Markus Selmke

Hot Brownian Motion

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.

Photothermal single-particle microscopy: detection of a nanolens.

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.

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.

Gaussian beam photothermal single particle microscopy

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.

Metal nanoparticle based all-optical photothermal light modulator.

We present a simple scheme for the manipulation of light intensity by light mediated by a dissipative process. The implementation employs the heat released by an optically excited plasmonic metal nanoparticle to control the size of an isotropic bubble in a nematic liquid crystal film. The nematic film is designed as a zero-order half-wave plate that rotates an incident probe light polarization by π/2 and is blocked by an analyzing polarizer behind the structure. The growing isotropic bubble disturbs the half-wave plate and causes the probe to be transmitted through the modulator structure. Our results demonstrate that dissipative processes may be advantageously used to control light by light.

Photothermal single particle microscopy using a single laser beam

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.

Twin-focus photothermal correlation spectroscopy

We introduce a novel concept for optical correlation spectroscopy of non-fluorescent absorbing nano-particles termed twin-focus photothermal correlation spectroscopy (Twin-PhoCS). This method exhibits a unique axial sensitivity, allowing for either the measurement of very slow axial dynamics or the determination of axial heterogeneities on sub-diffraction limited length-scales. To this end, the photothermal nano-lensing mechanism [Markus Selmke, Romy Schachoff, Marco Braun, and Frank Cichos, ACS Nano, 2012, 6(3), 2741] provides two sharply separated detection-subvolumes, comprising the twin-focus. The achieved axial sensitivity is superior to single detection-volume or dual-focus based fluorescence correlation spectroscopies. We demonstrate the sensitivity by measuring radiation-pressure induced flow velocities of diffusing 14 nm gold-colloids down to 10 nm ms−1 with the help of the provided analytical correlation functions.

Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics

Using Fermats least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens n(r)=n0+ΔnR/r is solved analytically. The solution gives a ray equation r(ϕ) that is closely related to Rutherford scattering trajectories; we therefore refer to this refraction process as “photonic Rutherford scattering.” It is shown that not only do the classical limits correspond but also the wave-mechanical pictures coincide—the time-independent Schrodingier equation and the Helmholtz equation permit the same mapping between the scattering of massive particles and optical scalar waves. Scattering of narrow beams of light finally recovers the classical trajectories. The analysis suggests that photothermal single-particle microscopy measures photonic Rutherford scattering in specific limits and allows for an individual single-scatterer probing. A macroscopic experiment is demonstrated to directly measure the scattering angle to impact parameter relation, whi...

Theory of Hot Brownian Motion

The erratic motion of suspended colloidal particles due to thermal fluctuations of the solvent molecules is well known as Brownian motion and has long found its theoretical explanation as an equilibrium phenomenon. In this work, we abandon the homogeneity of temperature and viscosity and address so-called hot Brownian motion [Rings et al., Phys. Rev. Lett., 2010, 105 (9), 090604] of (laser-)heated nanoparticles. We develop an effective Markovian equilibrium description for this non-equilibrium phenomenon by deriving the appropriate effective temperature and viscosity parameters from a generalized theory of fluctuating hydrodynamics. On the basis of our systematic mathematical formulation we propose a numerically accurate simplified model that yields analytical results.

Energy-redistribution signatures in transmission microscopy of Rayleigh and Mie particles

We describe the transmission characteristics for the interaction of an arbitrary beam with (possibly multilayered) spherical particles of arbitrary size and electric permeability. Within the generalized Lorenz-Mie theory, expressions that generalize the total cross sections to their fractional counterparts are presented, which allow for an analytic quantification of transmission signals, both on-axis and off-axis. For Gaussian (Davis) beams, the relative angular domain of collection as compared to the beams angle of divergence determines sensitively the shape and magnitude of the interference signal. Depending on the particles position within the beam, the transmission signatures related to a pure energy redistribution as well as to accompanying absorption are discussed for Rayleigh particles in terms of their complex-valued polarizability. Implications for positioning, temperature control, spectroscopy, and optimized extinction measurements are discussed.