Localized thermal emission from topological interfaces

Abstract

The control of thermal radiation by shaping its spatial and spectral emission characteristics plays a key role in many areas of science and engineering. Conventional approaches to tailoring thermal emission using metamaterials are hampered both by the limited spatial resolution of the required subwavelength material structures and by the materials' strong absorption in the infrared. In this work, we demonstrate an approach based on the concept of topology. By changing a single parameter of a multilayer coating, we were able to control the reflection topology of a surface, with the critical point of zero reflection being topologically protected. The boundaries between subcritical and supercritical spatial domains host topological interface states with near-unity thermal emissivity. These topological concepts enable unconventional manipulation of thermal light for applications in thermal management and thermal camouflage.

Fig. 1. Topological phase transition in a thermal emitter

A, Schematic of the thermal emitting surface consisting of a lossy metal (top surface, thickness t) separated by a dielectric layer from a metallic substrate (bottom surface). The thermal radiation from this lossy cavity shows topologically distinct behaviour defined by the balance between radiative Γ_r and intrinsic Γ_i losses as controlled by the thickness t of the top metal film. B, Photograph of the sample and its infrared camera images showing the variation of thermal radiation from the surface for three different thickness. IR images recorded from the sample placed on a hot plate at 70°C. At a critical thickness (t_c ≈ 2.3 nm) we observe near perfect thermal emissivity (ε ≈ 1). C, Variation of the far-IR thermal emissivity (λ = 13 μm) as a function the thickness t of the lossy metal on top. The solid line shows the emissivity calculated by the model. D, The complex reflectivity spectra r(ω) for the three cases of sub-critical (red), critical (black) and super-critical coupling (blue). The inset shows the reflection phase in parameter space around the critical coupling point, r_c = 0, where a phase vortex appears, and intrinsic cavity losses are matched by the radiative losses.

Fig. 2. Spectroscopic Assessment of Topological Phase Transition

A, Experimental configuration using a phase-sensitive Fourier-transform infrared spectrometer, with the sample functioning as a dynamic mirror within the Michelson interferometer. B, Magnitude |r(ω)|, and C, phase φ(ω) spectra of the Fresnel reflection coefficient for trivial (red curve, w=0, t=2.0 nm) and nontrivial (blue curve, w=1, t=2.7 nm) surfaces, revealing periodic resonance modes possessing a free spectral range of 1325 cm^-1. D, A complex representation of the measured reflection coefficient r(ω) depicts two distinct winding numbers, 0 and 1, for thicknesses when t<t_c and t>t_c, respectively. E, Experimentally obtained map of the reflection phase, highlighting a singularity endowed with a topological charge of +1. F, Spectrum of the reflection phase mapped on to the surface of a torus. Here, φ is the reflection phase and the rotation over ϕ represents frequency over a free spectral range of the cavity. The red and the blue curves are not isotopic on the surface of torus indicating different topologies.

Fig. 3. Localised thermal emission from a topological interface

A, Photograph of the sample, which includes a boundary between topologically distinct domains. B, IR thermograms of the sample, illustrating intense thermal emission localized at the boundary. C, Profile of the recorded temperature across the boundary, revealing localised emission. While both domains exhibit low thermal emissivity, the boundary itself presents an emissivity value of 1. The inset details the negligible polarization dependence of the emissivity. D, IR thermogram displaying thermal radiation along the boundary of a complex shape (map of the United Kingdom). Here, the different domains on either side of the boundary are realised by trivial and nontrivial topological phases, respectively, with the thermal radiation continuously tracing the map’s contour. The inset provides a magnified view of an island, surrounded by a continuous boundary mode. The scalebar in the inset is 100 μm.

Fig. 4. NanoIR spectroscopy of the topological edge mode

A, Schematic drawing of the sample geometry and the AFM-IR setup used to measure the local force generated by the photothermal expansion. B, C Resonant enhanced contact mode AFM-IR images and IR absorption profiles of a boundary between topologically different (B) and identical (C) domains. The images were obtained at the excitation wavenumber of 850 cm ^-1.