Unidirectional polarization beam splitter via an exceptional point and finite periodicity of non-Hermitian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry

We present a theoretical study of a polarization beam splitter (PBS), different from the conventional time-reversal symmetry one, where a specific linearly polarized light on two opposite sides can be totally reflected into the incident one and can be transparent to incident to its orthogonal linearly polarized light on only one side. We employ the mechanism via an exceptional point and finite periodicity of non-Hermitian $\mathcal{PT}$ symmetry. We design such a PBS made of a finite periodic structure in which each unit cell has a delicate balance of gain and loss in spatial distribution. In order to obtain total reflection for one of two orthogonal polarizations of the incident wave, the unit cell has to be operated at some $\mathcal{PT}$-symmetry phase of the reflection band. To have a single-sided transparency for its orthogonal polarized light, the unit cell should be designed at an exceptional point as well as have asymmetric reflectance. Interestingly, such a single-sided transparent phenomenon is independent of the total number of unit cells. We believe this unidirectional PBS may stimulate a new route to polarization control.