Abstract

Nonlinear optical properties of collagen type-I are investigated in thin tissue sections of pig tendon as a research model using a complete polarimetric second-harmonic generation (P-SHG) microscopy technique called double Stokes-Mueller polarimetry (DSMP). Three complex-valued molecular susceptibility tensor component ratios are extracted. A significant retardance is observed between the chiral susceptibility component and the achiral components, while the achiral components appear to be in phase with each other. The DSMP formalism and microscopy measurements are further used to explain and experimentally validate the conditions required for SHG circular dichroism (SHG-CD) of collagen to occur. The SHG-CD can be observed with the microscope when: (i) the chiral second-order susceptibility tensor component has a non-zero value, (ii) a phase retardance is present between the chiral and achiral components of the second-order susceptibility tensor and (iii) the collagen fibres are tilted out of the image plane. Both positive and negative areas of SHG-CD are observed in microscopy images, which relates to the anti-parallel arrangement of collagen fibres in different fascicles of the tendon. The theoretical formalism and experimental validation of DSMP imaging technique opens new opportunities for ultrastructural characterisation of chiral molecules, in particular collagen, and provides basis for the interpretation of SHG-CD signals. The nonlinear imaging of chiroptical parameters offers new possibilities to further improve the diagnostic sensitivity and/or specificity of nonlinear label-free histopathology.

Highlights

  • Www.nature.com/scientificreports by the second-order nonlinear susceptibility tensor, χ(2), which contains information about the structure of the material and its spatial symmetry

  • In the double Stokes-Mueller polarimetry (DSMP) formalism for SHG, the sample is represented by a 4 × 9 double Mueller matrix, which defines the relation between the polarisation states of incoming laser beam and the polarisation states of the outgoing SHG signal from the sample

  • The imaginary parts of all susceptibility components are small at this cut angle, indicating that all the observable susceptibility components are in phase with each other and so real-valued

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Summary

Introduction

Www.nature.com/scientificreports by the second-order nonlinear susceptibility tensor, χ(2), which contains information about the structure of the material and its spatial symmetry. Thirty-six measurements are needed to determine the Mueller matrix, from which the real and imaginary parts of six observable laboratory-frame χ(2) tensor components can be extracted[36]. Using DSMP formalism and measurements, SHG-CD results can be related to the complex-valued chiral components of the susceptibility tensor and the 3D orientation of collagen fibres. From these laboratory-frame components, three molecular-frame complex-valued susceptibility tensor component ratios are calculated for the first time These reveal the presence of significant imaginary values of the chiral nonlinear susceptibility component, the phase and amplitude of which are extracted. DSMP theory is used to formulate the SHG-CD response in terms of complex susceptibility tensor components and to determine the theoretical conditions under which SHG-CD has non-zero values. The SHG-CD response is deduced from a subset of DSMP measurements for a research model and the aforementioned theoretical conditions are experimentally validated

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