This interactive simulation (M. Selmke) allows the user to view the effect of a refractive index gradient on an incident beam of light as predicted by Fermat’s least optical path principle. 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 associated 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 simple 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 article “Photothermal Rutherford Scattering: A Classical and Quantum Mechanical Analogon in Ray- and Wave-Optics“, M. Selmke, F. Cichos, Am. J. Phys. 81, 405–413 (2013).