  The dispersion relation of surface plasmon polaritons in graphene that
includes optical losses is often obtained for complex wave vectors while the
frequencies are assumed to be real. This approach, however, is not suitable for
describing the temporal dynamics of optical excitations and the spectral
properties of graphene. Here, we propose an alternative approach that
calculates the dispersion relation in the complex frequency and real wave
vector space. This approach provides a clearer insight into the optical
properties of a graphene layer and allows us to find the surface plasmon modes
of a graphene sheet in the full frequency range, thus removing the earlier
reported limitation (1.667 < $\hbar\omega/\mu$ < 2) for the transverse-electric
mode. We further develop a simple analytic approximation which accurately
describes the dispersion of the surface plasmon polariton modes in graphene.
Using this approximation, we show that transverse-electric surface plasmon
polaritons propagate along the graphene sheet without losses even at finite
temperature.
