Huihuo Zheng

Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials

A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.

Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles

Vanadium dioxide (VO2) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post hoc adjustments to theory in order to be described properly. Here we report standard state-of-the-art first principles quantum Monte Carlo (QMC) calculations of the structural dependence of the properties of VO2. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when VO2 becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials.

Metamaterial slab as a lens, a cloak, or an intermediate

We show that a metamaterial slab with arbitrary values of epsilon and mu behaves as a cloak at a finite frequency for a small object located sufficiently close to it due to the suppression of the objects optical excitations by enhanced reflections. Reflections due to propagating components can partially suppress the excitation while evanescent components can cloak the object completely. In particular, a Veselago slab with epsilon = mu = -1 + i delta, as well as a class of anisotropic negative refractive index slabs, can completely cloak the small object placed within a finite distance from the slab when delta -> 0.

Sizable electromagnetic forces in parallel-plate metallic cavity

Using a boundary element method to calculate electromagnetic fields and the Maxwell stress tensor method to compute electromagnetic forces, we investigate electromagnetic wave induced forces acting on a pair of identical metal plates that form an electromagnetic resonance cavity. Different frequency regimes are considered, from infrared frequencies with micron-scale structures down to the microwave regime, which involves millimeter-scale structures. We found that at both length scales, electromagnetic-wave-induced forces can be significantly stronger than the usual photon pressure exerted by a laser beam if the cavity is excited at resonance, although the mechanisms that underlie the strong force are different at different length scales. In the infrared frequency regime, the strong force is induced by field penetration into the metal, whereas in the microwave regime, the electromagnetic force is induced by the leakage of electric field at the edges. At both frequency scales, we compare the results we obtained for Au metal plates with fictitious perfect electric conductor plates, so as to understand the effect of field penetration. We also showed that a transmission line model can give simple expressions that can capture the essence of the physics. The effects of surface corrugation and surface roughness are also investigated, and we find that corrugation/roughness generally induces attraction between the plates.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

Bipolar optical forces on dielectric and metallic nanoparticles by evanescent wave

We numerically show that both repulsive and attractive (bipolar) optical forces can be exerted on a dielectric or metallic cylindrical nanoparticle by a totally internal refracted wave. This requires that the particles possesses either a whispering gallery (WG) resonance or a localized surface plasmon (LSP) resonance. We further explore the force spectrum that is governed by competition between the separation-dependent resonant Q factor and the coupling strength of the nanoparticle to the evanescent wave. In spite of a much smaller Q of the LSP as compare to the WG resonances, the metallic particle gains much stronger trapping force.

Dirac cone and double zero materials

Materials with zero permittivity and zero permeability (double zero) possess very interesting wave manipulation characteristics. Systems with Dirac cones in the band structure also possess amazing wave transport properties. These two classes of material are actually related to each other. We show that dielectric photonic crystals can be designed and fabricated which exhibit Dirac cones at k = 0 at a finite frequency. A subset of such materials behave as if they have zero permittivity and zero permeability at the Dirac point, as well as exhibiting properties intrinsic to a Dirac cone.

Fast multipole boundary element method for three dimensional electromagnetic scattering problem

We developed a fast numerical algorithm for solving the three-dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nystroms quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.

Using metamaterials to create illusion and related subtle optical effects

Usage of metamaterial to create illusion and related subtle optical effects is reported. By using the concept of complementary medium or folded geometry, a remote illusion device can be designed, which is capable of transforming the stereoscopic image of an object into an arbitrary illusion at a distance. The illusion device can achieve cloaking at a distance. Finite element simulation (COMSOL) of an illusion device that optically transforms a 2D fish-like object (ε=2) into a star-like object (ε=4) is discussed.