  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.

Optics;Quantum Physics