A polarimetric second harmonic generation (SHG) microscope was used to analyze the dependence between polarization and SHG signal from collagen-based samples. A theoretical model was also developed to investigate the SHG intensity as a function of different polarization states for a set of quasiparallel fibers. Numerical simulations were compared to experimental SHG intensity values and a fairly good agreement was found. Linear polarized light produced periodical changes in the emitted SHG signal with a maximum of intensity corresponding to polarization parallel to the main orientation of the fibers, regardless the ratio of hyperpolarizabilities, ρρ . A similar behavior was found for elliptical states located along a vertical meridian on the Poincaré sphere (i.e., null azimuth) although the modulation of the SHG signal was different. Our numerical calculations described a dramatic change in this regular trend when ρρ changed from positive to negative values. Moreover, we provide an experimental method (based on the analysis of the modulation of the SHG signal) to determine the value of the ratio ρρ and, consequently, to obtain information about the internal organization of the collagen fibers.

We analyze the tunneling-time problem via the presence time formalism. With this method we reproduce previous results for very long wave packets and we are able to calculate the tunneling time for general wave packets of arbitrary shape and length. The tunneling time for a general wave packet is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wave packet evolution.

The spatial distribution of second harmonic generation (SHG) signal from collagen fibers for incident elliptical polarized light has been modeled. The beam was assumed to focus on a horizontal fiber through a microscope objective. For elliptical polarized states located along a vertical meridian of the Poincare sphere, the SHG intensity has been optimized in terms of the incident wavelength and the numerical aperture (NA) of the objective. Our results show that polarization modulates the SHG signal. Elliptical polarization can generate high signals (even greater than those corresponding to linear polarization) when combined with appropriate values of both incident wavelength and NA. On the other hand, the SHG intensity might also be identically zero for particular elliptical polarization states, a condition that depends exclusively on the ratio of hyperpolarizabilities of the collagen fibers. The highest forward-to-backward SHG signal distribution occurs along the propagating direction, depends on the incident wavelength, and reduces when NA increases. Furthermore, the direction of maximum SHG emission was found to be more sensitive to changes in the NA rather than variations in the incident wavelength. These findings could help to optimize the experimental conditions of multiphoton microscopes and to increase SHG signals from biological tissues containing collagen.

Collagen organization has been analyzed at both external and internal scales by combining Stokesvector polarimetry and second harmonic generation microscopy. A significant linear relationship between the diattenuation and the external collagen organization was found. The dominant orientation of the collagen fibers was found to run parallel to the axis of diattenuation. Information on the collagen chirality was obtained from the circular dichroism, which showed also a strong dependence with the internal collagen organization. The results show that certain polarimetric parameters might be useful to extract quantitative information and characterize collagen arrangement.

The response to polarization of second-harmonic generation (SHG) microscopy images of samples with different collagen distributions (quasialigned, partially organized, and nonorganized) has been analyzed. A linear decay relationship between the external arrangement and polarization sensitivity was found. SHG signal from nonorganized samples presented a large structural dispersion and a weak dependence with incident polarization. Polarization dependence is also associated with the internal organization of the collagen fibers, directly related to the ratio of hyperpolarizabilities ρ. This parameter can experimentally be computed from the modulation of the SHG signal. The results show that both external and internal collagen structures are closely related. This provides a tool to obtain information of internal properties from the polarimetric response of the external spatial distribution of collagen, which might be useful in clinical diagnosis of pathologies related to changes in collagen structure.