Directed emission from a dielectric microwave billiard with quadrupolar shape

Abstract

We present microwave measurements on dielectric billiards with mixed phase space. Transmission spectra were measured from a fixed antenna inside the billiard to a moveable antenna, thus scanning both the inside and outside region of the billiard. A Fourier transform of the transmission spectra yields the pulse propagation, which is used to study in particular the longtime dynamics of the system. The Poynting vector, which describes the energy flow of the microwaves, is obtained from the measurement for each time step of the pulse propagation. Close to the boundary of the billiard it reveals a characteristic directionality of the microwave emission, which is in accordance with measurements of the far-field intensities of micro-disc lasers of the same shape. To achieve a direct comparison to the internal dynamics of the classical system, the Husimi distributions of the pulse propagation are calculated. Averaging the Husimi distributions for the long-time dynamics provides a very clear picture of the internal dynamics in phase space. The results are in agreement with classical simulations. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.