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The introduction of topology unravels a new chapter of physics. Topological systems provide unique edge/interfacial quantum states which are expected to contribute to the development of novel spintronics and open the door to robust quantum…
Recently, a silicon micromachining method to produce tetrahedral silicon particles was discovered. In this report we determine, using band structure calculations, the optical properties of diamond-lattice photonic crystals when assembled…
The unusual surface states of topological semimetals have attracted a lot of attention. Recently, we showed [PNAS 113, 8648 (2016)] that for a Dirac semimetal (DSM) arising from band-inversion, such as Na$_3$Bi and Cd$_3$As$_2$, the…
We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to…
We show that a St\"{u}ckelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum with two gapped cones, we propose several…
Because phononic topological insulators have primarily been studied in discrete, graphene-like structures with C$_{6}$ or C$_{3}$ hexagonal symmetry, an open question is how to systematically achieve double Dirac cones and topologically…
One of the most striking predictions of quantum electrodynamics is that vacuum fluctuations of the electromagnetic field can lead to spontaneous emission of atoms as well as photon-mediated interactions among them. Since these processes…
PtTe$_2$ and PdTe$_2$ are among the first transition metal dichalcogenides that were predicted to host type-II Dirac fermions, exotic particles prohibited in free space. These materials are layered and air-stable, which makes them top…
We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive semidefinite (PSD) slack. Beyond that, we show that if the…
The Dirac point with a double-cone structure for optical fields, an optical analogy Dirac fermions in graphene, can be realized in optically homogenous metamaterials. The condition for the realization of Dirac point in optical systems is…
The PhD thesis is devoted to the study of second harmonic generation of narrow beams in photonic crystals. The basic idea is that if both frequencies, the fundamental and second harmonics are in the region of self-collimation, then the…
The artificial crystals for classical waves provide a good platform to explore the topological physics proposed originally in condensed matter systems. In this paper, acoustic Dirac degeneracy is realized by simply rotating the scatterers…
We discover an unusual phenomenon that occurs when a graphene monolayer is illuminated by a short and intense pulse at normal incidence. Due to the pulse-induced oscillations of the Dirac cones, a dynamical breaking of the layer's…
Two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted increasing interest. Tilt of Dirac cone can be realized in a number of materials, including deformed graphene, surface state of topological crystalline insulator,…
Freestanding photonic crystals can be used to trap both light and mechanical vibrations. These "optomechanical crystal" structures have already been experimentally demonstrated to yield strong coupling between a photon mode and a phonon…
In this paper, a systematic approach is employed to design a photonic crystal with a boundary between positive and negative refraction to boost the refractive properties of the crystal. Mathematical techniques are employed to turn the…
We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D…
We investigate the plasmonic response of single- and bilayer semi-Dirac materials under the influence of a tunable parameter $\delta$ that governs topological transitions via Dirac cone generation/merging and incorporating band inversion…
The topology, the symmetry involving the shape of dielectric cylinders, and the lattice structure are among the most important ingredients in the architecture of photonic crystals. In this paper, we present a systematic derivation of the…
Inspired by recent developments in self-assembled chiral nanostructures, we have explored the possibility of using spherical particles packed in cylinders as building blocks for chiral photonic crystals. In particular, we focused on an…