Photonic crystals to enhance light extraction from 2D materials
  We propose a scheme for coupling 2D materials to an engineered cavity based on a defective rod type photonic crystal lattice. We show results from numerical modelling of the suggested cavity design, and propose using the height profile of a 2D material transferred on top of the cavity to maximise coupling between exciton recombination and the cavity mode. The photonic structure plays a key role in enhancing the launch efficiency, by improving the directionality of the emitted light to better couple it into an external optical system. When using the photonic structure, we measured an increase in the extraction ratio by a factor of 3.4. We investigated the variations in the flux spectrum when the radius of the rods is modified, and when the 2D material droops to a range of different heights within the cavity. We found an optimum enhancement when the rods have a radius equal to 0.165 times the lattice constant, this enhancement reduces when the radius is reduced or increased. Finally, we discuss the possible use of solid immersion lenses, in combination with our photonic structure, to further enhance the launch efficiency and to improve vertical confinement of the cavity mode. 
Yasir J. Noori, Yameng Cao, Jonathan Roberts, Christopher Woodhead,   Ramon Bernardo-Gavito, Peter Tovee and Robert J. Young
quant-ph cond-mat.mes-hall physics.optics