Observation of bulk Fermi arc and polarization half charge from paired exceptional points

Abstract

The ideas of topology have found tremendous success in Hermitian physical systems, but even richer properties exist in the more general non-Hermitian framework. Here, we theoretically propose and experimentally demonstrate a new topologically-protected bulk Fermi arc which-unlike the well-known surface Fermi arcs arising from Weyl points in Hermitian systems-develops from non-Hermitian radiative losses in photonic crystal slabs. Moreover, we discover half-integer topological charges in the polarization of far-field radiation around the Fermi arc. We show that both phenomena are direct consequences of the non-Hermitian topological properties of exceptional points, where resonances coincide in their frequencies and linewidths. Our work connects the fields of topological photonics, non-Hermitian physics and singular optics, and paves the way for future exploration of non-Hermitian topological systems.In recent years, topological physics has been widely explored in closed and lossless Hermitian systems, revealing novel phenomena such as topologically non-trivial band structures [1][2][3][4][5][6][7][8][9] and promising applications including backscattering-immune transport [10][11][12][13][14][15][16][17][18][19][20][21]. However, most systems, particularly in photonics, are generically non-Hermitian due to radiation into open space or material gain/loss. NonHermiticity enables even richer topological properties, often with no counterpart in Hermitian frameworks [22][23][24][25]. One such example is the emergence of a new class of degeneracies, commonly referred to as exceptional points (EPs), where two or more resonances of a system coalesce in both eigenvalues and eigenfunctions [26][27][28]. So far, isolated EPs in parameter space [29][30][31][32][33][34][35] and continuous rings of EPs in momentum space [36][37][38] have been studied across different wave systems due to their intriguing properties, such as unconventional transmission/reflection [39][40][41], relations to parity-time symmetry [42][43][44][45][46][47][48], as well as their unique applications in sensing [49,50] and single-mode lasing [51][52][53].Here, we theoretically design and experimentally realize a new configuration of isolated EP pairs in momentum space, which allows us to reveal the unique topological signatures of EPs in the band structure and far-field polarization, and to extend topological band theory into the realm of non-Hermitian systems. Specifically, we demonstrate that a Dirac point (DP) with nontrivial Berry phase can split into a pair of EPs [54][55][56] when radiation loss-a form of non-Hermiticity-is added to a 2D-periodic photonic crystal (PhC) structure. The EPpair generates a distinct double-Riemann-sheet topology in the complex band structure, which leads to two novel consequences: bulk Fermi arcs and polarization half charges. First, we discover and experimentally demonstrate that this pair of EPs is connected by an open-ended isofrequency contourwe refer to it as a bulk Fermi arc-in direct contrast to the common intuiti...

Perspective on topological states of non-Hermitian lattices

“…From the experimental side, there have been many more experiments aimed at exceptional points in small systems (see discussion in section 5) than in lattices, as discussed here. One noteworthy exception is the experimental observation of bulk Fermi arcs originating from radiative losses in photonic crystal slabs [172]. The tipping point is expected to come when the loop closes by feeding new experiments, confirming or refuting existing theory.…”

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…Understanding the topological properties of non-Hermitian systems has also been the focus of many research efforts [55][56][57][58][59]. Initial interest revolved around exceptional points exhibiting unique topological features with no counterparts in Hermitian systems, such as Weyl exceptional rings [60], bulk Fermi arcs and half-integer topological charges [61]. Further observations of a seemingly breakdown of the bulk-boundary correspondence principle [62,63] has led to proposals for a general classification of the topological phases of non-Hermitian systems [55,56,64].…”

Transition from Dirac points to exceptional points in anisotropic waveguides

“…The isofrequency surface that encircles the EPs (the panel with green frame in Fig. 6(b)) shows the half-charge polarization winding near the EP described in [18]. A half topological charge is apparent starting from the vertical red polarization, traversing the full contour in the clockwise direction and returning to the same point.…”

“…Dirac points transform into EPs by introducing gain or losses in the system [18,22,23]. Thus, we open a non-conservative channel by placing a region with a high refractive index close to the film, which causes energy to leak away.…”