Using Fermat's least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens is solved analytically. The solution gives a ray equation 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 Schrödingier 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, which is otherwise accessible only indirectly in Rutherford-scattering experiments.
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June 2013
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June 01 2013
Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics
Markus Selmke;
Markus Selmke
Molecular Nanophotonics, Institute of Experimental Physics I,
Universität Leipzig
, 04103 Leipzig, Germany
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Frank Cichos
Frank Cichos
Molecular Nanophotonics, Institute of Experimental Physics I,
Universität Leipzig
, 04103 Leipzig, Germany
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a)
Author to whom correspondence should be addressed. Electronic mail: cichos@physik.uni-leipzig.de
b)
Group homepage: http://www.uni-leipzig.de/~physik/mona.html
Am. J. Phys. 81, 405–413 (2013)
Article history
Received:
November 09 2012
Accepted:
March 11 2013
Citation
Markus Selmke, Frank Cichos; Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics. Am. J. Phys. 1 June 2013; 81 (6): 405–413. https://doi.org/10.1119/1.4798259
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