Huygens’ principle derived by using momentum reciprocity theorem of electromagnetic field

Abstract

The classical reciprocity theorem of electromagnetic field proposed by Lorentz H.A. in 1896 is one of the important theories of electromagnetics. The Lorentz reciprocity theorem is widely used in many fields such as communication, antenna signal transmission, and electromagnetic imaging. The Lorentz reciprocity theorem is an “energy-based” reciprocity theorem. Over the past hundred years, some new reciprocity theorems of electromagnetic field have been discovered, including reciprocity theorems in frequency domain and time domain. In 2020, Lindell et al. extended the concept of the 'Rumsey reaction' in a differential form to include both the Lorentz force density reaction term and the power density reaction term. In the same year, Liu et al. derived the momentum reciprocity theorem from the Maxwell's equations. The momentum reciprocity theorem, like the Lorentz reciprocity theorem, can be used for both theoretical analysis and practical applications. Huygens’ principle is usually derived by the Lorentz reciprocity theorem. In this paper, the momentum reciprocity theorem is employed to derive the Huygens’ principle.