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The THz Catastrophe. Part 2: the EM Degrees of Freedom due to Thermal Agitation
  • Andrea Neto
Andrea Neto

Corresponding Author:[email protected]

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Abstract

The energy associated to the elecromagnetic (EM) field due to thermal agitation in homogeneous ohmic media is evaluated. To this goal I propose an expansion of electromagnetic fields in terms of orthogonal modal functions that are eigen-vector of Maxwell's. These fields are recognized as the degrees of freedom of the field and the energy associated to each of them is represented using the Johnson thermal voltage sources associated to the dissipative part of the impedance of the modes. At low frequency the conduction currents are dominant and in phase with the agitation of the electrons: the thermal energy is thus efficiently transferred to the EM field. At higher frequencies the radiated displacement currents overshadow the conduction currents. However, since the displacement currents are out of phase with the agitation of the electrons, the thermal energy is not efficiently transferred to the EM field. The model, which is entirely analytical, first provides the thermally generated EM energy per unit of volume. Then, relying on a number of simplifications commonly adopted in radiometry, provides the energy radiated outside the warm bodies. This latter radiated energy is finally compared with recent measurements for moderate conductivity silicon presented in a companion paper [11]. The model's accuracy with respect to measurements is within 1 dB, while the application of Planck's law, even mediated by the emissivity, is clearly off target.
27 May 2024Submitted to TechRxiv
03 Jun 2024Published in TechRxiv