Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals

TL;DR

The paper addresses how non-Hermiticity interacts with higher-order topology in photonic crystals and whether Bloch-based bulk-boundary intuition remains valid. It designs a non-Hermitian gyromagnetic photonic kagome crystal with balanced gain/loss and broken time-reversal symmetry, and analyzes PBC/OBC spectra, edge/corner modes, and bulk polarization, introducing a point-gap winding $W(k_x,f_0)$ to characterize the non-Hermitian skin effect (NHSE). The study finds that non-Hermiticity lifts corner-mode degeneracy, induces a bipolar NHSE where bulk states accumulate at opposite corners, and drives a breakdown of the conventional Bloch bulk-boundary correspondence, with the point-gap topology explaining the NHSE and HOT phase shifts. These results establish a general framework for non-Hermitian higher-order photonics and suggest routes to tailorable, strongly localized photonic devices.

Abstract

Non-Hermitian photonics provides a fertile platform for exploring phenomena with no Hermitian counterparts, including the non-Hermitian skin effect and exceptional points, with direct relevance for integrated photonic technologies. In this work, we investigate the properties of non-Hermitian second-order topological phases by constructing a photonic kagome crystal with balanced gain and loss, and reveal the interplay between higher-order topology and the non-Hermitian skin effect. We demonstrate that non-Hermiticity not only lifts the degeneracy of the topological corner modes but also drives bulk states to accumulate at corners, giving rise to bipolar non-Hermitian skin effect. By defining the point-gap topology, we uncover the fundamental topological origin of the non-Hermitian skin effect. More interestingly, the non-Hermitian skin effect induces a fundamental breakdown of the conventional bulk-boundary correspondence based on the Bloch band theory. Our findings establish a general framework for non-Hermitian higher-order photonic systems and open avenues toward tailorable topological photonic devices exploiting non-Hermitian enhanced localization.

Figures (7)

• Figure 1: Topological phase transition and band structure of non-Hermitian photonic kagome crystals. (a) Unit cell of the gyromagnetic non-Hermitian photonic kagome crystal, where gain and loss are introduced in red and blue dielectric columns, respectively. (b) Photonic band gap as functions of $t$ at $\gamma=6$ under PBC and OBC. The blue circular dots represent the Bloch topological bulk polarization. The inset shows the Wannier center at $t=0.55$ and $t=1.35$, respectively. (c) The band diagrams for $t=0.57$, $1.27$ and $1.35$ with $\gamma=6$.
• Figure 2: NHSE and HOT corner modes in non-Hermitian photonic crystal rhombic supercell ($t=1.27$) under OBC. (a) Rhombic supercell composed of $24\times24$ topologically nontrivial non-Hermitian unit cells, enclosed by six layers of trivial Hermitian unit cells. (b) Complex eigenfrequencies spectrum showing bulk (B$_{1}$, B$_{2}$), edge (E$_{1}$-E$_{4}$), and topological corner modes (CI and CII). The gray-shaded region denotes the photonic band gap (BG). CI$_1$ has a purely real eigenfrequency, while CI$_2$ and CII appear as complex-conjugate pairs. (c), (d) Normalized eigenmode field profiles of the type-I HOT corner modes CI$_1$ and CI$_2$. (e) Normalized eigenmode field profile of the type-II HOT corner mode CII. (f), (g) Normalized eigenmode field profiles of bulk states B$_1$ and B$_2$, exhibiting the NHSE.
• Figure 3: Topological edge modes in non-Hermitian photonic crystal rhombic supercell ($t=1.27$) under OBC. (a)-(d) Normalized eigenmode field profiles corresponding to topological edge modes E$_{1}$-E$_{4}$ in Fig. \ref{['figobc']}(b). These edge modes localized at four different edges of the supercell, respectively.
• Figure 4: Topological properties of non-Hermitian photonic crystal supercell with PBC$_x$-OBC$_y$ at $t=1.27$. (a) Schematic depiction of the ribbon non-Hermitian photonic crystal supercell under PBC$_x$-OBC$_y$. The supercell comprises non-Hermitian extended unit cells and Hermitian shrunken unit cells, with the pink line indicating their domain boundary. (b) The projected band structure of the supercell. Gray curves represent bulk states (one highlighted in blue), while red curves denote topological edge modes. The gray-shaded region indicates the photonic band gap. The corresponding eigenmode field profiles of the marked states are shown in (c).
• Figure 5: Point-gap topology of the PBC eigenfrequencies spectra. (a), (b) The eigenfrequencies spectra at the two $k_x$ points corresponding to green dots B and D in Fig. \ref{['fig1Dobc']}(b). The grayscale curves represent the PBC eigenfrequencies spectra, while colored points indicate the OBC$_y$ eigenfrequencies spectra. The corresponding normalized eigenmode field profiles are shown on the right.