Nano-lens diffraction around a single heated nano particle

TL;DR

This paper presents an analytical diffraction model for a nano-lens effect around heated nanoparticles, clarifying the photothermal signal mechanism and enabling estimation of signal shape and magnitude in microscopy.

Contribution

It introduces a simplified analytical diffraction model that captures the lens-like action of heated nanoparticles, extending previous electrodynamic approaches.

Findings

The model provides explicit expressions for the axial signal shape and magnitude.

The lens-like mechanism explains the photothermal signal despite nanoscopic origins.

Gouy-phase does not influence the forward photothermal signal.

Abstract

The action of a nanoscopic spherically symmetric refractive index profile on a focused Gaussian beam may easily be envisaged as the action of a phase-modifying element, i.e. a lens: Rays traversing the inhomogeneous refractive index field n(r) collect an additional phase along their trajectory which advances or retards their phase with respect to the unperturbed ray. This lens-like action has long been understood as being the mechanism behind the signal of thin sample photothermal absorption measurements [1, 2], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic (EM) scattering treatment was established [3] during the emergence of this new technique. Our recent study extended [4] this EM-approach into a full ab-initio model describing the reality of the situation encountered and showed for the first time that the mechanism behind the signal, despite its nanoscopic origin, is also the lens-like action of the induced refractive index profile only hidden in the complicated guise of the theoretical Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial PT signal shape and magnitude and its angular distribution, all showing the clear lens-signature. It is further demonstrated, that the Gouy-phase of a Gaussian beam does not contribute to the relative photothermal signal in forward direction, a fact which is not easily evident from the more rigorous EM treatment. The model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.