Boundary-element method for the calculation of electronic states in semiconductor nanostructures

Chaotic Resonance Modes in Dielectric Cavities: Product of Conditionally Invariant Measure and Universal Fluctuations

We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on multifractality and universal fluctuations, which is conceptually different from periodic-orbit scarring.

Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices

The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling, we realize the strong coupling regime in a moiré superlattice, characterized by cascades of robust flat bands at large twist-angles. Surprisingly, we find that these flat bands are characterized by a non-trivial band topology, the origin of which is the moiré pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge, protected by the reflection symmetry of the moiré superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations, we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.

Quantum phase extraction in isospectral electronic nanostructures

Quantum phase is not directly observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures with matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these "quantum drums"-degenerate two-dimensional electron states on the copper(111) surface confined by individually positioned carbon monoxide molecules-reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.

Finite-difference calculation of the Green's function of a one-dimensional crystal: application to the Krönig-Penney potential

We present a finite-difference scheme for computing the Green's function of a one-dimensional crystal. The method enables one to derive the band structure and the density of states of this type of structures, whatever the particular values of the potential energy. The technique also enables one to compute the influence of defects on the density of states and on the scattering of the eigenstates of the crystal. The technique is applied to the Krönig-Penney potential. In particular, we study the bound states of a square potential introduced in the crystal and their influence on the conductance of the system. We also determine the surface states induced by a termination of the Krönig-Penney potential. Our results turn out to be in excellent agreement with analytical expressions, which proves their validity and the versatility of the technique.

Spatial coherence effects in light scattering from metallic nanocylinders

We study the scattering of a partially coherent electromagnetic beam from metallic nanocylinders and analyze the effects of plasmon resonances on the coherence and polarization properties of the optical near field. We employ the coherent-mode representation for the incident field and solve the scattering problem independently for each mode by using a boundary-integral method. Our results show that the plasmon resonances may significantly affect the coherence and polarization characteristics of the near field and that partial coherence influences the energy flow in nanocylinder arrays.

Scattering matrix approach to the resonant states and Q values of microdisk lasing cavities

We develop a scattering matrix approach for the numerical calculation of resonant states and Q values of a nonideal optical disk cavity with an arbitrary shape and with an arbitrary varying refraction index. The developed method is applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness (deltar < or approximately equal to lambda/50) can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of the numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface, combined with an examination of Poincaré surfaces of section and of Husimi distributions.

Isomeric photonic molecules formed from coupled microresonators

Isomeric photonic molecules were formed by connecting four identical cavities in different geometries: a chain, a square, and a T shape. The optical mode spectrum in these structures exhibits three-dimensionally confined photonic states, which have been studied by photoluminescence spectroscopy. The energies of the optical modes depend strongly on the molecule geometry. The experimental data are in good agreement with detailed calculations of the fields in the cavities.

Classical and quantum chaos in a circular billiard with a straight cut

We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaré surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos.