  The paper provides a new understanding of light propagation and light-matter
interactions by examining the physical implications of group velocity,
electromagnetic (EM) power flow, Poynting theorem, energy conservation law, and
Fermat's principle. A criterion is set up to identify the justification of the
group velocity definition, and a modified definition is proposed to remove the
flaws that the classical definition has. It is reasonably argued that energy
conservation law and Fermat's principle are physical postulates independent of
Maxwell equations. A ``superluminal power flow'' is constructed to show that
Poynting theorem cannot uniquely define the EM power flow if the energy
conservation law or Fermat's principle is not taken into account. As an
application, associated basic concepts in textbooks and experimental
observations reported in recent research works are also reviewed, including:
why the traditional formulation of Fermat's principle has a limited
application; how the Fermat's principle is formulated for a plane wave; why the
Fermat's principle is consistent with Maxwell EM theory; what the significant
difference is between Poynting theorem and energy conservation law; why
Poynting vector as EM power flow may break energy conservation law and Fermat's
principle in an anisotropic medium; why the physical explanations for
``spatially structured'' photons in Giovannini-coworkers experiments are not
consistent with the principle of relativity; why the traditionally-argued
invariance of information velocity contradicts Maxwell equations; and why the
superluminal light pulse propagation claimed in Wang-Kuzmich-Dogariu
experiments voilates Einstein causality.
