arXiv subjects

Takuma Isobe

Publications and source records attributed to Takuma Isobe.

6 recordsLinked to original sources

arXiv2025

Topological photonics of generalized and nonlinear eigenvalue equations

Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they are described by generalized or nonlinear eigenvalue equations. In this article, we review the topological band theory of this category. In the first part, we discuss topological photonics of generalized eigenvalue equations where the band structure may take complex values even when the involved matrices are Hermitian. These complex bands explain the characteristic dispersion relation of hyperbolic metamaterials. In addition, our numerical analysis predicts the emergence of symmetry-protected exceptional points in a photonic crystal composed of negative index media. In the second part, by introducing auxiliary bands, we establish the nonlinear bulk-edge correspondence under ``weak" nonlinearity of eigenvalues. The nonlinear bulk-edge correspondence elucidates the robustness of chiral edge modes in photonic systems where the permittivity and permeability are frequency dependent.

physics.optics↗

arXiv2024

Band structures of generalized eigenvalue equation and conic section

Band structures of several metamaterials are described by generalized eigenvalue equations where complex bands emerge even if the involved matrices are Hermitian. In this paper, we provide a geometrical understanding of the real-complex transition of the band structures. Specifically, our analysis, based on auxiliary eigenvalues, elucidates the correspondence between the real-complex transition of the generalized eigenvalue equations and Lifshitz transition in electron systems. Furthermore, we elucidate that real (complex) bands of a photonic system correspond to the Fermi surfaces of type-II (type-I) Dirac cones in electron systems when the permittivity $\varepsilon$ and the permeability $\mu$ are independent of frequency. In addition, our analysis elucidates that EPs are induced by the frequency dependence of the permittivity $\varepsilon$ and the permeability $\mu$ in our photonic system.

physics.optics↗

arXiv2024

Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues

Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate that such nonlinear systems may exhibit exceptional points and non-Hermitian skin effects which are unique non-Hermitian topological phenomena. The robustness of these non-Hermitian phenomena is clarified by introducing the topological invariants under nonlinearity which reproduce the existing ones in linear systems. Furthermore, our analysis elucidates that exceptional points may emerge even for systems without an internal degree of freedom where the equation is single component. These nonlinearity-induced exceptional points are observed in mechanical metamaterials, e.g., the Kapitza pendulum.

cond-mat.mes-hall↗

arXiv2023

Bulk-edge correspondence for nonlinear eigenvalue problems

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.

cond-mat.mes-hall↗

arXiv2023

A symmetry-protected exceptional ring in a photonic crystal with negative index media

Non-Hermitian topological band structures such as symmetry-protected exceptional rings (SPERs) can emerge for systems described by the generalized eigenvalue problem (GEVP) with Hermitian matrices. In this paper, we numerically analyze a photonic crystal with negative index media, which is described by the GEVP with Hermitian matrices. Our analysis using COMSOL Multiphysics demonstrates that a SPER emerges for photonic crystals composed of split-ring resonators and metal-wire structures. We expect that the above SPER can be observed in experiments as it emerges at a finite frequency.

cond-mat.mes-hall↗

arXiv2021

Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry

So far, topological band theory is discussed mainly for systems described by eigenvalue problems. Here, we develop a topological band theory described by a generalized eigenvalue problem (GEVP). Our analysis elucidates that non-Hermitian topological band structures may emerge for systems described by a GEVP with Hermitian matrices. The above result is verified by analyzing a two-dimensional toy model where symmetry-protected exceptional rings (SPERs) emerge although the matrices involved are Hermitian. Remarkably, these SPERs are protected by emergent symmetry, which is unique to the systems described by the GEVP. Furthermore, these SPERs elucidate the origin of the characteristic dispersion of hyperbolic metamaterials which is observed in experiments.

physics.optics↗