We propose a class of synthetic optical materials in which the refractive index satisfies $n(-\mathit{x})=-n^{*}\left(\mathit{x}\right)$. We term such systems antisymmetric parity-time ($\mathcal{APT}$) structures. Unlike $\mathcal{PT}$-symmetric systems, which require balanced gain and loss, i.e., $n(-\mathit{x})=n^{*}\left(\mathit{x}\right)$, $\mathcal{APT}$ systems consist of balanced positive- and negative-index materials. Despite the seemingly $\mathcal{PT}$-symmetric optical potential $V\left(\mathit{x}\right)\equiv n{\left(\mathit{x}\right)}^2{\omega }^2/c^2$, $\mathcal{APT}$ systems are not invariant under combined $\mathcal{PT}$ operations due to the discontinuity of the spatial derivative of the wave function. We show that $\mathcal{APT}$ systems can display intriguing properties, such as spontaneous phase transition of the scattering matrix, a flat total transmission band, and a continuous lasing spectrum.

• Received 22 August 2012

DOI:https://doi.org/10.1103/PhysRevA.88.053810