Diattenuation and retardance signature of plasmonic gold nanorods in turbid media revealed by Mueller matrix polarimetry

Abstract

Plasmonic gold nanorods (GNRs) are finding increasing use in biomedicine due to their unique electromagnetic properties, optical contrast enhancement and biocompatibility; they also show promise as polarization contrast agents. However, quantification of their polarization-enhancing properties within heterogeneous turbid media remains challenging. We report on polarization response in controlled tissue phantoms consisting of dielectric microsphere scatterers with varying admixtures of GRNs. Experimental Mueller matrix measurements and polarization sensitive Monte-Carlo simulations show excellent agreement. Despite the GNRs' 3D random orientation and distribution in the strong multiply scattering background, significant linear diattenuation and retardance were observed. These exclusive measurable characteristics of GNRs suggest their potential uses as contrast enhancers for polarimetric assessment of turbid biological tissue.

Figure 1

Experimental polarimetry set up and system calibration for exact backscattering configuration. (a) Schematic diagram of the experimental polarimetry system for measurements in exact backscattering configuration, comprised of an excitation laser (λ = 633 nm), a polarization state generator unit (PSG: rotating linear polarizer P1 and quarter wave plate Q1), a polarization state analyzer unit (PSA: rotating quarter wave plate Q2 and linear polarizer P2), beam splitter (BS), collection lenses and a photodetector. Actual experimental form of the (b) PSG matrix W and (c) PSA matrix A. (d) The experimental Mueller matrix from a cuvette filled with distilled water resembles an identity matrix as expected, with individual elements exhibiting an error $\le 0.05$.

Figure 2

Polarization effects in microspheres-only phantom system. Dependence of the Mueller matrix-derived polarization parameters of a controlled turbid media (microsphere phantom) on the diameter and scattering coefficient. MC-simulated (red symbols) and experimentally obtained (black symbols) variations of the (a) diattenuation and (b) retardance with microsphere diameters for a fixed scattering coefficient ${\mathrm{\mu }}_S=102{\text{cm}}^{-1}$. Near zero diattenuation stems from isotropic nature of the spherical scatterers, and non-zero retardance ($\sim 1.5$ radians) likely arises from the detection geometry effects and particle diameters (for details, see text). The simulated (red symbols) and experimental (black symbols) variations of (c) diattenuation and (d) retardance with optical turbidity (${\mathrm{\mu }}_S$ range from 16 to 621 cm⁻¹) for a fixed scatterer diameter ($d=0.42\mathrm{\mu }$m) exhibit similar trends of near zero diattenuation and finite retardance (− 1.4 to 1.5 radians). The corresponding variation of the simulated and experimental degree of polarization with turbidity shown in (e). Note: in Figs. 2 and 3, symbols are experimental and simulations results, and lines are guides for the eye.

Figure 3

Polarization effects in a composite microsphere + GNRs phantom system. Mueller matrix simulated (red symbols) and experimentally obtained (black symbols) variation of the (a) diattenuation and (b) retardance with GNR's aspect ratio $\in$ for a fixed scattering coefficient of the composite system(${\mathrm{\mu }}_{{}_S}=102{\text{cm}}^{-1}$ due to microspheres plus $16{\text{cm}}^{-1}$ due to GNRs). Increasing diattenuation and retardance with aspect ratio suggests size-dependent increase of the optically anisotropic nature of GNRs. Simulated (red symbols) and experimental (black symbols) variation of diattenuation and retardance with GNRs concentration in a turbid phantom of fixed microsphere scattering properties (diameter = $0.42\mathrm{\mu }$m, ${\mathrm{\mu }}_S=102{\text{cm}}^{-1}$). The geometrical parameters of GNRs were length $l=70\text{nm}$ diameter $d=25\text{nm}$(aspect ratio $\in =2.8$). Both $D$ and $R$ exhibit significantly higher values (better contrast) at lower nanorod concentrations (${\mathrm{\mu }}_S=16{\text{cm}}^{-1}$), implying strong orthogonal dipolar plasmon polarizabilities even for 3D random orientations of GNRs (for details, see text). The corresponding variation of the simulated and experimental degree of polarization on the GNR concentration shown in (e).