Thermal Emission of Spinning Photons from Temperature Gradients

P.Y. Chen, C. Khandekar, R. Ayash, Z. Jacob, and Y. Sivan

Phys. Rev. Applied 18, 014052 – Published 21 July 2022

Abstract

The fluctuational electrodynamic investigation of thermal radiation from nonequilibrium or nonisothermal bodies remains largely unexplored because it necessarily requires volume integration over the fluctuating currents inside the emitter, which quickly becomes computationally intractable. Here, we put forth a formalism combining fast calculations based on modal expansion and fluctuational electrodynamics to accelerate research at this frontier. We employ our formalism on a sample problem: a long silica wire held under temperature gradient within its cross section. We discover that the far-field thermal emission carries a nonzero spin, which is constant in direction and sign, and interestingly, is transverse to the direction of the power flow. We clearly establish the origin of this transverse spin as arising from the nonequilibrium intermixing of the cylindrical modes of the wire, and not from any previously studied or intuitively expected origins such as chiral or nonisotropic materials and geometries, magnetic materials or fields, and mechanical rotations. This finding of nonequilibrium spin texture of emitted heat radiation can prove useful for advancing the noninvasive thermal metrology or infrared-imaging techniques.

Received 14 April 2022
Revised 6 May 2022
Accepted 26 May 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.014052

Physics Subject Headings (PhySH)

Angular momentum of light Heat radiation Light-matter interaction Nanophotonics Polarization of light Thermal energy harvesting devices Thermal photovoltaics

Coupled mode theory

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

P.Y. Chen^1,*, C. Khandekar², R. Ayash¹, Z. Jacob², and Y. Sivan ¹

¹School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel
²School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA

^*parryyu@post.bgu.ac.il

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Vol. 18, Iss. 1 — July 2022

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Images

Figure 1
(Left) An example geometry that can be treated by our formalism for nonequilibrium fluctuation electrodynamics. A temperature gradient is maintained across the cross section of a circular silica rod, which extends infinitely along the $z$ direction. Heat flux, characterized by Poynting’s vector, is generated along the radial direction. More notably, spin fields are generated that are in plane, characterized by a spin vector, which is perpendicular to both the plane and the Poynting vector. The circular arrows representing the spin are an artistic depiction rather than an actual indication of its magnitude. (Right) The spin extends into the far field, $D ≫ r$ , where $r$ is the radius of the cylinder and $D$ is the radius of the far-field contour. The normalized quantity $⟨ S_{z} ⟩ ω / ⟨ W ⟩$ converges to the displayed nonzero values. The sign and the magnitude of the far-field spin vector changes as a function of the in-plane polar angle, but does not substantially change at scales of the order of the wavelength.
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Figure 2
The magnitude of the far-field spin generated by thermal emission is approximately linearly proportional to the temperature gradient. Along the horizontal axis, the size of $Δ T$ varies, defined by the hottest and coldest points of the rod in Fig. 3. The vertical axis is the resulting normalized spin density.
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Figure 3
Emission from a linear temperature gradient. (a) Temperature profile across the cross section of the rod standing in vacuum, featuring the same linear gradient as Fig. 1. (b) Axial spin generated by the radiating rod ( $S_{z}$ normalized by $W$ ). In this $x$ - $y$ plane, there exists a plane of symmetry that coincides with the temperature profile. A different view of the angular variation of $S_{z}$ is presented in Fig. 1. (c) Axial spin (normalized by $W$ ), with a strength that does not diminish into the far field; the maximal values of the spin are obtained already about a wavelength away from the rod center, so that the role of the evanescent modes (which are not calculated) are expected to have, at most, a small effect on them. The trajectory for the $x$ axis is along the dotted line of (b) (i.e., $x < 0$ , $y = 0$ ). The plot domain changes drastically across the subfigures.
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Figure 4
As in Fig. 3, but with a linear temperature profile with four lobes. (a) Temperature profile over the rod cross section. (b),(c) Axial spin (normalized by $W$ ).
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Figure 5
The radial flux associated with the temperature profiles of (a) Fig. 3 and (b) Fig. 4. The difference of the Poynting flux produced by the two temperature profiles is quantitative rather than qualitative. For example, no other nodes are introduced when the symmetry of the temperature profile is changed.
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Figure 6
Emission from a uniform temperature gradient, as a function of the propagation constant $β$ along the cylinder axis. The result is calculated in two different ways: using the formalism developed in this paper (blue line with dots) and the method of Ref. [35] based on the reciprocity theorem (red line).
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