  Electromagnetic wave is reflected and refracted at interfaces, satisfying
Fresnel-Snell law which is required by conservations of energy and momentum. If
the incident angle is lower than the critical angle, we can use this
Fresnel-Snell law, but the Fresnel-Snell law is modified in the case of
existence of dissipation ($\tilde{n} = n + i\kappa, \kappa > 0$) or in the
condition of total internal reflection. In the cases, we have to extend the
angle of refraction from real number to complex number ($\theta \rightarrow
\tilde{\theta} = \theta + i\psi, \psi \neq 0$). In this paper, by using
complex-angle approach, we analyse the behaviour of electromagnetic waves in
various kind of interfaces: dielectric - dielectric system, dissipative
dielectric - dielectric system, and metal - dielectric system. We show that
iso-frequency curves in wavenumber space is opened in the case where $n, \kappa
> 0$, and closed either when $n \rightarrow 0$ or when $\kappa \rightarrow 0$
("Lifshitz transition" of electromagnetic waves). Excess momentum (wavenumber)
and anomalous spin (circular polarization) emerging with the transition are
also discussed.
