Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
arXiv:2401.12536 · doi:10.1103/PhysRevResearch.6.033167
Abstract
As one indispensable type of nonreciprocal mechanism, a system with temporal modulations is intrinsically open in the physical sense and inevitably non-Hermitian, but the space and time degrees of freedom are nonseparable in a large variety of circumstances, which restrains the non-Bloch band theory to apply. Here, we investigate the spatially photonic crystals (PhCs) composed of spatiotemporal modulation materials (STMs) and homogeneous media, dubbed as the STM-PhC, wherein the spatial and temporal modulations are deliberately designed to be correlated. To bypass the difficulty of the spatiotemporal correlation, we first employ the effective medium theory to account for the dispersion of fundamental bands under the influence of Floquet sidebands. Based on the dynamical degeneracy splitting viewpoint and continuum generalized Brillouin zone condition, we then analytically give the criteria for the existence of the non-Hermitian skin effect in the STM. Assisted by developing a numerical method that embeds the plane wave expansion in the transfer matrix, we establish the non-Bloch band theory for the low-frequency Floquet bands in the STM-PhCs, in which the central is the identification of the generalized Brillouin zone. We finally delve into the topological properties, including non-Bloch Zak phases and delocalization of topologically edge states. Our work validates that effective medium assists the non-Bloch band theory applied to the STM-PhCs, which delivers a prescription to broaden the horizons of non-Bloch theory.
arXiv comment37 pages, 6 figures
References in corpus (62)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Edge states and topological invariants of non-Hermitian systems
- Complex Extension of Quantum Mechanics
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Topological Origin of Non-Hermitian Skin Effects
- Topological Band Theory for Non-Hermitian Hamiltonians
- Non-Bloch Band Theory of Non-Hermitian Systems
- Correspondence between winding numbers and skin modes in non-hermitian systems
- Observation of bulk boundary correspondence breakdown in topolectrical circuits
- Non-Hermitian Boundary Modes
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- What is Nonreciprocity?
- Non-Hermitian Topology and Exceptional-Point Geometries
- Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
- Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
- Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
- Universal non-Hermitian skin effect in two and higher dimensions
- Non-Hermitian topological phenomena: A review
- The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
- Topology of photonic time-crystals
- Non-Hermitian Morphing of Topological Modes
- Amplified Emission by Atoms and Lasing in Photonic Time Crystals
- Observation of Temporal Reflections and Broadband Frequency Translations at Photonic Time-Interfaces
- Lasing from multipole topological corner states
- Double-slit time diffraction at optical frequencies
- Observation of a continuous time crystal
- Fresnel drag in space-time modulated metamaterials
- Broadband Nonreciprocal Amplification in Luminal Metamaterials
- Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
- Experimental demonstration of an anisotropic exceptional point
- Measuring the knot of non-Hermitian degeneracies and non-commuting braids
- Homogenisation Theory of Space-Time Metamaterials
- Complex k band diagrams of 3D metamaterial/photonic crystals
- Temporal Brewster angle
- Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
- Photonic Floquet media with a complex time-periodic permittivity
- Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
- Space-time crystal and space-time group
- Delocalization of topological edge states
- Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
- Non-Bloch bands in two-dimensional non-Hermitian systems
- Non-Hermitian waves in a continuous periodic model and application to photonic crystals
- Non-Hermitian Floquet Topological Matter -- A Review
- Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
- Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
- Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
- Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
- New Electromagnetic Modes in Space-Time Modulated Dispersion-Engineered Media
- Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
- Exceptional points and their coalescence of PT-symmetric interface states in photonic crystals
- Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
- Edge theory of non-Hermitian skin modes in higher dimensions
- Imaginary gauge transformation in momentum space and Dirac exceptional point
- Non-Bloch band theory of generalized eigenvalue problems
- Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in -Symmetric Phononic Materials
- Spatiotemporal coupled-mode equations for arbitrary pulse transformation
- Fixed points on band structures of non-Hermitian models: Extended states in the bandgap and ideal superluminal tunneling