Evaluating the Purcell factor in hyperbolic metamaterials

We compare two simulation methods of calculating the Purcell factor in a hyperbolic metamaterial and validate our simulations with measurements. We calculate the Purcell factor from a direct calculation of the local density of states from the band structure of the periodic unit cell. We compare this method with calculations of the Purcell factor obtained from the finite difference time domain (FDTD) calculations of the impedance of a dipole antenna located inside the structure. We show that we can study the Purcell factor in transverse electric (TE) and transverse magnetic (TM) polarisations by using electric and magnetic dipoles, we support our argument by analysing the dispersion relations of the structure.