When light is emitted or scattered from a revolving medium, it exhibits a dispersion splitting- – angular Doppler effect (ADE) – which depends on the circular polarization handedness (the photon's spin) [1-2]. The dispersion splitting is attributed to a spin-dependent correction of the momentum term in the wave equation due to a rotation of the emitting medium. This splitting is the manifestation of the spin-orbit interaction, which is the basis for optical spin-Hall, Magnus, and Coriolis effects [3]. Here, we report on a geometric Doppler effect manifested by a spin-dependent dispersion splitting of thermal radiation emitted from a structure whose local anisotropy is rotated along x-axis (superstructure).  The observed effect is attributed to the dynamics of the thermally excited surface wave propagating along the superstructure [1].

         Surface phonon polaritons (SPhPs) are surface-confined electromagnetic waves due to the resonant collective lattice vibrations in polar crystals. The coupling of non-radiative surface modes to radiative modes can be achieved by performing a periodic perturbation on the surface, which provides a momentum-matching that produces a coherent and polarized emission. Thermal emission has been shown to be modified by interaction with surface   waves.

         In our experiment a subwavelength 1.2 μm ´ 4.8 μm rod array with a periodicity of  μm was etched to a depth of 1 μm on a SiC substrate (a). In the part (b) of the figure, we present the measured dispersion of the thermal emission from the homogeneous rod array locally oriented at an angle of 30˚ (a-top). The plot consists of a fast mode related to the usual delocalized surface waves, and a slow mode attributed to coupled, localized phonon- polaritons. By applying polarization measurements, we verified that the polarization direction of the slow mode follows the rods' orientation. Next, an array of rods whose orientation was gradually rotated along the x-axis was studied (a - bottom). In the measured dispersion (c) the slow mode exhibits a clear splitting in the momentum.

         The above phenomenon can be elucidated when considering surface waves propagation. As SPhPs travel along the superstructure, they radiate a linearly polarized field that rotates at a spatial rate  ( - local rod's orientation). This rotation induces coupling between the intrinsic and the extrinsic degrees of freedom – spin-orbit interaction – which leads to a spin-dependent perturbation of the momentum , where  is the spin state [1-3]. By solving the perturbated Helmholtz equation we derive the dispersion shift in the momentum dimension, . Therefore, the original dispersion of the homogeneous structure is split into two emitted modes with opposite spin states. To verify the proposed model, we measured the spin-projected dispersion emitted from the element by measuring the Stokes' parameter S₃, which represents the circular polarization portion. This measurement reveals that the slow mode is indeed shifted by , as predicted (d).

         In summary, we observed a new phenomenon – geometric Doppler effect in thermal emission. Our experiment paves the way to manipulate spontaneous emission with the photons' intrinsic degree of freedom and provides the basis for future spinoptics devices.

References

1. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner and E. Hasman “Geometric Doppler effect: spin-split dispersion of thermal radiation",      Phys. Rev. Lett. 105, 136402 (2010).
2. Y. Gorodetski, S. Nechayev, V. Kleiner and E. Hasman “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter”, Phys. Rev. B 82, 125433 (2010).
3. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Nature Photon. 2, 748 (2008).