arXiv subjects

Andrey E. Miroshnichenko

Publications and source records attributed to Andrey E. Miroshnichenko.

At least 37 records · Page 2Linked to original sources

arXiv2019

On beautiful analytic structure of the S-matrix

For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residues. Beautiful hidden structures can be revealed by its domain coloring. A fundamental property of the S-matrix is that any bound state corresponds to a pole of the S-matrix on the physical sheet of the complex energy plane. For a repulsive exponentially decaying potential, none of infinite number of poles of the $s$-wave S-matrix on the physical sheet corresponds to any physical state. On the second sheet of the complex energy plane, the S-matrix has infinite number of poles corresponding to virtual states and a finite number of poles corresponding to complementary pairs of resonances and anti-resonances. The origin of redundant poles and zeros is confirmed to be related to peculiarities of analytic continuation of a parameter of two linearly independent analytic functions. The overall contribution of redundant poles to the asymptotic completeness relation, provided that the residue theorem can be applied, is determined to be an oscillating function.

quant-ph↗

arXiv2019

On the Heisenberg condition in the presence of redundant poles of the S-matrix

For the same potential as originally studied by Ma [Phys. Rev. {\bf 71}, 195 (1947)] we obtain analytic expressions for the Jost functions and the residui of the S-matrix of both (i) redundant poles and (ii) the poles corresponding to true bound states. This enables us to demonstrate that the Heisenberg condition is valid in spite of the presence of redundant poles and singular behaviour of the S-matrix for $k\to \infty$. In addition, we analytically determine the overall contribution of redundant poles to the asymptotic completeness relation, provided that the residuum theorem can be applied. The origin of redundant poles and zeros is shown to be related to peculiarities of analytic continuation of a parameter of two linearly independent analytic functions.

math-ph↗

arXiv2019

Constraint polynomial approach -- an alternative to the functional Bethe Ansatz method?

Recently developed general constraint polynomial approach is shown to replace a set of algebraic equations of the functional Bethe Ansatz method by a single polynomial constraint. As the proof of principle, the usefulness of the method is demonstrated for a number of quasi-exactly solvable (QES) potentials of the Schrödinger equation, such as two different sets of modified Manning potentials with three parameters, an electron in Coulomb and magnetic fields and relative motion of two electrons in an external oscillator potential, the hyperbolic Razavy potential, and a (perturbed) double sinh-Gordon system. The approach enables one to straightforwardly determine eigenvalues and wave functions. Odd parity solutions for the modified Manning potentials are also determined. For the QES examples considered here, constraint polynomials terminate a finite chain of orthogonal polynomials in an independent variable that need not to be necessarily energy. In the majority of cases the finite chain of orthogonal polynomials is characterized by a positive-definite moment functional ${\cal L}$, implying that a corresponding constraint polynomial has only real and simple zeros. Constraint polynomials are shown to be different from the weak orthogonal Bender-Dunne polynomials. At the same time the QES examples considered elucidate essential difference with various generalizations of the Rabi model. Whereas in the former case there are $n+1$ polynomial solutions at each point of a $n$th baseline, in the latter case there are at most $n+1$ polynomial solutions on entire $n$th baseline.

quant-ph↗

arXiv2019

Extreme defect sensitivity from large synthetic dimensionality

The geometric dimensionality of a physical system significantly impacts its fundamental characteristics. While experiments are fundamentally limited to the maximum of three spatial dimensions, there is a growing interest in harnessing additional synthetic dimensions. In our work, we introduce a new paradigm for the experimental realization of excitation dynamics associated with many-dimensional systems. Crucially, it relies solely on static one-dimensional equivalent structures with judiciously tailored parameters to faithfully reproduce the same optical spectrum and density of states of the high-dimensional system to be represented. In order to showcase the capabilities of our approach, we fabricate 1D photonic lattices that exhibit the characteristic non-monotonic excitation decays associated with quantum walks in up to 7D square lattices. Furthermore, we find that a new type of bound state at the edge of the continuum emerges in higher-than-three dimensions and gives rise to a sharp localisation transition at defect sites. In a series of experiments, we implement the mapped equivalent lattices of up to 5D systems and observe an extreme increase of sensitivity with respect to the detuning of the respective anchor sites. Our findings demonstrate the feasibility and applicative potential of harnessing high-dimensional effects in planar photonics for ultra-sensitive switching or sensing. Notably, our general approach is by no means limited to optics, and can readily be adapted to a variety of other physical contexts, including cold atoms and superconducting qubits with exclusively nearest-neighbour interactions, promising to drive significant advances in different fields including quantum simulations and information processing.

physics.optics↗

arXiv2019

Linear control of light scattering with multiple coherent light excitation

With the wave interferometric approach, we study how extrinsically multiple coherent waves excitation can dramatically alter the overall scattering states, resulting in tailoring the energy assignment among radiation and dissipation. To explore the concept, we derive the corresponding formulas for dissipation and scattering powers for cylindrical passive systems encountered by general configurations of incident waves with various illuminating directions, phases, and intensities. We demonstrate that a linear superposition of incident waves extrinsically interferes the target channels in a desirable way. Moreover, the interferometric results can be irrespective to the inherent system configurations like size, materials, and structures. The extrinsic interfering waves pave a non-invasive solution to manipulate light and matter interaction, with potential applications in metasurfaces, nanophotonics, and metadevices.

physics.optics↗

arXiv2018

Isotropic Magnetic Purcell Effect

Manipulating the spontaneous emission rate of optical emitters with all-dielectric nanoparticles benefits from their low-loss nature and thus provides relatively large extrinsic quantum yield. However, such Purcell effect greatly depends on the orientation of the dipole emitter. Here, we introduce the concept of isotropic magnetic Purcell effect with Purcell factors about 300 and large extrinsic quantum yield (more than 80%) for a magnetic dipole emitter of arbitrary orientation in an asymmetric silicon nanocavity. The extrinsic quantum yield can be even boosted up to nearly 100% by utilizing a GaP nanocavity. Isotropy of the Purcell factor is manifested via the orientation-independent emission of the magnetic dipole source. This isotropic Purcell effect is robust against small displacement of emitter on the order of 10 nm, releasing the requirement of precise alignment in experiments.

physics.optics↗

arXiv2018

Dynamic Fano resonances: From toy model to resonant Mie scattering

Based on the substantial difference in the response time for the resonant and background partitions at stepwise variations of the exiting signal, a simple exactly integrable model describing the dynamic Fano resonance (DFRs) is proposed. The model does not have any fitting parameters, may include any number of resonant partitions and exhibits high accuracy. It is shown that at the point of the destructive interference any sharp variation of the amplitude of the excitation (no matter an increase or a decrease) gives rise to pronounced "flashes" in the intensity of the output signal. In particular, the flash should appear behind the trailing edge of the exciting pulse, when the excitation is already over. The model is applied to explain the DFRs at the light scattering by a dielectric cylinder with two resonant modes excited simultaneously and exhibits the excellent agreement with the results of the direct numerical integration of the Maxwell equations.

physics.optics↗

arXiv2017

Beam steering with dielectric metalattices

We study optical wave manipulations through high-index dielectric metalattices in both diffractionless metasurface and diffractive metagrating regimes. It is shown that the collective lattice couplings can be employed to tune the excitation efficiencies of all electric and magnetic multipoles of various orders supported by each particle within the metalattice. The interferences of those adjusted multipoles lead to highly asymmetric angular scattering patterns that are totally different from those of isolated particles, which subsequently enables flexible beam manipulations, including perfect reflection, perfect transmission and efficient large-angle beam steering. The revealed functioning mechanism of manipulated interplays between lattice couplings and multipolar interferences can shed a new light on both photonic branches of metasurfaces and metagratings, which can potentially inspire many advanced applications related to optical beam controls.

physics.optics↗

arXiv2017

Scattering invisibility with free-space field enhancement of all-dielectric nanoparticles

Simultaneous scattering invisibility and free-space field enhancement have been achieved based on multipolar interferences among all-dielectric nanoparticles. The scattering properties of all-dielectric nanowire quadrumers are investigated and two sorts of scattering invisibilities have been identified: the trivial invisibility where the individual nanowires are not effectively excited; and the nontrivial invisibility with strong multipolar excitations within each nanowire, which results in free-space field enhancement outside the particles. It is revealed that such nontrivial invisibility originates from not only the simultaneous excitations of both electric and magnetic resonances, but also their significant magnetoelectric cross-interactions. We further show that the invisibility obtained is both polarization and direction selective, which can probably play a significant role in various applications including non-invasive detection, sensing, and non-disturbing medical diagnosis with high sensitivity and precision.

physics.optics↗

arXiv2017

All-Dielectric Nanophotonic Structures: Exploring the Magnetic Component of Light

We discuss nanophotonic structures composed of high-index dielectric nanoparticles and present several basic approaches for numerical study of their collective optical response. We also provide comparison on the collective optical properties of dielectric and plasmonic structures, and review experimental demonstrations of Fano resonances in all-dielectric nanoparticle oligomers.

physics.optics↗

arXiv2017

Active tuning of high-Q dielectric metasurfaces

We demonstrate the active tuning of all-dielectric metasurfaces exhibiting high-quality factor (high-Q) resonances. The active control is provided by embedding the asymmetric silicon meta-atoms with liquid crystals, which allows the relative index of refraction to be controlled through heating. It is found that high quality factor resonances ($Q=270\pm30$) can be tuned over more than three resonance widths. Our results demonstrate the feasibility of using all-dielectric metasurfaces to construct tunable narrow-band filters.

physics.optics↗

arXiv2017

Revisit Kerker's conditions by means of the phase diagram

For passive electromagnetic scatterers, we explore a variety of extreme limits on directional scattering patterns in phase diagram, regardless of details on the geometric configurations and material properties. By demonstrating the extinction cross-sections with the power conservation intrinsically embedded in phase diagram, we give an alternative interpretation for Kerker first and second conditions, associated with zero backward scattering (ZBS) and nearly zero forward scattering (NZFS). The physical boundary and limitation for these directional radiations are illustrated, along with a generalized Kerker condition with implicit parameters. By taking the dispersion relations of gold-silicon core-shell nanoparticles into account, based on the of phase diagram, we reveal the realistic parameters to experimentally implement ZBS and NZFS at optical frequencies.

physics.optics↗

arXiv2017

White light emission from silicon nanoparticles

As one of the most important semiconductors, silicon (Si) has been used to fabricate electronic devices, waveguides, detectors, and solar cells etc. However, its indirect bandgap hinders the use of Si for making good emitters1. For integrated photonic circuits, Si-based emitters with sizes in the range of 100-300 nm are highly desirable. Here, we show that efficient white light emission can be realized in spherical and cylindrical Si nanoparticles with feature sizes of ~200 nm. The up-converted luminescence appears at the magnetic and electric multipole resonances when the nanoparticles are resonantly excited at their magnetic and electric dipole resonances by using femtosecond (fs) laser pulses with ultralow low energy of ~40 pJ. The lifetime of the white light is as short as ~52 ps, almost three orders of magnitude smaller than the state-of-the-art results reported so far for Si (~10 ns). Our finding paves the way for realizing efficient Si-based emitters compatible with current semiconductor fabrication technology, which can be integrated to photonic circuits.

physics.optics↗

arXiv2017

Multimode directionality in all-dielectric metasurfaces

We demonstrate that spectrally diverse multiple magnetic dipole resonances can be excited in all-dielectric structures lacking rotational symmetry, in contrast to conventionally used spheres, disks or spheroids. Such multiple magnetic resonances arise from hybrid Mie-Fabry-Pérot modes, and can constructively interfere with induced electric dipole moments, thereby leading to novel multi-frequency unidirectional scattering. Here we focus on elongated dielectric nanobars, whose magnetic resonances can be spectrally tuned by their aspect ratios. Based on our theoretical results, we suggest all-dielectric multimode metasurfaces and verify them in proof-of-principle microwave experiments. We also believe that the demonstrated property of multimode directionality is largely responsible for the best efficiency of all-dielectric metasurfaces that were recently shown to operate across multiple telecom bands.

physics.optics↗

arXiv2017

Ideal magnetic dipole scattering

We introduce the concept of tunable ideal magnetic dipole scattering, where a nonmagnetic nanoparticle scatters lights as a pure magnetic dipole. High refractive index subwavelength nanoparticles usually support both electric and magnetic dipole responses. Thus, to achieve ideal magnetic dipole scattering one has to suppress the electric dipole response. Such a possibility was recently demonstrated for the so-called anapole mode, which is associated with zero electric dipole scattering. By overlapping magnetic dipole resonance with the anapole mode we achieve ideal magnetic dipole scattering in the far-field with tunable high scattering resonances in near infrared spectrum. We demonstrate that such condition can be realized for two subwavelength geometries. One of them is core-shell nanosphere consisting of Au core and silicon shell. It can be also achieved in other geometries, including nanodisks, which are compatible with current nanofabrication technology.

physics.optics↗

arXiv2016

Interplay of magnetic responses in all-dielectric oligomers to realize magnetic Fano resonances

We study the interplay between collective and individual optically-induced magnetic responses in quadrumers made of identical dielectric nanoparticles. Unlike their plasmonic counterparts, all-dielectric nanoparticle clusters are shown to exhibit multiple dimensions of resonant magnetic responses that can be employed for the realization of anomalous scattering signatures. We focus our analysis on symmetric quadrumers made from silicon nanoparticles and verify our theoretical results in proof-of-concept radio frequency experiments demonstrating the existence of a novel type of magnetic Fano resonance in nanophotonics.

physics.optics↗

arXiv2016

Suppression of scattering for small dielectric particles: an anapole mode and invisibility

We reveal that an isotropic homogeneous subwavelength particle with a high refractive index can produce ultra-weak total scattering due to vanishing contribution of the electric dipole moment. This effect can be explained with the help of the Fano resonance and scattering efficiency associated with the excitation of an anapole mode. The latter is a nonradiative mode emerging from destructive interference of electric and toroidal dipole moments, and it can be employed for a design of highly transparent optical materials.

physics.optics↗

arXiv2016

Q-factor and absorption enhancement for plasmonic anisotropic nanoparticles

We investigate the scattering and absorption properties of anisotropic metal-dielectric core-shell nanoparticles. It is revealed that the radially anisotropic dielectric layer can accelerate the evanescent decay of the localized resonant surface modes, leading to Q-factor and absorption rate enhancement. Moreover, the absorption cross section can be maximized to reach the single resonance absorption limit. We further show that such artificial anisotropic cladding materials can be realized by isotropic layered structures, which may inspire many applications based on scattering and absorption of plasmonic nanoparticles.

physics.optics↗