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Register a new userExceptional Surfaces in PT-Symmetric Photonic Systems
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Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions.
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Over the past decade, parity-time ($mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam propagation method analysis. Our results pave a robust way toward studying the interplay between passive $mathcal{PT}$ transitions and quantum effects in dissipative photonic configurations.
Parity-time (PT) symmetry has attracted a lot of attention since the concept of pseudo-Hermitian dynamics of open quantum systems was first demonstrated two decades ago. Contrary to their Hermitian counterparts, non-conservative environments a priori do not show real energy eigenvalues and unitary evolution. However, if PT-symmetry requirements are satisfied, even dissipative systems can exhibit real energy eigenvalues, thus ensuring energy conservation in the temporal average. In optics, PT-symmetry can be readily introduced by incorporating, in a balanced way, regions having optical gain and loss. However, all optical realizations have been restricted so far to a single transverse dimension (1D) such as optical waveguide arrays. In many cases, only losses were modulated relying on a scaling argument being valid for linear systems only. Both restrictions crucially limit potential applications. Here, we present an experimental platform for investigating the interplay of PT-symmetry and nonlinearity in two dimensions (2D) and observe nonlinear localization and soliton formation. Contrary to the typical dissipative solitons, we find a one-parametric family of solitons which exhibit properties similar to its conservative counterpart. In the limit of high optical power, the solitons collapse on a discrete network and give rise to an amplified, self-accelerating field.
In this work we first examine transverse and longitudinal fluxes in a $cal PT$-symmetric photonic dimer using a coupled-mode theory. Several surprising understandings are obtained from this perspective: The longitudinal flux shows that the $cal PT$ transition in a dimer can be regarded as a classical effect, despite its analogy to $cal PT$-symmetric quantum mechanics. The longitudinal flux also indicates that the so-called giant amplification in the $cal PT$-symmetric phase is a sub-exponential behavior and does not outperform a single gain waveguide. The transverse flux, on the other hand, reveals that the apparent power oscillations between the gain and loss waveguides in the $cal PT$-symmetric phase can be deceiving in certain cases, where the transverse power transfer is in fact unidirectional. We also show that this power transfer cannot be arbitrarily fast even when the exceptional point is approached. Finally, we go beyond the coupled-mode theory by using the paraxial wave equation and also extend our discussions to a $cal PT$ diamond and a one-dimensional periodic lattice.
We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {epsilon}/{mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.
We study interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. Such a defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of anti-symmetric solitons is more complex, showing domains of successive broadening of the beam and of the beam splitting in two outwards propagating solitons, in addition to the single breather generation and blow up. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough the only observable outcome of the soliton-defect interaction is the generation of the breather.
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