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We explore the absorption and scattering properties of one dimensionalparity-time ($\mathcal{PT}$)-symmetric photonic crystal. In addition to thefamiliar transmittance and reflectance, we give the definition of thegeneralized absorptance to include the amplifying effect of the dielectric withnegative imaginary part of the permittivity, moreover, we present themathematical expressions of the transmittance, reflectances and absorptancesfrom both sides of this photonic crystal with N periods in terms of theelements of the transfer matrix of the primitive cell. The complex bandstructure of this photonic crystal is studied and the corresponding evolutionsof the exceptional points, $\mathcal{PT}$-exact phase and $\mathcal{PT}$-brokenphase are disclosed. Near the exceptional points, we find some singularbehaviors, the transmittance and reflectances from both sides are all greaterthan one and even all reach large values at the same time, then thecorresponding absorptances from both sides are negative. In the band gap, thetransmittance is zero, the reflectance form one side can be very large, whilethe reflectance from the other side is very small, we call this phenomenonunidirectional weak visibility. We believe that these phenomena are verybeneficial for the design of the optical devices.

Unidirectional weak visibility in band gap and singular scattering in conduction band of one-dimensional parity-time symmetric photonic crystal