Spectral Singularities in the TE and TM modes of a PT Symmetric Slab System: Optimal conditions for realizing a CPA Laser
Among the interesting outcomes of the study of the physical applications of spectral singularities in PT symmetric optical systems is the discovery of CPA lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA laser, namely a PT symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts as a laser (CPA) We also investigate the behavior of the time averaged energy density and Poynting vector for these waves. This is necessary for determining the optimal values of the physical parameters of the system that make it act as a CPA laser. These turn out to correspond to situations where the separation distance $s$ between the gain and loss layers is an odd multiple of a characteristic length scale $s_0$ A curious by product of our study is that, except for the cases where $s$ is an even integer multiple of $s_0$ there is a critical angle of polarization beyond which the energy of the waves emitted from the lossy layer can be larger than the energy of those emitted from the gain layer.