Topological Bulk Lasing Modes Using an Imaginary Gauge Field

Topological edge modes, which are robust against disorders, have been used to enhance the spatial stability of lasers. Recently, it was revealed that topological lasers can be further stabilized using a novel topological phase in non-Hermitian photonic topological insulators. Here we propose a procedure to realize topologically protected modes extended over a d-dimensional bulk by introducing an imaginary gauge field. This generalizes the idea of zero-energy extended modes in the one-dimensional Su-Schrieffer-Heeger lattice into higher dimensional lattices allowing a d-dimensional bulky mode that is topologically protected. Furthermore, we numerically demonstrate that the topological bulk lasing mode can achieve high temporal stability superior to topological edge mode lasers. In the exemplified topological extended mode in the kagome lattice, we show that large regions of stability exist in its parameter space.Comment: 10 pages, 10 figure

Transverse-electric surface plasmon polaritons in periodically modulated graphene

Transverse-electric (TE) surface plasmon polaritons are unique eigenmodes of a homogeneous graphene layer that are tunable with the chemical potential and temperature. However, as their dispersion curve spectrally lies just below the light line, they cannot be resonantly excited by an externally incident wave. Here, we propose a way of exciting the TE modes and tuning their peaks in the transmission by introducing a one-dimensional graphene grating. Using the scattering-matrix formalism, we show that periodic modulations of graphene make the transmission more pronounced, potentially allowing for experimental observation of the TE modes. Furthermore, we propose the use of turbostratic graphene to enhance the role of the surface plasmon polaritons in optical spectra.Comment: 15 pages, 13 figure

Extended frequency range of transverse-electric surface plasmon polaritons in graphene

The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a graphene sheet in the full frequency range, thus removing the earlier reported limitation (1.667 < $\hbar\omega/\mu$ < 2) for the transverse-electric mode. We further develop a simple analytic approximation which accurately describes the dispersion of the surface plasmon polariton modes in graphene. Using this approximation, we show that transverse-electric surface plasmon polaritons propagate along the graphene sheet without losses even at finite temperature.Comment: 13 pages, 7 figure

Sign freedom of non-abelian topological charges in phononic and photonic topological semimetals

Abstract: The topological nature of nodal lines in three-band systems can be described by non-abelian topological charges called quaternion numbers. Due to the gauge freedom of the eigenstates, the sign of quaternion numbers can be flipped by performing a gauge transformation, i.e., choosing a different basis of eigenstates. However, the sign flipping has not been explicitly shown in realistic systems such as phononic and photonic topological semimetals. Here, we elaborate on the sign freedom of non-abelian topological charges by visualizing numerically calculated topological charges in phononic and photonic topological semimetals. For this, we employ a common reference point method for multiple nodal lines and thus confirm that the sign flipping does not cause any inconsistency in building the quaternion group

Nature of topological protection in photonic spin and valley Hall insulators

Recent interest in optical analogs to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method comprehensively characterizes possible two-dimensional hexagonal designs and reveals their topological nature, potential, and limits

Surface potential-adjusted surface states in 3D topological photonic crystals

Surface potential in a topological matter could unprecedentedly localize the waves. However, this surface potential is yet to be exploited in topological photonic systems. Here, we demonstrate that photonic surface states can be induced and controlled by the surface potential in a dielectric double gyroid (DG) photonic crystal. The basis translation in a unit cell enables tuning of the surface potential, which in turn regulates the degree of wave localization. The gradual modulation of DG photonic crystals enables the generation of a pseudomagnetic field. Overall, this study shows the interplay between surface potential and pseudomagnetic field regarding the surface states. The physical consequences outlined herein not only widen the scope of surface states in 3D photonic crystals but also highlight the importance of surface treatments in a photonic system

Extended frequency range of transverse-electric surface plasmon polaritons in graphene

The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a graphene sheet in the full frequency range, thus removing the earlier reported limitation (1.66