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

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.Comment: 24 pages, 11 figure

Semi-classical energy of elliptic Nambu-Goto string

Po zhrnutí potrebných teoretických základov a predošlého výskumu v ob- lasti, prezentujeme semi-klasickú kvantovaciu schému pre uzavretú Nambuovu- Gotovu strunu. Týmto zovšeobecňujeme predošlú prácu, ktorá bola vykonaná pre otvorenú strunu a uzavretú strunu kruhového tvaru. Pomocou metód kvan- tovej teórie po©a v zakrivených priestoročasoch počítame strednú hodnotu vo©- ného Hamiltoniánu struny rotujúcej v dvoch na seba kolmých priestorových rovinách v priestoročase všeobecnej dimenzie. Táto hodnota je priamo úmerná kvantovej korekcii k celkovej energii struny, ktorá má formu tzv. Reggeovho interceptu. Výslednú hodnotu Reggeovho interceptu porovnávame s predošlým výskumom. Taktiež uvádzame porovnanie získaného spektra fyzikálnych stavov struny kvantovanej našou metódou so spektrom odvodeným pomocou kovariant- ného kvantovania.

Termální vývoj Saturnova měsíce Enceladu

We study thermal evolution of Enceladus on very long time scales. In order to do so, we created a Fortran program modeling tidal deformation and thus induced heat dissipation as well as conductive transport of the heat in the body of the moon. Effect of long-lived radioactive isotopes decay in the core on the heat generation is included. We show the dependence of a thermal scenario character on different minimal viscosity and constant eccentricity values and study chosen cases in detail. We further demonstrate that, if orbital eccentricity evolution is incorporated, its initial value has no essential effect on the thermal evolution result, with the body always freezing quickly. Lastly, we examine the dependence of a thermal scenario on added values of hydrothermal heating power from the core and present that a power magnitude can be found, with which the satellite does not freeze, nor overheats in the first 4 billions of years what is necessary for maintaining a thermal activity on Enceladus since its formation to the present time.

Semiklasická energie eliptické Nambuovy-Gotovy struny

Po zhrnutí potrebných teoretických základov a predošlého výskumu v ob- lasti, prezentujeme semi-klasickú kvantovaciu schému pre uzavretú Nambuovu- Gotovu strunu. Týmto zovšeobecňujeme predošlú prácu, ktorá bola vykonaná pre otvorenú strunu a uzavretú strunu kruhového tvaru. Pomocou metód kvan- tovej teórie po©a v zakrivených priestoročasoch počítame strednú hodnotu vo©- ného Hamiltoniánu struny rotujúcej v dvoch na seba kolmých priestorových rovinách v priestoročase všeobecnej dimenzie. Táto hodnota je priamo úmerná kvantovej korekcii k celkovej energii struny, ktorá má formu tzv. Reggeovho interceptu. Výslednú hodnotu Reggeovho interceptu porovnávame s predošlým výskumom. Taktiež uvádzame porovnanie získaného spektra fyzikálnych stavov struny kvantovanej našou metódou so spektrom odvodeným pomocou kovariant- ného kvantovania. 1Ústav teoretické fyzikyInstitute of Theoretical PhysicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Estimate of the regularly gridded 3D vector flow field from a set of tomographic maps

Time-distance inversions usually provide tomographic maps of the interesting plasma properties (we focus on flows) at various depths. These maps, however, do not correspond directly to the flow field, but rather to the true flow field smoothed by the averaging kernels. We introduce a method to derive a regularly gridded estimate of the true velocity field from a set of tomographic maps. We mainly aim to reconstruct the flow on a uniform grid in the vertical domain. We derive the algorithm, implement it and validate using synthetic data. The use of the synthetic data allows us to investigate the influence of random noise and to develop the methodology to deal with it properly

Strongly inhibited spontaneous emission of PbS quantum dots covalently bound to 3D silicon photonic band gap crystals

We present an optical study of the spontaneous emission of lead sulfide (PbS) nanocrystal quantum dots in three-dimensional (3D) photonic band gap crystals made from silicon. The nanocrystals emit in the near-infrared (NIR) range to be compatible with the 3D silicon nanophotonics. The nanocrystals are covalently bonded to polymer brush layers that are grafted from the Si-air interfaces inside the nanostructure using surface-initiated atom transfer radical polymerization (SI-ATRP), and their presence and position of the quantum dots was previously characterized by synchrotron X-ray fluorescence tomography. We report both continuous wave (cw) emission spectra and time-resolved time-correlated single photon counting. In time-resolved measurements, we observe that the total emission rate greatly increases when the quantum dots are transferred from suspension to the silicon nanostructures, likely due to quenching (or increased non-radiative decay) that is tentatively attributed to the presence of Cu-catalyst during the synthesis. In this regime, continuous wave emission spectra are known to be proportional to the radiative rate and thus to the local density of states. In spectra normalized to those taken on flat silicon outside the crystals, we observe a broad and deep stop band that we attribute to a 3D photonic band gap with a relative bandwidth up to 26%. The shapes of the relative emission spectra match well with the theoretical density of states spectra calculated with the plane wave expansion. The observed inhibition is 5 to 30 times, similar to previously reported record inhibitions, yet for completely coincidental reasons. Our results are relevant to applications in photochemistry, sensing, photovoltaics, and to efficient miniature light sources