  We investigate through analytic calculations the surface plasmon dispersion
relation for monolayer graphene sheets and a separated parallel pair of
graphene monolayers. An approximate form for the dispersion relation for the
monolayer case was derived, which was shown to be highly accurate and offers
intuition to the properties of the supported plasmon mode. For parallel
graphene pairs separated by small gaps, the dispersion relation of the surface
plasmon splits into two branches, one with a symmetric and the other with an
antisymmetric magnetic field across the gap. For the symmetric (magnetic field)
branch, the confinement may be improved at reduced absorption loss over a wide
spectrum, unlike conventional SP modes supported on metallic surfaces that are
subjected to the trade-off between loss and confinement. This symmetric mode
becomes strongly suppressed for very small separations however. On the other
hand, its antisymmetric counterpart exhibits reduced absorption loss for very
small separations or long wavelengths, serving as a complement to the symmetric
branch. Our results suggest that graphene plasmon structures could be promising
for waveguiding and sensing applications in the mid-infrared and terahertz
frequencies.
