I. Introduction
The proposal in 1998 by Bender and Boettcher that the concept of respecting parity-time (PT) symmetry “non-Hermitian Hamiltonians” could stand as a complex extension of the conventional quantum mechanics quickly became a new paradigm in theoretical physics [1], [2]. Adapting the concept in optics, the refractive index of PT symmetric structures is complex-valued with adequately incorporated gain and loss in spatially separated regions of the system. The spatial distributions of gain-loss can either occur in the direction transverse to the light propagation, as in the case of the coupled directional couplers, or along the light propagation direction, as in the case of the PT-symmetric Bragg gratings (PTBGs) shown in Fig. 1. Apart from fundamental research motivations, the interest in these artificial systems is strongly driven by the practical outcomes from two unique properties of PTBGs:
Sketch of a PT-symmetric Bragg mirror and associated complex index profile nre + inim .
Spatial (modal) non-reciprocity [3]–[9], different from that based on the Faraday magneto-optical effect. As illustrated in Fig. 1 the reflectivity of a PTBG can be extremely low for light incident from one side, and extremely high when light is incident from the opposite side. This property can even be obtained without any gain by using a fully passive approach, provided that an appropriate amount of loss is incorporated in the system [10]–[12].
A large evolution of dispersion properties and band gap behavior of a PTBG induced by a limited variation of the gain-loss level [5], [6]. Such dispersion changes can be advantageously exploited for implementing switches and modulators controlled by tuning of the gain-loss level [13] –[20].