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

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