Photothermal Single Particle Detection in Theory & Experiments

The dissertation presents theoretical and experimental studies on the physical origin of the signal in photothermal microscopy of single particles. This noninvasive optical far field microscopy scheme allows the imaging and detection of single absorbing nanoparticles. Based on a heat-induced pertur- bation in the refractive index in the embedding medium of the nanoscopic absorber, a corresponding probe beam modification is measured and quantified. The method is well established and has been applied since its first demonstration in 2002 to the imaging and characterization of various absorbing particle species, such as quantum dots, single molecules and nanoparticles of different shapes. The extensive theoretical developments presented in this thesis provide the first quantitative assess- ment of the signal and at the same time enlarge its phenomenology and thereby its potential. On the basis of several approximation schemes to the Maxwell equations, which fundamentally gov- ern the interaction of light with inhomogeneities, several complementing models are devised which describe the photothermal signal both qualitatively and quantitatively. In succession an interdepen- dent and self-consistent set of theoretical descriptions is given and allows important experimental consequences to be drawn. In consequence, the photothermal signal is shown to correspond to the action of a nanoscopic (thermal) lens, represented by the spherically symmetric refractive index pro- file n(r) which accompanies the thermal expansion of the absorber’s environment. The achieved quantification allows the direct measurement of absorption cross-sections of nanoparticles. Further, a qualitatively new phenomenology of the signal is unraveled and experimentally demonstrated. The separate roles of the probing and the heating beams in photothermal microscopy is dismantled and the influence of their relative alignment shown to allow for a controlled adjustment of the effective detection volume. For the first time, both positive and negative signals are demonstrated to occur and to be the characteristic signature of the lens-like action on the probe beam. The detection of the probe beam’s modification is also shown to sensitively depend on the aperture used in the detection chan- nel, and a signal optimization is shown to be feasible. Also, a generalization of the detectable signal via the use of a quadrant photodiode is achieved. Specifically, measuring the far field beam deflec- tion the result of the beam passing the lens off-center manifests in a laterally split detection volume. Hereby, finally each classical photothermal spectroscopic techniques has been shown to possess its microscopic counterpart. Central to the understanding of this generalized and new phenomenology is a scalar wave-optical model which draws an analogy between the scattering of a massive particle wave-packet by a Coulomb potential and the deflection of a focused beam by a photonic potential connected with the thermal lens. The significance of the findings is demonstrated by its methodological implications on photother- mal correlation spectroscopy in which the diffusion dynamics of absorbing colloidal particles can be studied. The unique split focal detection volumes are shown to allow the sensitive measurement of a deterministic velocity field. Finally, the method is supplemented by a newly introduced sta- tistical analysis method which is capable of characterizing samples containing a heterogeneous size distribution.:Contents Bibliographic description Abbreviations 1 Introduction 2 Theoretical Background 2.1 The current literature on the subject of the photothermal signal 2.2 Thermal conduction, and the temperature field around heated nanoparticles 2.3 The linear thermo-refractive response and the thermal lens 2.4 MAXWELL equations and approximation schemes 2.4.1 The MAXWELL equations 2.4.2 HELMHOLTZ equations 2.4.3 Paraxial HELMHOLTZ equation for the field components 2.4.4 Geometrical optics and the eikonal ansatz 2.5 Diffraction and the optical resolution limit in far field microscopy 2.5.1 Transmission scanning microscopy 2.5.2 Point spread functions and aberrations 2.5.3 Scalar diffraction approximation for weakly focused beams 2.5.4 Vectorial diffraction for highly focused electromagnetic fields 2.5.5 Theoretical description of transmission signals 2.6 Elastic scattering of light 2.6.1 Overview of optical elastic scattering theory 2.6.2 The integral equation of potential scattering and the BORN approximation 2.6.3 The generalized LORENZ-MIE theory 2.6.4 The electromagnetic fields 2.6.5 Description of the incident field: beam shape coefficients 2.6.6 Multilayered scatterers 2.6.7 POYNTING vector and field decomposition 2.6.8 Energy balance & total cross-sections 2.6.9 Optical theorem & the extinction paradox 2.6.10 Small particle scattering: the RAYLEIGH-limit 2.7 Optical properties of gold nanoparticles & Surface plasmon resonances 2.7.1 Dielectric function of gold 2.7.2 Total cross-sections of plasmonic nanoparticles properties of gold nanoparticles & Surface plasmon resonances 2.8 (Hot) BROWNian motion, diffusion and their statistical analysis 2.8.1 (Hot) BROWNian motion 2.8.2 Diffusion and correlation analysis 2.8.3 Methods regarding the signal statistics of diffusing tracer particles 2.9 RUTHERFORD scattering of charged particles 2.9.1 Classical RUTHERFORD scattering 2.9.2 Quantum mechanical COULOMB scattering 3 Experimental Setup 3.1 Sample preparation 3.2 Photothermal microscopy setup 4 Photothermal Imaging: Results and Discussion 4.1 MAXWELL equations: Exact treatment of the PT signal 4.1.1 Angularly resolved powers: Fractional cross-sections 4.1.2 Incident power and background normalization 4.1.3 Fractional scattering and extinction cross-sections (off-axis) 4.1.4 Fractional scattering and extinction cross-sections (on-axis) 4.1.5 Small particle approximation(on-axis) 4.1.6 General properties of transmission scans 4.1.7 The thermal lens n(r) in the MIE-scattering framework 4.1.8 The photothermal signal F in the MIE scattering framework 4.2 Geometrical optics: Photonic RUTHERFORD scattering (ray optics) 4.2.1 FERMAT’s principle for a thermal lens medium 4.2.2 Gaussian beam transformation by a thermal lens 4.2.3 Experiments using weakly focused, i.e. nearly Gaussian beams 4.3 HELMHOLTZ equation: Photonic RUTHERFORD scattering (wave optics) 4.3.1 Plane-wave scattering 4.3.2 Focused beam scattering 4.3.3 Connection to the far field 4.3.4 Photothermal Rutherford scattering microscopy 4.3.5 Photothermal half-aperture measurements 4.4 Paraxial HELMHOLTZ equation: FRESNEL diffraction by a thermal lens 4.4.1 The diffraction integral and the phase mask for a thermal lens 4.4.2 The photothermal signal expressed via the image plane field 4.4.3 Experimental demonstration of the signal inversion 4.4.4 Connection to photothermal RUTHERFORD scattering 4.5 Plane-wave extinction & scattering by a thermal lens 4.5.1 The BORN approximation for the ideal and time-dependent thermal lens 4.5.2 The eikonal approximation for the ideal thermal lens and x>>1 4.5.3 Lessons to be learned from plane-wave scattering by thermal lenses 4.6 What is a lens? And is n(r) a lens? 5 Methodological Applications of the Results 5.1 Generalized photothermal correlation spectroscopy (incl. twin-PhoCS) 5.2 Photothermal signal distribution analysis (PhoSDA) 6 Summary and Outlook 6.1 Summary of the results 6.2 Outlook 7 Appendix 7.1 Material parameters 7.2 Calculation parameters 7.3 Interactive simulation scripts (Processing) 7.4 Vectorial scattering in the BORN-approximation 7.5 Details regarding the scattering framework 7.5.1 Connection between Gmn,TE,TM of Ref.1 and gmn,TE,TM in the GLMT 7.5.2 Off-axis BSCs including aberration (single interface) 7.5.3 Details on the incidence power Pinc 7.5.4 Details on the incidence power Pinc for arbitrary beams 7.5.5 Explicit expressions for the spherical field components of Es,i and Hs,i 7.5.6 Note on the time-dependence and the corresponding sign-conventions in M 7.5.7 Recurrence relation for Pn and tn 7.5.8 Gaussian beam shape coefficients: Off-axis 7.5.9 Multilayered Scatterer 7.5.10 POYNTING-vector and energy flow fields 7.5.11 Convergence 7.5.12 Further evaluations in the GLMT framework 7.5.13 Diffraction model: Comparison of angular PT signal pattern to the GLMT 7.6 Details on geometrical optics models 7.6.1 Geometrical optics: Exact solution r(f) for |bx|<1 7.6.2 Correspondences in photonic and partile RUTHERFORD scattering 7.6.3 On the difference in the definition of optical energy 7.6.4 Ray-opticsphotothermalsignal 7.6.5 Thick lens raytracing and the equivalent lens shape for a given aberration 7.7 Thermal lens around a wire of radius R 7.8 Twin-PhoCS: Graphic illustration of the CCF integrand Curriculum Vitae Publications Declaration Acknowledgements List of Tables List of Figures Bibliograph

Photothermal Single Particle Microscopy

Photothermal microscopy has recently complemented single molecule fluorescence microscopy by the detection of individual nano-objects in absorption. Photothermal techniques gain their superior sensitivity by exploiting a heat induced refractive index change around the absorbing nano-object. Numerous new applications to nanoparticles, nanorods and even single molecules have been reported all refering to the fact that photothermal microscopy is an extinction measurement on a heat induced refractive index profile. Here, we show that the actual physical mechanism generating a photothermal signal from a single molecule/particle is fundamentally different from the assumed extinction measurement. Combining photothermal microscopy, light scattering microscopy as well as accurate Mie scattering calculations to single gold nanoparticles, we reveal that the detection mechanism is quantitatively explained by a nanolensing effect of the long range refractive index profile. Our results lay the foundation for future developments and quantitative applications of single molecule absorption microscopy.Comment: main manuscript (5 figures), 1 supplement (3 figures

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle 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 nano-particles and provide a practical rational basis for emerging photothermal technologies.Comment: 10 pages, 5 figure

Hot Brownian motion and photophoretic self-propulsion

We describe the motion of heated particles in a simple liquid, for which we can theoretically derive generalized fluctuation-dissipation relations that hold far from equilibrium, as we demonstrate both experimentally and via molecular-dynamics simulations. Due to persistent laser-light absorption, these particles excite a radially symmetric or asymmetric (Janus particles) temperature profile in the solvent, which affects their random (Brownian) and systematic (self-phoretic) motion. In case of a radially symmetric temperature profile, we show that the particles perform “hot Brownian motion” (HBM), with different effective temperatures pertaining to their various degrees of freedom. We moreover predict and experimentally observe a peculiar dependence of their diffusivity on the particle size. In case of an asymmetric temperature profile, we find a superimposed self-phoretic directed motion. To adjust the importance of this “active” motion relative to the random hot Brownian motion, the shape of the particle is modified by binding DNA molecules and DNA origami to Janus beads. The persistence of the directed transport can thereby greatly be enhanced