These structures allow for extra freedom in photonic design and more cost-effective and large-area fabrications. In Section " Aperiodicity and randomness", we discuss aperiodic or random structures that break translational symmetry. In Section " Anisotropy", we review anisotropic metastructures with in-plane or out-of-plane anisotropy. The review is organized as follows: Section " Breaking geometric symmetries" reviews metastructures with broken geometric symmetries. We will schematically illustrate the physical mechanisms and practical applications for each type of reduced symmetries. 1, in contrast to general thermal photonic structures or structures with high symmetry. In this review, we will examine the important physical consequences of symmetry breaking on thermal radiation, as shown in Fig. As a simple but important example, we note that any linear time-invariant thermal emitter needs be lossy, and thus must break energy conservation and time-reversal symmetry however, it can either obey or violate Lorentz reciprocity. For example, any thermal emitter is fundamentally characterized by two key quantities: the angular spectral absorptivity \(\alpha \left(\omega ,-\widehat\right).\) Conversely, breaking these symmetries can remove such constraints. These symmetries have important implications for thermal radiation. The non-geometric symmetries include reciprocity, energy conservation, and time-reversal symmetry, which are invariance under the corresponding internal transformations of linear photonic systems. The geometric symmetries refer to the invariance of the system, including both the thermal emitter and its environment, under the usual spatial transformation such as rotation, reflection, and inversion. In this context, the relevant symmetries include the geometric and non-geometric ones. Symmetries also play an important role in thermal radiation. For example, the temporal translation symmetry gives rise to the conservation of energy. The continuous symmetries of a physical system are intimately related to the conservation laws characterizing that system. Continuous symmetries are described by Lie groups while discrete symmetries are described by finite groups. Symmetries are mathematically described by groups. The transformations may be continuous or discrete, which give rise to the corresponding types of symmetries. A symmetry of a physical system is a physical feature that remains invariant under some transformation. ![]() Symmetries are of fundamental importance in physics. ![]() Several review papers have comprehensively overviewed the field of thermal photonics, specifically the radiative heat transfer in near-field and far-field. Fruitful achievements propel the development of thermal photonics which improves energy utilization efficiency and revolutionizes many energy applications. Narrowband, directional, or polarized thermal emissions are all proposed and experimentally demonstrated using metamaterials. Thanks to the rapid development of nanophotonics, researchers demonstrated that thermal emission, similar to spontaneous emission of light, can be engineered or manipulated with the use of artificial or naturally occurring micro/nanostructures. In conventional systems, thermal emission tends to be broadband, incoherent, omnidirectional, and unpolarized, due to fluctuating electromagnetic fields thermally generated inside materials. The second law of thermodynamics governs the irreversibility of energy transfer in thermal emission. Planck’s law characterizes the spectral distribution of emitted power. In physics, thermal emission originates from electromagnetic radiation induced by the thermal motion of charged particles inside materials. Any object with a temperature above absolute zero exchanges thermal energy with the environment. Radiative heat transfer is a ubiquitous physical process in our universe.
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