By reducing the number of dimensions that light can propagate in from three to
two, control over the properties of propagation can be achieved.
The plasmonic modes of planar metal-dielectric heterostructures
will confine light in one dimension, enhancing the
electromagnetic fields within the structure.
This thesis focuses on two particular aspects of active
nanoplasmonics in planar systems, stopped light lasing and plasmons with gain in
nonequilibrium graphene.

For stopped-light lasing, a plasmonic waveguide mode is designed to have two
points of zero group velocity in a narrow frequency range, in order to increase
the local density of optical states that a gain medium can emit into.
The two stopped light points form a band of slow light that supports a wide
range of wavevectors, allowing localisation over a sub-wavelength gain medium
and providing the feedback required for lasing.
This results in a new type of laser that does not rely on predefined cavity
modes, in fact is cavity-free in 2D, dynamically forming its lasing mode
about a locally pumped region of carrier inversion.

Graphene, a single-atom thick semimetal, provides the ultimate miniaturisation
as a truly 2D material.
It is shown that graphene can support plasmons with gain, under realistic
conditions of collision loss, temperature, doping, and carrier relaxation via
amplified spontaneous emission.
This is made possible by developing a scheme to evaluate polarisabilities
for nonequilibrium carrier distributions, allowing the calculation of the exact
RPA complex-frequency plasmon dispersion solutions.
The rates of spontaneous emission are calculated and are critically dependant on
the exact dispersion relation.
The instantaneous rates are found to be 5 times faster than previously reported
and, when coupled with phonons, lead to carrier relaxations on 100 fs
timescales.
The polarisability and relaxation rates must form the basis of any active
graphene device, where electromagnetic energy is coupled to an evolving
electronic system.