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We propose a new class of synthetic optical materials in which the refractiveindex satisfies $n(-\bx)=-n^*(\bx)$. We term such systems antisymmetricparity-time (APT) structures. Unlike PT-symmetric systems which requirebalanced gain and loss, i.e. $n(-\bx)=n^*(\bx)$, APT systems consist ofbalanced positive and negative index materials. Despite the seeminglyPT-symmetric optical potential $V(\bx)\equiv n(\bx)^2\omega^2/c^2$, APT systemsare not invariant under combined PT operations due to the discontinuity of thespatial derivative of the wavefunction. We show that APT systems can displayintriguing properties such as spontaneous phase transition of the scatteringmatrix, bidirectional invisibility, and a continuous lasing spectrum.

Antisymmetric PT-photonic structures with balanced positive and negative index materials