Optical forces and directionality in one-dimensional PT -symmetric photonics

We discuss the optical forces exerted on parity-time $(\mathcal{PT})$ symmetric heterostructures under normal incidence of a single and two counterpropagating plane waves. The underlying strategy is through generalized parametric space, stemming from consideration of the $\mathcal{PT}$-symmetry condition and Lorentz reciprocity theorem. In such a generalized parametric space, we are able to not only exhaustively indicate various $\mathcal{PT}$ phases and extraordinary wave phenomena but also deduce the directionality and magnitudes of optical forces. We find that when the system is illuminated by a normally incident wave, it can exhibit the symmetric pushing effect in the exact symmetry phase, unidirectional null, and bidirectional null forces (BNF) at the exceptional point, and pulling-pushing flipped forces in the broken symmetry phase, with BNF found at the pushing-pulling turning point. In two counterpropagating plane wave interferences, the magnitudes as well as the directionality of the resultant optical force can be tuned by a relative phase of incident waves. More interestingly, we observe that a null force independent of the relative phase occurred in a specific region of the broken symmetry phase and exceptional point. In addition, we offer several $\mathcal{PT}$-symmetric heterostructures to support our findings. Our results may benefit applications in $\mathcal{PT}$ optomechanics and force rectifiers.