceptibility ratios of collagen fibers in the molecular frame of reference.