  A physically interesting {\it effective rest mass} of photons in
electromagnetic media, which is independent of wave frequency $\omega$, is
defined in the present paper. It is verified that this frequency-independent
effective rest mass of photons can be easily read off from the optical
refractive index squared $n^{2}(\omega) $ of commonly-seen electromagnetic
media. As an illustrative example, we extract the frequency-independent
effective rest mass of photons from $n^{2}(\omega) $ in the {\it two time
derivative Lorentz material} (2TDLM) model. The connection between effective
rest mass and electromagnetic parameters of electric permittivity ($\epsilon $)
and magnetic permeability ($\mu $) in left-handed media is also briefly
discussed.
