arXiv subjects

Taewoo Ha

Publications and source records attributed to Taewoo Ha.

4 recordsLinked to original sources

arXiv2026

Upper bounds for the Laplacian spectral radius: Proofs and counterexamples

The Laplacian spectral radius of a graph is the largest eigenvalue of its Laplacian matrix. Previously, upper bounds for the Laplacian spectral radius were proposed using a backward-reconstruction procedure starting from expressions equal to $2x$ and substituting local degree data. A numbered list of 68 such candidate bounds was subsequently investigated, resulting in the refutation of 30 of these bounds; two additional bounds were later refuted in a separate study. This paper updates the status of the remaining 36 candidate bounds. Of these remaining bounds, we confirm 22 and refute 12, leaving only two upper bounds open. The valid bounds follow primarily from classical Laplacian spectral radius bounds and the Collatz--Wielandt comparison; the refutations are carried out through explicit counterexamples relying on equitable partitions.

math.CO↗

arXiv2022

Non-Hermitian chiral degeneracy of gated graphene metasurfaces

Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction of an eigenspace dimensionality at the EP has been investigated mostly in a passive repetitive manner. Here, we propose an electrical and spectral way of resolving chiral EPs and clarifying the consequences of chiral mode collapsing of a non-Hermitian gated graphene metasurface. More specifically, the measured non-Hermitian Jones matrix in parameter space enables the quantification of nonorthogonality of polarisation eigenstates and half-integer topological charges associated with a chiral EP. Interestingly, the output polarisation state can be made orthogonal to the coalesced polarisation eigenstate of the metasurface, revealing the missing dimension at the chiral EP. In addition, the maximal nonorthogonality at the chiral EP leads to a blocking of one of the cross-polarised transmission pathways and, consequently, the observation of enhanced asymmetric polarisation conversion. We anticipate that electrically controllable non-Hermitian metasurface platforms can serve as an interesting framework for the investigation of rich non-Hermitian polarisation dynamics around chiral EPs.

physics.optics↗

arXiv2019

Observation of an exceptional point in a non-Hermitian metasurface

Exceptional points, also known as non-Hermitian degeneracies, have been observed in parity-time symmetric metasurfaces as the parity-time symmetry breaking point. However, the parity-time symmetry condition puts constraints on the metasurface parameter space, excluding full examination of the unique properties that stem from an exceptional point. Here, we thus design a general non-Hermitian metasurface with a unit cell containing two orthogonally oriented split-ring-resonators with overlapping resonance but different scattering rates and radiation efficiencies. Such a design grants us full access to the parameter space around the exceptional point. The parameter space around the exceptional point is first examined by varying the incident radiation frequency and coupling between split-ring resonators. We further demonstrate that the exceptional point is also observable by varying the incident radiation frequency along with the incident angle. Through both methods we validate the existence of an exceptional point by observing unique level crossing behavior, eigenstate swapping under encirclement and asymmetric transmission of circularly polarized light.

cond-mat.mes-hall↗

arXiv2019

Extremely broadband topological surface states in a photonic topological metamaterials

Metamaterials, artificially engineered materials consisting of subwavelength unit cell, have shown potentials in light manipulation with their extraordinary optical properties. Especially, topological metamaterials possessing topologically protected surface states enable extremely robust control of light. Here, we demonstrate extremely broadband topological phase in a photonic topological metamaterials with double helix structure. In particular topological surface states are observed for all the frequencies below a certain cut-off, originating from a double Weyl point at zero frequency. The extreme bandwidth and robustness of the photonic topological metamaterial are beneficial for practical applications such as one-way waveguide and photonic integrated systems but also advantageous in design and fabrication since the only necessary condition is to satisfy the effective hyperbolic and chiral properties, without entailing strict periodic arrangement.

physics.optics↗