$\mathcal{PT}$-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 $\epsilon (-\mathbf{r})={\epsilon }^{*}(\mathbf{r})$ 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.

Figure 1

(a) Schematic of wave scattering in a one-dimensional optical structure with complex dielectric constant $\epsilon (x)$. (b) Schematic of a laser oscillator comprising two equal lossless mirrors filled with a gain medium. (c) Distributed-feedback structure, consisting of a uniform index grating with two homogeneous and symmetric gain and loss regions, that realizes a $\mathcal{PT}$ CPA laser.

Figure 2

(a) Behavior of the overall reflection or transmission coefficient $\Theta$ (on a logarithmic scale) versus frequency detuning $\omega -{\omega }_0$ for the transfer matrix defined by Eqs. (7, 8, 9, 10) and for parameter values $\alpha =3$, $\beta =0.3$, $\epsilon =0.02$, and $\kappa =1$. Solid curve, two-port coherent input excitation with $d/a={\mathcal{M}}_{21}({\omega }_0)$; dashed curve, two-port incoherent input excitation with $d/a=|{\mathcal{M}}_{21}({\omega }_0)|\exp (i\varphi )$, averaged over the random phase $\varphi$; dotted curve, single-port excitation ($d=0$). (b) Same as (a), but for the distributed-feedback structure in Fig. 1c for parameter values $q_{0}L=1$ and $\mathit{gL}=4.43$. The normalized frequency detuning in the horizontal axis is defined as $\delta =(\omega -{\omega }_B)n_{0}L/c_0$, where ${\omega }_B$ is the Bragg reference frequency.