Review of research on nonreciprocal thermal radiation

(a) Energy flow graphs satisfying the reciprocity theorem^[34]；(b) The photonic crystal structure consists of an n-InAs grating on a homogeneous metal layer with parameters (μm): p = 7.24, w = 3.2, t₁ = 1.981, t₂ = 0.485. Absorption and emissivity spectra of the top structure of the mirror at θ = 61.28°, B = 0 T or B = 3 T, and absorption and emissivity spectra of the top structure of the aluminum mirror at θ = 61.28°and B = 3 T^[34]；(c) Schematic representation of a blackbody shell with isotropic hemispherical and directional characteristics^[35]；(d) Schematic diagram of a translucent film in an anisotropic shell where the incident wave has both p and s components and the output wave is p-polarized or s-polarized; Incident waves are either p or s polarized, while reflected and transmitted waves contain both p and s polarized components^[35]；(e) Variation of reflectance of single hBN film with azimuth angle^[35]

(a) Heat flux between two planes of isotropic plasma media and anisotropic materials with asymmetric permittivity tensor^[46]; (b) Schematic diagram of the geometric structure of the total reflection attenuated by the external magnetic field along the y-axis of the magneto-optical material InAs surface. Right pannels indicate the dielectric constant component of the InAs and the absorption and emissivity when B=3 T^[47]; (c) Schematic diagram of the Thue-morse aperiodic structure and Fibonacci photonic crystal structure based on Tamm excitation^[48-49]; (d) Schematic diagram of grating structures with a graphene layer^[50]; (e) Magnetic field distribution and the effects of geometric parameters on emissivity and absorptivity of the grating structure at strongly non-reciprocal wavelengths after the graphene layer is removed^[51]; (f) Schematic diagram of the structure of the strong non-reciprocal radiation in the middle of the grating layer^[52]

(a) Schematic diagram of a dual-frequency non-reciprocal heat emitter^[53]; (b) Schematic diagram and geometric parameters of the strong dual-frequency non-reciprocal radiation structure, with the external magnetic field along the y-axis; Absorption (α) and emission (e) spectra at θ = 25° for B= 0 T and B= 3 T^[54]; (c) Schematic diagram of strong non-reciprocal radiation using MPCs; (d) Schematic diagram of grating structures with B=0.3 T to achieve non-reciprocal thermal radiation; Magnetic field distribution of θ =±1° and θ =±65°^[58]; (e) Schematic representation of wide-angle narrow-band non-reciprocal structural bodies, non-reciprocity of the structures at 6.52 and 7.18 μm over a wide angle range from 0° to 89°^[59]; (f) Left: schematic diagram of multi-band non-reciprocal thermal radiation based on machine learning. Middle: difference between absorptivity and emissivity when B= 5 T and B=3 T. Right: difference of absorption and emission with wavelength, InAs layer and SiO₂ layer thickness, respectively^[60]; (g) Nonreciprocities under different defect locations^[61]

(a) Three-dimensional view and xz plane view of dual-polarized nonreciprocal radiation of silicon-based nanopore arrays, showing the changes of absorption, emission and nonreciprocity of structures with wavelength under TE and TM polarized waves^[62]; (b) Schematic diagram of a near-infrared dual-polarization narrow-band nonreciprocal radiator, showing the absorption and emission spectra of TE polarized wave and TM polarized wave at 0.8° incidence angle, and the field distribution of TE polarized electric field |E_y| at the resonance wavelength of 1684.90 nm and TM polarized magnetic field |H_y| at the resonance wavelength of 1669.74 nm^[63]

(a) Customized infrared MO Kerr effect characterization device, dielectric grating diagram on a single layer structure, and nonreciprocal spectra of simulation and experiment at θ= ± 60° and B= 1.5 T^[64]; (b) Schematic diagram of magnetized ENZ multilayers with gradient n_e, real part diagram of permittivity of InAs films with different doping concentrations, and measured and simulated asymmetric absorption spectra for 14 and three-layer samples at θ= 60°^[64]; (c) Customized schematic diagram of the measurement scheme and the maximum absorptivity of the TM polarized wave as a function of the magnetic field and the incidence angle^[65]

(a) Schematic diagram of Weyl semi-metallic photonic crystals with dielectric constant tensor components (${\varepsilon _{\rm{d}}}$and ${\varepsilon _{\rm{a}}}$diagonal and non-diagonal components, respectively) and non-reciprocal thermal emission^[69]; (b) Geometry of the attenuated total reflection of the Weyl semi-metal surface. The plane of incidence is the x-z plane^[70]; (c) Schematic diagram of a non-reciprocal heat radiator. The MWSM film of thickness d₁ is located on top of the metal substrate^[71]; (d) Schematic diagram of the multilayer structure of Weyl semi-metallic and dielectric photonic crystals, and diagram of the internal magnetic field intensity distribution of the third multilayer structure^[72-74]; (e) Schematic diagram of a non-reciprocal heat emitter consisting of a ZCG, WSM layer, and Ag substrate; the amplitude distribution of H_y at a wavelength of 10.39 µm at θ =±1°^[75]; (f) Schematic design of extremely wide-angle non-reciprocal thermal radiation effects^[76]

(a) Structure and effect diagram of hybridized graphene-Weyl^[77]; (b) KRS5/Air/ α-MoO₃ /WSM/Ag structure; non-reciprocal value with or without α-MoO₃^[78]; (c) Schematic diagram of multi-layer photonic crystal structures that achieve multi-band nonreciprocity^[79]; (d) Optimizing photonic crystal sequences for Fibonacci multilayers to achieve four-channel nonreciprocal radiation^[80]; (e) Schematic diagram of a non-reciprocal heat emitter consisting of a WSM film, a dielectric spacer and a rear reflector and non-reciprocal values at wavelengths 8-20 µm^[81]; (f) Schematic design of wideband extremely wide-angle non-reciprocal thermal radiation effects^[82]

(a) Schematic diagram of the thermal emitter composed of a WS film and a Ag layer to achieve non-reciprocity under TE wave, showing the absorption rate, emissivity, and non-reciprocity values^[83]; (b) ZCG, WSM layer, and Ag substrate composition structure diagram and electric field distribution diagram at 10.32 µm^[84]; (c) Schematic diagram of the structure composed of silicon gratings, a silver interlayer supported by a SiO₂ substrate and a WS film, showing the absorptivity, emissivity, and non-reciprocal values^[85]; (d) Schematic diagram of a dual-polarization non-reciprocal heat emitter^[86]; (e) Schematic diagram of Weyl semimetallic dual-polarized radiator, showing the TE and TM polarization absorptivity, emissivity, and angle non-reciprocity of 1.6° and corresponding electric field distribution diagram^[87]; (f) Structural diagram consisting of VO₂, Ge, WSM layers, and a Mo substrate, showing the absorption rate, emissivity, and non-reciprocal value of VO₂ for nonmetallic and metallic properties^[88]

(a) Traditional STPV and non-reciprocal STPV systems^[92]; (b) Nonreciprocal multijunction solar cells and efficiency limits^[97]; (c) Schematic diagram of the Landsberg limit system combining radiant cooling and solar heating^[98]