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An optical topological transition is defined as the change in the photonicisofrequency surface around epsilon-near-zero (ENZ) frequencies which canconsiderably change the spontaneous emission of a quantum emitter placed near ametamaterial slab. Here, we show that due to the strong Kerr nonlinearity atENZ frequencies, a high power pulse can induce a sudden transition in thetopology of the iso-frequency dispersion curve, leading to a significant changein the transmission of propagating as well as evanescent waves through themetamaterial slab. This evanescent wave switch effect allows for the control ofspontaneous emission through modulation of the Purcell effect. We develop atheory of the enhanced nonlinear response of ENZ media to s and p polarizedinputs and show that this nonlinear effect is stronger for p polarization andis almost independent of the incident angle. We perform finite-differencetime-domain (FDTD) simulations to demonstrate the transient response of themetamaterial slab to an ultrafast pulse and fast switching of the Purcelleffect at the sub-picosecond scale. The Purcell factor changes at ENZ by almosta factor of three which is an order of magnitude stronger than that away fromENZ. We also show that due to the inhomogeneous spatial field distributioninside the multilayer metal-dielectric super-lattice, a unique spatialtopological transition metamaterial can be achieved by the control pulseinduced nonlinearity. Our work can lead to ultra-fast control of quantumphenomena in ENZ metamaterials.

Switching Purcell effect with nonlinear epsilon-near-zero media