PT -symmetric laser absorber

In a recent work, Y. D. Chong et al. [Phys. Rev. Lett. 105, 053901 (2010)] proposed the idea of a coherent perfect absorber (CPA) as the time-reversed counterpart of a laser, in which a purely incoming radiation pattern is completely absorbed by a lossy medium. The optical medium that realizes CPA is obtained by reversing the gain with absorption, and thus it generally differs from the lasing medium. Here it is shown that a laser with an optical medium that satisfies the parity-time $(mathcal{PT})$ symmetry condition $ensuremath{epsilon}(ensuremath{-}mathbf{r})={ensuremath{epsilon}}^{*}(mathbf{r})$ for the dielectric constant behaves simultaneously as a laser oscillator (i.e., it can emit outgoing coherent waves) and as a CPA (i.e., it can fully absorb incoming coherent waves with appropriate amplitudes and phases). Such a device can thus be referred to as a $mathcal{PT}$-symmetric CPA laser. The general amplification or absorption features of the $mathcal{PT}$ CPA laser below lasing threshold driven by two fields are determined.