  This paper demonstrates that there is much similarity in the mathematical
formalisms between the optical constants of artificial electromagnetic media
(such as chiral media, left-handed media, photonic crystals and EIT media) and
some physical phenomena in field theory, including general relativity, quantum
mechanics, energy band theory, etc. The significance of such comparisons lies
in that: (i) the unification in mathematical descriptions shows that many
physical phenomena and effects, which seem to have no connections between them,
actually share almost the same mathematical structures; (ii) it can provide
clue to us on suggesting more new effects which is similar in mathematical
descriptions to the familiar phenomena in other areas.
