Combining quantitative photothermal microscopy and light scattering microscopy as well as accurate MIE scattering calculations on single gold nanoparticles, we reveal that the mechanism of photothermal single-molecule/particle detection is quantitatively explained by a nanolensing effect. The lensing action is the result of the long-range character of the refractive index profile. It splits the focal detection volume into two regions. Our results lay the foundation for future developments and quantitative applications of single-molecule absorption microscopy.

We derive the markovian description for the nonequilibrium brownian motion of a heated nanoparticle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nanoparticles and provide a practical rational basis for emerging photothermal tracer and nanoparticle trapping and tracking techniques.

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.

Temperature dependent measurements of the rotational diffusion of single dye molecules in the polymer poly(methyl acrylate) (PMA) are presented and compared to shear viscosity data and numerical simulations of the rotational diffusion process. It is found that single molecule rotational diffusion very accurately follows the Debye-Stokes-Einstein predictions for the shear viscosity without any additional parameter. We employ a simple model of dynamic changes of the rotational speed of a single molecule. This dynamic heterogeneity model is based on a Gaussian distribution of activation energies in a VFTH (Vogel-Fulcher-Tammann-Hesse) type temperature dependence of the polymer viscosity. The simulations explain all experimental details concerning the stretched exponential single molecule relaxation dynamics and the related distributions. They also reveal that the observed distributions are related to the intrinsic physical properties of the polymer but do not in general reflect the instantaneous spread of local viscous properties.

We explore the intuitive lensing picture of laser-heated nanoparticles occurring in single particle photothermal (PT) microscopy. The effective focal length of the thermal lens (TL) is derived from a ray-optics treatment and used to transform the probing focused Gaussian beam with ABCD Gaussian matrix optics. The relative PT signal is obtained from the relative beam-waist change far from the TL. The analytical expression is semiquantitative, capable of describing the entire phenomenology of single particle PT microscopy, and shows that the signal is the product of the point-spread functions of the involved lasers times a linear function of the axial coordinate. The presented particularly simple and intuitive Gaussian beam lensing picture compares favorably to the experimental results for 60 nm gold nanoparticles and provides the prescription for optimum setup calibration.

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Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments. It uses a weak laser to stochastically and adaptively turn on and off the swimmer's propulsion when the swimmer, through rotational diffusion, points towards or away from its target, respectively. This contribution presents a theoretical framework for the statistics of both 2D and 3D controls. The main results are: the on- and off-time distributions for the controlling laser, the arrival time statistics for the swimmer to reach a remote target, and how the experimentally accessible control parameters influence the control, e.g., the optimal acceptance angle for directed transport. The results are general in that they are independent of the propulsion or the actuation mechanisms. They provide a concrete physical picture for how a single artificial micro-swimmer could be navigated under thermal fluctuations-insights that could also be useful for understanding biological micro-swimmers.

We introduce a single-laser-beam photothermal microscopy scheme for the detection of single absorbing nano-objects. Here, a modulated incident laser beam with a constant intensity offset serves as pump and probe beam at the same time. Using the out-of-phase scattering response of the retarded thermorefractive wave field, the method provides a selective contrast for absorbers over a possible background of scatterers. The use of a single wavelength and a single beam, considerably simplifies the setup and integration of photothermal detection in existing microscopy schemes.