Below you will find a short summary of the research I am currently involved in or have been doing in the past.
Everyday Optics Phenomena
My most recent research activities have focused on everyday optics phenomena.
Among those studies is one on the beautiful caustics produced by glass of wine. Surprisingly, they share some aspects with the world of halos.
Another study was on the astroid caustics below individual floating bubbles on (soapy) water, along with its surprising relation to the long-known shadow sausage effect (see Adler 1967, Lock et al. 2003).
Artificial Halos & other Atmospheric Optics Phenomena
What began as a personal aha moment, a conscious experience of the quite common atmospheric optics phenomenon known colloquially as sun dogs, became quite a passion for me. Since then, I have followed that passion both in terms of efforts to photographically capture these often-times stunning displays, as well as efforts to scientifically approach the subject.
Although superb webpages dedicated to the collection of halo displays from all over the world exist, there is nothing quite like experiencing and capturing a prominent display on your own. My results of the effort are can be seen in the photography section of my page.
On the scholarly side, I have attempted to understand and unravel the details of the parhelic circle and its artificial counterparts. I have therefore recreated those in carefully designed experiments by using glass hexagons, resembling the natural ice prisms which cause halo displays. The insight gained from those studies resulted in two publications so far, along with software to reproduce and decompose rather exactly the intensity distribution experimentally observed over many decades in intensity. Embedded parhelia are readily observed and can be attributed to complex and adventurous paths the light takes through those crystals.
Further efforts have been directed towards the reproduction of various more complex halos, associated with non-trivial orientation classes.This has lead to the (maybe?) first-ever artificially reproduced Lowitz arc halos (see image on the right), as well as one of the first two circular 22° halo machines reported within the same year. Also, the construction of a modular machine covering many orientation classes allowed for a first-ever composition of an artificial complex halo display resembling more closely some of nature's most stunning displays.
My latest project in this direction has been the realization of a Parry halo box made of numerous small glass crystals. A further recent publication was on a classical rainbow demonstration experiment and a novel volumetric version of the glass bead bow experiment.
Photon Nudging / Artificial Brownian Micro-Swimmers
During my time as a post-doc in Princeton I collaborated on a project involving the steering and manipulation of microscopic artificial swimmers in a 3D liquid environment. Upon illumination with a laser operating at a suitable resonant wavelength, the anisotropic gold-capped polystyrene microspheres self-propel along their symmetry axis. Using this in combination with a live feedback monitoring setup (using a carefully calibrated and precision-adjusted darkfield microscopy and tracking setup equipped with a multiple APD feedback circuit to lock-on onto a particle in focus) allows for full 3D navigation in a liquid. This purposeful driving competes with non-directional random Brownian motion, rotational as well as translational.
The image on the left depicts the scenario in cartoon-style: whenever the particle randomly reorientates via thermal fluctuations such that its symmetry axis points towards an arbitrarily defined target position, the heating laser is switched on to drive the particle with a traget-directed velocity component towards it. The on- and off-times describing the statistics of these phases are well modeled by first-passage times and their distributions, whereas the overall positional statistics can be modeled by continuum physics, i.e. interpreting the velocity as a target directed influx competing with diffusion.
The theoretical description of this complex rotational-translational coupled stochastic system proved to be a rich problem. Combining thus concepts of both continuum fluid dynamics and stochastic first passage times, I have developed a framework describing the dynamics and average statistics of this feedback driven non-equilibrium thermodynamic system. The results will be published in a two-piece article to be submitted soon.
I have been working for about 4 years on the topic of photothermal (PT) microscopy. It is an imaging technique similar to fluorescence microscopy which is able to detect absorbing nanoparticles (NPs) of sizes down to 1nm and even single absorbing molecules. The particles must not be fluorescent and are the typically chosen metallic nanoparticles are inert and very stable, for instance gold NPs (AuNPs). Labeling with sulfur-functionalized AuNPs has the potential to complement biological studies that have previously been done with fluorescent organic moleucle markers and has the advantage of an unlimited observation time. My work has provided an intuitive and quantitative understanding of this important signal mechanism and will provide the theoretical standard for the promising future of this ever-more-popular technique.
The Principle of the PT Detection:
A resonant heating laser (for AuNPs: 532 nm, surface plasmon resonance) with a wavelength that is absorbed by the species of interest as well as a non-resonant probing laser (typically long wavelength, i.e. 635nm) are both focused co-axially onto the same sample. The heating laser is modulated at a high frequency of about 200kHz while the probing laser power transmitted through the sample and collected above is demodulated on the same frequency (i.e. its modulation amplitude obtained). The power absorbed by the NP and provided by the heating laser creates almost instantaneously a temperature profile T(r) around the particle. Since the refractive index of the embedding material (water, cell-plasma, polymer) is temperature depenent a corresponding profile n(r) of the refractive index is thereby created. The gradient of the refractive index thus generated with the frequency of the heating laser constitutes a thermal (divergent) lens. This lens affects the propagation of the probing laser and leads to a modulated transmitted power which is detected with a photodiode. Demodulation and normalization by the background detected power yields the rel. photothermal signal.
For an illustration of the photothermal signal phenomenology, see the interactive Photothermal Microscopy Simulator!
The typical experimental setup for PT microscopy is very similar to a regular confocal microscope. One micoscope objective focuses the laser beams onto the sample while a second one collects the transmitted beams behind the sample. The transmitted light is then separated with a dichroic mirror and the sample can be scanned with the piezo-scanner onto which the sample is mounted. Typical collected intensities for such particle scans are shown in the image. The corresponding laser beam intensities (PSF, point spread functions) are shown, too. The theory of the observable checker-board like patterns extends the generalized Lorenz Mie theory (GLMT) and has been developed over the past 2 years to perfectly match the observation (see published papers, ACS Nano). The Mie-Theory is the framework of light-particle interaction (spherical in shape) which predicts rainbows and halos.
I have adapted the 100year old Mie-Theory for the purpose of this very special kind of light-particle interaction by the extension of the already generalized Mie theory (which was adapted by G. Gouesbet et al. to non-planar waves) to finite collection angle domains. This important extension then allows the calculation of the collected transmitted power after the light - particle/refractive index gradient interaction. The refractive index gradient (hot environment) around the particle has been included by the discretization into a finely layered sphere with the public c-code scatnlay.
The scatter-images and the absorbed power map (i.e. the point-spread-function PSF of the high-NA illumination used in the experiments) as calculated with the theory as presented in the ACS Nano paper (see also image above) are availiable as printable obj.-files on the homepage of the 3D-printing service shapeways. You may find a variety of printible versions on my personal shapeways-page.
The Photothermal Signal Theory:
My major contribution (see publushed papers) to the field has been the theoretical descricption and quantification of the rel. PT signal magnitude and shape. No model capable of predicting the PT signal magnitude nor a model for the various parameter dependencies did exist. I have therefore developed 3 different models of varying degree of abstraction and accuracy, all of which are quantitative to within at least a factor 2 and all of which correctly reproduce the entire phenomenology enountered in the experiments. The quantification of the signal becomes valuable if one wishes to determine absorption coefficients of nano-particles, while the signal shape unveiled by the experiments and theories leads to the developement of a special kind of correlation spectroscopy (TwinPhoCS, twin-focus phototh. corr. spectr.).
Photonic Rutherford Scattering:
Photonic Rutherford scattering is the wave- and ray-optical analogy of the photothermal scatterin process with QM- and classical Rutherford / Coulomb scattering of charged particles.
Hot Brownian Motion:
The diffusion of colloidal particles by the thermal agitation due to stochastic forcing by solven particles has been termed "Brownian Motion", named after Robert Brown who discovered it first by looking at pollens under a microscope. The erratic motion is a universial and important concept not only in biology , where it describes the transport of relevant molecule and protein species as well as the nutrition uptake in cells, related to the meanfield concept of diffusion.
I have been involved in a project (cooperation with the theory department) describing the Brownian motion of hot particles such as AuNPs which carry around with them a temperature field (a "hot halo", see picture) created by the power-uptake from a heating laser. The "Hot Brownian Motion" theory describes this special kind of non-equilibrium phenomenon and is of interest to the ever-growing optical tweezer-community.
Photothermal (Cross-) Correlation Spectroscopy (PhoCS):
The (hot) brownian motion of absorbing particles can be studied by PhoCS, Photothermal Correlation Spectroscopy. The PT signal is recorded in a time-trace. Whenever a particle moves through the focus, a signal burst is detected. The correlation of these data-sets yields information on the mobility of the diffusing species, or vice versa the viscosity of the solute (cell-plasma, cell-tissue, membrane, water, glycerol). I have derived analytical expressions for the autocorrelation functions and the signal histograms of such traces. This opens the field for future quantitative studies on absorbing particles where previously photobleaching fluorophores molecules were used.
Photothermal Signal Distribution Analysis (PhoSDA):
This technique rests on the analysis of the occurrence statistics of the magnitudes of photothermal signals as recorded for absorbing particles in solution. The theory as presented in the article (see published papers) incorporates the general twin-focal detection volume in PT microscopy and provides fit functions for the data. Heterogeneous particle size distributions are hereby resolvable which are otherwise unresolvable by PhoCS alone.
Single Molecule Dynamics in Polymers
I have worked for some time on the rotational dynamics of single fluorescent molecules embedded in polymers. They perform, similar to translational Brownian motion, a random reorientational Brownian motion, i.e. a rotational diffusion. The time-scale on which they reorient is a measure for the viscosity of the environment. Although the theoretical description is based on a continuum-mechanical concept of rotational drag in a newtonian liquid (Stokes-Einstein Relation), we have nontheless shown it to be correct down to a single randomly rotating molecule in a polymer close to its glass-transition temperature (close to its kinetic freezing). (see published papers)
Rotational Brownian motion may be envisaged as regular translational Brownian motion of the orientation-vector on the surface of a sphere (see image). Since the fluorescent molecules used are dipole-emitters (the transotion dipole-moment of the electronic transition is rigidly connected to the orientation of the molecule), the collected intensity and polarization collected with the microscope objective above the sample depends on the molecules' oreintation (see Dipole radiation here). This allows the extraction of the orientation dynamics either with pattern analysis in defocused imaging, or via the analysis of two polarization channels.
In connection with this topic I have worked with the wavelet analysis method, correlation analysis of the recorded linear dichroisms of single molecules and extensive and automated image analysis (incl. pattern recognition) and ensemble statistics of molecules.
In a cooperation with the mop-group at the Leipzig University dielectric measurements on our thin polymer films of PMA (poly-methyl acrylate) have been performed. The measurements of the complex dielectric constant covered the frequency and temperature dependence and yields the dynamics of the chain-segments of the polymer. I have analysed them with the 11-parameter semi-empirical Havriliak-Negami model and compared them to our finding from the single-molecule experiments. These studies are carried on on our group and will be published soon.