Nano-lens diffraction around a single heated nano particle

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 [Appl. Opt. 34, 41-50 (1995)], [Jpn. J. Appl. Phys. 45, 7141-7151 (2006)], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic scattering treatment was established [Phys. Rev. B 73, 045424 (2006)] during the emergence of this new technique. Our recent study [ACS Nano, DOI: 10.1021/nn300181h] extended this approach into a full ab-initio model 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 generalized Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial photothermal 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 presented model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.