The nontrivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature of non-Hermitian systems is the nontrivial winding of the energy band in the complex energy plane. We provide experimental demonstrations of such nontrivial winding by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations, and by directly characterizing the complex band structures. Moreover, we show that the topological winding can be controlled by changing the modulation waveform. Our results allow for the synthesis and characterization of topologically nontrivial phases in nonconservative systems.
We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called "point-gap" and "line-gap" schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from Z winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups Z n (rather than Z Chern number). We interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.
In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical, using both a general thermodynamic argument, and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton remains bidirectional for all frequencies. This work overturns a long-held belief in nonreciprocal photonics, and highlights the importance of quantum plasmonic concepts for the understanding of nonreciprocal plasmonic effects.
Wireless functionality is essential for the implementation of wearable systems, but its adaptation in stretchable electronic systems has had limited success. In this paper, the electromagnetic properties of stretchable serpentine mesh-based systems is studied, and this general strategy is used to produce high-performance stretchable microwave systems. Stretchable mechanics are enabled by converting solid metallic sections in conventional systems to subwavelength-scale serpentine meshes, followed by bonding to an elastomeric substrate. Compared to prior implementations of serpentine meshes in microwave systems, this conversion process is extended to arbitrary planar layouts, including those containing curvilinear shapes. A detailed theoretical analysis is also performed and a natural tradeoff is quantified between the stretching mechanics and microwave performance of these systems. To explore the translation of these concepts from theory to experiment, two types of stretchable microwave devices are fabricated and characterized: a stretchable far-field dipole antenna for communications and a stretchable midfield phased surface for the wireless powering of biomedical implanted devices.
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