An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

Abstract This work develops an analogical study between electromagnetic and elastic wave fields, with a one-to-one correspondence principle established regarding the basic wave equations, the physical quantities as well as the differential operations. Using the electromagnetic-to-elastic substitution, the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields. Moreover, the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state, which describe the interaction between two elastic wave systems from the perspective of energy and momentum, respectively. The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems, but also find potential applications in relevant fields such as medical imaging, non-destructive evaluation, acoustic microscopy, seismology and exploratory geophysics.