Software and Scripts

Scattering Computation scripts

Interference Signal for Rayleigh scatterers

(the theoretical work upon which this code is based is not yet published. It is to be submitted soon as "Energy Redistribution signatures in Transmission Microscopy of Rayleigh- and Mie-particles")

This processing script (or the compiled application for MAC OS) visualizes the predictions of the generalized Lorenz-Mie theory concering the relative transmission signal ΔP(x,z)/P in a scanning sample microscopy setup for a small Rayleigh particle (M. Selmke). Herein, x and z denote the lateral and axial offset of the particle relative to the incident Gaussian beam's focus. Small means that the size-parameter x=kR should be smaller than about λ/20.

tl_files/mona/images/Photothermal Detection/PolarizabilityCMRRMie.png

The complex-valued polarizability of the nanoparticle determines the transmission signal in combination with two setup-parameters: The focusing parameter s (the ratio of the beam waist to the Rayleigh-range) and the ratio of the collection angle to the beam's angle of divergence (θ_max/(2s)). 

The application uses 48 pre-computed dats-sets of 21x31 pixels (x/w0=0..4, z/2zR=0...3) for selected combinations of setup-parameter (10 collection angle ratios: {0.01, 0.21, 0.41, 0.61, 0.81, 1.01, 1.21, 1.41, 1.61, 1.81} and 11 focusing parameters: {0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275, 0.3}) using n=150 multipoles. The complex-valued polarizability α = Re(α) -i Im(α) changes their relative weight. The exact polarizability may be obtained from the first Mie coefficient, while a the value corresponding to a radiative reaction corrected Clausius-Mosotti polarizability provides an easily computed approximate expression. 

The relative transmission signal is the change in collected transmission normalized to the background. It may be either positive (blue), indicating an enhanced transmission due to the corresponding placement of the Rayleigh-particle in the focal region, or the signal may be negative (red), indicating a reduced / diminished transmission for that position. 

  • Large negative imaginary parts of the particle's polarizability α result in a large absorption and therefore in n enhanced weighting of a dip-like and negative component. This component grows and saturates when the collection angle exceeds the beams angle of divergence (the collection angle ratio becomes larger than 1).
  • Large positive real parts of the particle's polarizability α result in a dispersive signal shape, indicating the energy-redistribution. Also, for large collection angles this component disappears in magnitude. The scattering contribution which would then dominate (for small but non-negligible x) is neglected here. The neglect is justified for x<0.1 up to collection angle ratios of about 2.

The 2D-bilinear interpolation ( of the used data-sets is the default. In this setting, contours may be displayed statically, i.e. by pressing "Do Contours".

If the 2D-bilinear interpolation may be turned off to display the original data, i.e. the spatial sampling of the data set of Ax. 

For the proccesing source code only: The script requires an installation of the blobDetection library and the ControlP5 library. 

Program shortcuts:

  • "b": draw beam-waist on/off
  • "g": grid on/off
  • "x": plot x-axis and z-axis on/off
  • "i": 2D-interpolate on/off
  • "p": switch through profile mode (x,z,none)

download processing script: Script

download MacOS application (compiled): App

tl_files/mona/images/Photothermal Detection/Processing_T1.png tl_files/mona/images/Photothermal Detection/Processing_T3.png

Mathematica GLMT Scripts

These Mathematica script files (M. Selmke) allow the extensive study of light-particle interaction phenomena enountered in coherent focused beam illumination of spherical (multilayered) scatterers, e.g. to compute the intensity collected by a detection microscope objective and recorded with a photo-diode, radiation pressures, the rel. photothermal signal, sopectra, Poynting vector flows and near fields among other things. The extensive theory can be found in the supplement of the ACS article "Photothermal Single Particle Microscopy: Detection of a Nano-Lens" and free in the supplement of an earlyArXiv-version. The Gaussian on-axis modeling, which the scripts cover mostly, is also described somewhat more detailed in section 4 of our Optics Express article "Nano-lens diffraction around a single heated nano-particle".

The .zip file includes functions and parameter definitions in the Mathematica files "GaussGLMT.nb" and "GaussGLMT.nb.m". Examples of their use and plots are found in the files: "GaussGLMT_Examples_RadPressure.nb" (calculation of radiation pressures, i.e. Fx, Fy, Fz), "GaussGLMT_Examples_FarField_Photothermal.nb" (scatter images and photothermal signals), "GaussGLMT_Examples_NearField.nb" (Poynting vector plots, near field calculations)
Dieletric constant vs. wavelengh for Gold: "au_diel.txt"

tl_files/mona/images/Photothermal Detection/MathematicaGLMT.png

The code allows for the individual inspection of the constituting parts of the photothermal signal, i.e. the scatter flux and the interference flux encountered in the artificial total-field decomposition in the generalized Lorenz-Mie theory. The example shows the contributions vs. particle temperature (thermal lens strength) at the axial positions of maximum and minimum PT signal (zp=-250nm and zp=+450nm):

tl_files/mona/images/Photothermal Detection/MathematicaGLMT2.png

The off-axis BSCs allow the calculation of recorded scatter images, i.e. scans of nano-particles (NPs) across the focal region of a focused laser beam from which the transmitted intensity is recorded on a photodiode. Thes exemplary images to the left can be found in the article "Gaussian beam photothermal single particle microscopy" (seepublications) Fig. 4 where they were compared to actual measurements. The ability to compute these images allows for the extraction of the actual NP porition inside an optical trap for instance. While for resonant beams (see green image) the dip in the recorded scatter-image closely follows the laser-particle offset, the off-resonant (red image) image shows a dispersive structure with the NP being in the focus halfway in the dispersive structure.

tl_files/mona/images/Photothermal Detection/MathematicaGLMT3.png

Interactive Simulations

Photonic Rutherford Scattering

This interactive simulation (M. Selmke) allows the user to view the effect of a refractive index gradient on a incident beam of light as predicted by Fermat's least optical path priciple. For a given refractive index profile (blue plot) a ray of light will propagate in such a way as to minimize its optical path and will thereby bend towards the medium with higher refractive index. This principle is also the explanation for the mirage effect which can be seen above hot asphalt where at grazing view angle a reflection can be observed.

The simulator allows the changing of the refractive index profile n(r)=n_0 + (dn/dT)*DT*R/r by two sliders. A convergent lensing or a divergent lensing may be adjusted by changing the sign of the thermorefractive index (dn/dT), and the amplitude of the refractive index perturbation is simulated by the slider which controls the AuNP temperature (red plot). A single ray (orange) or many rays (red) may be visualized. For the single ray its asymptotes are shown. The cut with the optical axis defines the focal length assiciated with the lensing. If many rays are shown, they will follow an adjustable gaussian intensity distribution.

A warped checkerboard/net/quads texture may also be displayed by the appropriate checkboxes in the bottom right corner. It reproduces an experiment where a siple checkerboard texture is imaged through the n(r) profile medium.

One may also switch between the exact and the approximate ray-solutions, i.e. including the perturbation term or neglecting it. See also the ArXiv article "Photothermal Rutherford Scattering: A classical and quantum mechanical analogon in Ray- and Wave-optics", M. Selmke and F. Cichos, 2012.

Download: MaxOSX, Windows

tl_files/mona/images/Photothermal Detection/PhotonicRutherfSimu2.png tl_files/mona/images/Photothermal Detection/PhotonicRutherfordSim2.png

Photothermal Signal Simulator

This applet-simulator (M. Selmke) shows the key parts of a typical photothermal confocal microscopy setup: A piezo scanner (black) which can move the sample (purpleblue) which is fixed to it in lateral and axial directions, the heatingand the detection laser, the two microscope objectives and the transmission detecting photo-diode. For a detailed account see publications (ACSNano article).

The axial coordinate can be controlled by the particle position slider in the top right corner. Moving the piezo stage has the effect of moving a particle in the sample relative to the fixed focused beams (red and green). A continuous particle position scan can be done by clicking the checkbox.

The laser powers can be adjusted in the bottom left corner. The green heating laser can be modulated with the modulation checkbox above and the modulation frequency may be adjusted. The green heating laser can further be offset relative to the probing beam (controller and illustration in the bottom left).

The resulting PT signal (red/blue) is plotted in the top left corner, while its angular distribution is shown in the very top right corner. Here, also the probe-beam modification is illustrated. The temperature and refractive index profiles around the particle may be shown by clicking on the big particle.

Download: MacOSX, Windows

tl_files/mona/images/Photothermal Detection/PTSignalSimu1.png

Hot Brownian Motion & Photon Nudging Simulator

An interactive simulator (M. Selmke) showing a random diffusion process for a gold-nanoparticle which is heated in the shown green laser focus, i.e. hot Brownian motion (see Publications).

The particle may be dragged to the central region where it is heated and will experience enhanced diffusion, or it may be dragged to a region in which it will not be heated by the laser and will thus perform normal Brownian motion. The temperature and viscosity profiles around the AuNP can be displayed and illustrate the fact that they are quasi-instantaneously carried along with the AuNP (since heat diffsion is very fast).

Also shown are the time-trace of the rel. PT signal as it would be recorded with a photothermal microscope (see working principle above), the induced particle temperature and the instantaneous hot Brownian Diffusion coefficient and the efective HBM temperatures for rotational and translational diffusion.

Further, the radiation pressure can be simulated and the corresponding advection in axial direction induced by the force may be observed.

tl_files/mona/images/Photothermal Detection/HBMSimu2.png

An extension of this simulator also allows for Photon Nudging (see publications). The self-thermophoretic drift-velocity induced upon heating is used to steer an asymmetric Janus particle to a desired target location.

The bottom right panel allows to activate "Photon Nudging" via a toggle. Then, manual photon nudging is availiable upon pressing the enter-key. If furthermore the "target"-option is activated, a target may be specified with the mouse double-click to which the automatic nudging tries to navigate the particle to. Above these toggles, the active swimmer's velocity and the acceptance angle for automatic steering may be set. One may also set an external magnetic field (B-field) to harmonically fix the janus particle's orientation for manual steering. The field-direction is adjustable with a slider or the arrow-keys. The strength of the field determines how well the particle will be aligned against thermal fluctuations.

Also, changing the particle radius changes the ratio of translational to rotational motion. Not showing the particle image (deactivate Particle toggle) but only the trajectory runs the simulation faster.

Download: MS WindowsMacOS

tl_files/mona/images/Photothermal Detection/PhotNudging2.png