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Photonic systems with parity-time (PT) symmetry and topology are attracting considerable attentions. In this work, topological near-zero edge states are studied in PT-symmetric photonic lattice and the results indicate that the near-zero edge states can be broken spontaneously in spite of the unbroken PT symmetry. To achieve the stable topological near-zero mode, a binary lattice with carefully designed PT-symmetric is proposed. Further study shows such a structure supports a stable topological interface state experiences phase transition similar to the bulk states in infinite lattice and thus possess real-eigenvalues even with unbroken PT phase. Our study enriches the content of non-Hermitian topological physics and might have potential applications in the fields of topological lasing and quantum computation.
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We find that a new type of non-reciprocal modes exist at an interface between two emph{parity-time} ($mathcal{PT}$) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. The new mode is non-propagating and purely magnetic when the two MDs are semi-infinite while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if $mathcal{PT}$-symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a new approach to the design of compact optical isolator.
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.
We demonstrate the creation of robust localized zero-energy states that are induced into topologically trivial systems by insertion of a PT-symmetric defect with local gain and loss. A pair of robust localized states induced by the defect turns into zero-energy modes when the gain-loss contrast exceeds a threshold, at which the defect states encounter an exceptional point. Our approach can be used to obtain robust lasing or perfectly absorbing modes in any part of the system.
We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point, the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter thus allowing one to control the imaging process.
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of PT-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken PT symmetry. Another noteworthy finding is the possibility of restoration of the PT symmetry, following its original loss, in the course of the variation of the parameters.
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