2015/03/05 by Shuang-ren Zhao, Shuang-Ren Zhao, Kevin Yang +8 · 2 citations
Physics and Astronomy · #83C50 #FOS: Physical sciences #General Physics (physics.gen-ph) #Theoretical and Computational Physics #msc:83C50 #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1503.02006
Derivation of the mutual energy theorem from Fourier domain is added. Time-reversed transform, time-reversed mutual energy theorem, time reversed reciprocity theorem, mixed mutual energy theorem are added, Complementary theorems are added
openalex publication_date 2015/03/05 · arxiv created 2015/03/20 · arxiv updated 2016/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the retarded potential and advanced potential, time-offset field. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Mixed mutual energy theorem is derived. We derive the mutual energy from Fourier domain. We obtain the time-reversed mutual energy theorem and the mutual energy theorem. Then we derive the mutual energy theorem in time-domain. The instantaneous modified mutual energy theorem is derived. Applying time-offset transform and time integral to the instantaneous modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are two electromagnetic fields one is retarded potential and one is advanced potential, the convolution reciprocity theorem can be derived. Corresponding to the modified time-correlation mutual energy theorem and the time-convolution reciprocity theorem in Fourier domain, there is the modified mutual energy theorem and the Lorentz reciprocity theorem. Hence all mutual energy theorem and the reciprocity theorems are put in one frame of the concept of the mutual energy. 3 new Complementary theorems are derived. The inner product is introduced for two different electromagnetic fields in both time domain and Fourier domain for the application of the wave expansion.