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Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics
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Image of Fig. 1.
Fig. 1.

(Color online) Artist's rendering of photonic wave packet scattering by a thermal lens () [Eq. (5) ] around a hot nanoparticle.

Image of Fig. 2.
Fig. 2.

(Color online) Annotated sketch of a typical ray trajectory (thick line) [Eq. (10) ] through the refractive index fields () [Eq. (5) ] with (a) (attractive) and (b) (repulsive).

Image of Fig. 3.
Fig. 3.

(Color online) Absolute scattering/deflection angle (left axis) and the normalized distance of closest approach (right axis) vs. the normalized impact parameter for fixed interaction strength . Black dashed-solid lines: Rutherford scattering; red (or dark gray) lines: exact solution; orange (or light gray) dashed lines: attractive. Clearly visible is the effect of the additional attractive perturbative force allowing closer approaches and weaker deflections for the repulsive case ( ) and stronger deflection in the attractive case ( ). For the results converge—photonic Rutherford scattering is a good approximation to the exact solution.

Image of Fig. 4.
Fig. 4.

(Color online) Macroscopic experiment on a single Rutherford-like photonic scatterer. A sphere of radius  = 0.5 cm (with a small hole to enhance absorption efficiency) is embedded in an acrylic block (PMMA, 65-mm cube) with material properties , and . The plot shows the results of an experiment with  = 2.98 m. The heating laser power was , giving a temperature estimate [Eq. (4) ] of . A fit of the data (solid line and confidence band) with Eq. (18) gives and thereby , revealing probably additional convective heat transport. The error bars were estimated using a read-off accuracy of the laser spot's center of intensity. The remaining systematic deviation is likely due to the single-mold manufacturing process.

Image of Fig. 5.
Fig. 5.

(Color online) (a) Camera setup to for the photonic scatterer. The laser-heated metal sphere in transparent resin is placed 18 cm in front of a square lattice pattern (lattice constant 0.43 mm). (b) The square pattern photographed through the medium appears warped by the thermal lens. The deflection of rays by the photonic 1/ potential gives the illusion of a crunching of the original image photographed before the heating process (darker lines) (enhanced online). [URL: http://dx.doi.org/10.1119/1.4798259.1]doi: 10.1119/1.4798259.1.

Image of Fig. 6.
Fig. 6.

(Color online) Plane-wave Rutherford scattering. Change in the wave amplitude upon scattering , from Eq. (20) . The dark shaded bands alternate between positive and negative values. Parameters are . Dashed lines show the interference zone extent .

Image of Fig. 7.
Fig. 7.

(Color online) Initial wavepacket [Eq. (24) ] (image and solid contours) and scattered wave packet [Eq. (28) ] (dashed contours). The parameters were , with corresponding width scale and a Gaussian beam waist of .

Image of Fig. 8.
Fig. 8.

(Color online) Two different individually scattered/deflected focusedbeams [Eq. (28) ] positioned at and with a spreading of and a corresponding width scale of . The strength of the potential was and the wave number was . The scattered wave packets/beams follow the classical photonic Rutherford trajectories [Eq. (16) ] (dashed), similar to Fig. 2(b) , and avoid the shadow region (textured area). The contours show the initial wave packet/beam amplitudes from Eq. (24) .


Generic image for table
Table I.

Corresponding expressions in photonic and massive-particle Rutherford scattering.



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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics