Does the Poynting vector always represent electromagnetic power flow?

TL;DR

This paper challenges the conventional view that the Poynting vector always represents electromagnetic power flow, demonstrating through Maxwell equations, Fermat's principle, and relativity that it may not in certain anisotropic media.

Contribution

It reveals that the Poynting vector does not always correspond to electromagnetic power flow in anisotropic media, revising long-held assumptions.

Findings

Poynting vector may not represent power flow in anisotropic media

Supports conclusions with Maxwell equations, Fermat's principle, and relativity

Revises conventional understanding of electromagnetic power flow

Abstract

Poynting vector as electromagnetic power flow has prevailed over one hundred years in the community. However in this paper, it is shown from Maxwell equations that the Poynting vector may not represent the electromagnetic power flow for a plane wave in a non-dispersive, lossless, non-conducting, anisotropic uniform medium; this important conclusion revises the conventional understanding of Poynting vector. It is also shown that this conclusion is clearly supported by Fermat's principle and special theory of relativity.