Modeling super-resolution SERS using a T-matrix method to elucidate molecule-nanoparticle coupling and the origins of localization errors

Abstract

A computational method to model diffraction-limited images from super-resolution surface-enhanced Raman scattering microscopy is introduced. Despite significant experimental progress in plasmon-based super-resolution imaging, theoretical predictions of the diffraction limited images remain a challenge. The method is used to calculate localization errors and image intensities for a single spherical gold nanoparticle-molecule system. The light scattering is calculated using a modification of generalized Mie (T-matrix) theory with a point dipole source and diffraction limited images are calculated using vectorial diffraction theory. The calculation produces the multipole expansion for each emitter and the coherent superposition of all fields. Imaging the constituent fields in addition to the total field provides new insight into the strong coupling between the molecule and the nanoparticle. Regardless of whether the molecular dipole moment is oriented parallel or perpendicular to the nanoparticle surface, the anisotropic excitation distorts the center of the nanoparticle as measured by the point spread function by approximately fifty percent of the particle radius toward to the molecule. Inspection of the nanoparticle multipoles reveals that distortion arises from a weak quadrupole resonance interfering with the dipole field in the nanoparticle. When the nanoparticle-molecule fields are in-phase, the distorted nanoparticle field dominates the observed image. When out-of-phase, the nanoparticle and molecule are of comparable intensity and interference between the two emitters dominates the observed image. The method is also applied to different wavelengths and particle radii. At off-resonant wavelengths, the method predicts images closer to the molecule not because of relative intensities but because of greater distortion in the nanoparticle. The method is a promising approach to improving the understanding of plasmon-enhanced super-resolution experiments.

Mislocalization in Plasmon-Enhanced Single-Molecule Fluorescence Microscopy as a Dynamical Young’s Interferometer

“…For spherical nanoantenna geometries, Mie theory provides a middle ground, combining analytical insight with simulation. Toward understanding the origins of mislocalization in surfaceenhanced Raman scattering, 26 generalized Mie theory has demonstrated the importance of interference among higherorder plasmon modes on image distortion when the molecule is located within the fluorescence quenching zone (≲5 nm from the nanoantenna surface) necessary for Raman scattering. Despite this body of work, to date, there has been no simple theoretical model that describes the mislocalization problem completely analytically.…”

$T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles

“…In conjunction with the definition of the single sphere SH Tmatrix (33), a relation between the SH external field expansion coefficients can now be derived:…”

“…The surface integral equations (SIEs) are usually satisfied on the boundary-surface of the homogeneous particle [25][26][27], by imposing appropriate boundary conditions, and numerically solved in the framework of the method of moments (MoM) [28]. Another way to solve SIEs is using the extended-boundary-condition (EBC) method, also called the null-field approach, initially introduced for the analysis of perfect electric conductors [29] and subsequently extended to dielectrics [30,31], multiparticle systems [32], and efficient analysis of Raman scattering from molecules [33]. In this method, the SIEs are imposed on two surfaces defined inside and outside of the physical interface, by exploiting the Huygens equivalence principle.…”

Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes

“…In consequence, the decomposition is used in many streams of research. Prime examples would be the study of optical nanoantennas [3][4][5][6][7] , the study of meta-atoms and metamaterials [8][9][10][11] or the analysis of the interaction of scatterers with isolated molecules [12][13][14] . Using the multipole expansion we can also construct the T-matrix of a scatterer that entirely expresses how an arbitrary incident field is scattered by the pertinent object 15,16 .…”