  Transient optical heating provides an efficient way to trigger phase
transitions in naturally occurring media through ultrashort laser pulse
irradiation. A similar approach could be used to induce topological phase
transitions in the photonic response of suitably engineered artificial
structures known as metamaterials. Here, we predict a topological transition in
the isofrequency dispersion contours of a layered graphene metamaterial under
optical pumping. We show that the contour topology transforms from elliptic to
hyperbolic within a subpicosecond timescale by exploiting the extraordinary
photothermal properties of graphene. This new phenomenon allows us to
theoretically demonstrate applications in engineering the decay rate of
proximal optical emitters, ultrafast beam steering, and dynamical far-field
subwavelength imaging. Our study opens a disruptive approach toward ultrafast
control of light emission, beam steering, and optical image processing.
