We investigate the temperature and size dependencies of thermal emission by homogeneous spheres as a function of their dielectric properties. Different power laws obtained in this work show that the emitted power can depart strongly from the usual fourth power of temperature given by Planck's law and from the square or the cube of the radius. We also show how to optimize the thermal emission by selecting permittivities leading to resonances, which allow for the so-called super-Planckian regime. These results will be useful as spheres, i.e. the simplest finite objects, are often considered as building blocks of more complex objects.

中文翻译：

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球体的温度相关和优化的热发射

我们研究了均质球体的热发射的温度和尺寸依赖性作为其介电特性的函数。在这项工作中获得的不同幂律表明，发射功率可能与普朗克定律给出的通常的温度四次幂以及半径的平方或立方有很大差异。我们还展示了如何通过选择导致共振的介电常数来优化热辐射，这允许所谓的超普朗克机制。这些结果将作为球体有用，即最简单的有限对象，通常被认为是更复杂对象的构建块。