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Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures

The phenomenon of half-spectral unidirectional invisibility is introduced for one-dimensional periodic optical structures with tailored real and imaginary refractive index distributions in a non-$\mathcal{PT}$-symmetric configuration. The effect refers to the property that the optical medium appears to be invisible, both in reflection and transmission, below the Bragg frequency when probed from one side, and above the Bragg frequency when probed from the opposite side. Half-spectral invisibility is obtained by a combination of in-phase index and gain gratings whose spatial amplitudes are related each other by a Hilbert transform.