arXiv subjects

Marek Kozoň

Publications and source records attributed to Marek Kozoň.

4 recordsLinked to original sources

arXiv2023

Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices

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 photonic band gap, using a diamond-like inverse woodpile crystal structure, and exhibit 'Cartesian' hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D confined bands. In our analysis we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid state physics. We also discover pairs of degenerate 3D confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states (LDOS) for cavity quantum electrodynamics (cQED) applications. We find that donor-like superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptor-like structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly-coupled cavities.

physics.optics↗

arXiv2023

Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures

We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering.

physics.optics↗

arXiv2022

Scaling theory of wave confinement in classical and quantum periodic systems

Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defects are usually modelled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly non-trivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of the confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities to certain powers yield the confinement dimensionality of each band. This classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave in both quantum and classical regimes, and any dimension. In the quantum case, we illustrate our method on electronic confinement in 2D hexagonal BN with a nitrogen vacancy, which confirms the previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptor-like behavior.

cond-mat.dis-nn↗

arXiv2019

The semi-classical energy of closed Nambu-Goto strings

We compute semi-classical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond.

hep-th↗