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We theoretically and numerically reveal that under a given level of extinction cross section and with definite angular momentum channels dominant, there exists a physical limitation for absorption cross section being maximum and scattering cross section being minimum. In addition, any scattering systems operated at this condition would be accompanied by a needle Dirac-delta-like far-field radiation pattern, reducing to perturb the background field except in the forward direction. We therefore refer to this outcome as dark superabsorbers. Moreover, by considering the mathematical Gibbs phenomenon, we find that a completely equivalent Dirac-delta far-field radiation is excluded even we could properly design the scatterers operated at such conditions. We believe this finding has potential applications in design of dark energy harvesting, lower-visibility receivers, superdirective light-matter interaction, and Fresnel diffractive imaging.

The remarkable properties of toroidal metasurfaces, featuring ultrahigh-Q bound states in the continuum (BIC) resonances and nonradiating anapole modes, have garnered significant attention. The active manipulation of quasi-BIC resonance characteristics offers substantial potential for advancing tunable metasurfaces. Our study explores explicitly the application of vanadium dioxide, a phase change material widely used in active photonics and room-temperature bolometric detectors, to control quasi-BIC resonances in toroidal metasurfaces. The phase change transition of vanadium dioxide occurs in a narrow temperature range, providing a large variation in material resistivity. Through heating thin film patches of vanadium dioxide integrated into a metasurface comprising gold split-ring resonators on a sapphire substrate, we achieve remarkable control over the amplitude and frequency of quasi-BIC resonances due to their high sensitivity to losses present in the system. Breaking the symmetry of meta-atoms reveals enhanced tunability. The predicted maximum change in the quasi-BIC resonance amplitude reaches 14 dB with a temperature variation of approximately 10 {\deg}C., Comment: Submitted to Advanced Photonics Research

Recent advances in nonlocal metasurfaces have enabled unprecedented success in shaping the wavefront of light with spectral selectivity, offering new solutions for many emerging nanophotonics applications. The ability to tune both the spectral and spatial properties of such a novel class of metasurfaces is highly desirable, but the dynamic nonvolatile control remains elusive. Here, we demonstrate active narrowband wavefront manipulation by harnessing quasi-bound states in the continuum (quasi-BICs) in phase-change nonlocal metasurfaces. The proof-of-principle metasurfaces made of Sb$_2$S$_3$ allow for nonvolatile, reversible, and tunable spectral control over wavefront and switchable spatial response at a given wavelength. The design principle mainly builds upon the combination of the geometry phase of quasi-BICs and the dynamic tunability of phase-change meta-atoms to tailor the spatial response of light at distinct resonant wavelengths. By tuning the crystallization level of Sb$_2$S$_3$ meta-atoms, the dynamic nonlocal wavefront-shaping functionalities of beam steering, 1D, and 2D focusing are achieved. Furthermore, we demonstrate tunable holographic imaging with active spectral selectivity using our phase-change nonlocal metasurface. This work represents a critical advance towards developing integrated dynamic nonlocal metasurface for future augmented and virtual reality wearables.

Symmetry breaking plays a crucial role in understanding the fundamental physics underlying numerous physical phenomena, including the electromagnetic response in resonators, giving rise to intriguing effects such as directional light scattering, supercavity lasing, and topologically protected states. In this work, we demonstrate that adding a small fraction of lossy metal (as low as $1\times10^{-6}$ in volume), to a lossless dielectric resonator breaks inversion symmetry thereby lifting its degeneracy, leading to a strong bianisotropic response. In the case of the metasurface composed of such resonators, this effect leads to unidirectional perfect absorption while maintaining nearly perfect reflection from the opposite direction. We have developed more general Onsager-Casimir relations for the polarizabilities of particle arrays, taking into account the contributions of quadrupoles, which shows that bianisotropy is not solely due to dipoles, but also involves high-order multipoles. Our experimental validation demonstrates an extremely thin terahertz-perfect absorber with a wavelength-to-thickness ratio of up to 25,000, where the material thickness is only 2% of the theoretical minimum thickness dictated by the fundamental limit. Our findings have significant implications for a variety of applications, including energy harvesting, thermal management, single-photon detection, and low-power directional emission.

The fusion of metasurface antennas and computational imaging facilitates the design of microwave imaging systems which require no lenses, phase shifters or moving parts. The technique involves the generation of appropriately designed diverse measurement modes to encode the scene information into a small number of measurements. We propose a novel boundary-tunable parallel plate waveguide-based metasurface antenna for computational microwave imaging. The proposed antenna leverages a switchable boundary of two layers of vias, to efficiently change the waveguide modes supported by the antenna cavity, leading to diverse measurement modes in the scene plane. The superiority of the boundary tuning approach over the frequency diversity approach for the same antenna is confirmed using the singular value decomposition. Synthetic imaging is performed using a coupled dipole model, which quantitatively proves the efficacy of the proposed antenna along with the robustness against noise down to 15 dB SNR.

The ultrafast response and broadband absorption of all-optical graphene switches are highly desirable features for on-chip photonic switching. However, because graphene is an atomically thin material, its absorption of guided optical modes is relatively low, resulting in high saturation thresholds and switching energies for these devices. To boost the absorption of graphene, we present a practical design of an electrically-biased all-optical graphene switch that is integrated into silicon slot waveguides, which strongly confine the optical mode in the slotted region and enhance its interaction with graphene. Moreover, the design incorporates a silicon slab layer and a hafnia dielectric layer to electrically tune the saturation threshold and the switching energy of the device by applying DC voltages of <0.5 V. Using this device, a high extinction ratio (ER) of 10.3dB, a low insertion loss (IL) of <0.7dB, and an ultra-efficient switching energy of 79fJ/bit at 0.23V bias are attainable for a 40um long switch. The reported performance metrics for this device are highly promising and are expected to serve the needs of next-generation photonic computing systems., Comment: Accepted for publication in the Journal of Optics

Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we proposed a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrated that FW BICs can be achieved with arbitrary two degenerate resonances in a closed resonator regardless of whether they have the same or opposite parity. Moreover, their eigenmode profiles can be arbitrarily engineered by adjusting the position of attached waveguide. That suggests an effective way of continuous switching the nature of BIC from FW BIC to symmetry-protected BIC or accidental BICs. Also, such BICs are sustained in the coupled waveguide-resonator system with shapes such as rectangle, ellipse, and rhomboid. These interesting phenomena are well explained by the two-level effective non Hermitian Hamiltonian, where two strongly coupled degenerate modes play a major role in forming such FW BICs. Besides, we found that such an open system also supports accidental BICs in geometry space instead of momentum space via tuning the position of attached waveguide, which are attributed to the quenched coupling between the waveguide and eigenmodes of the closed cavity. Finally, we fabricated a series of 3D coupled-resonator-waveguide and experimentally verified the existence of FW BICs and accidental BICs by measuring the transmission spectra. Our results complement the current BIC library in acoustics and provide new routes for designing novel acoustic devices, such as in acoustic absorbers, filters and sensors., Comment: 20 pages, 6 figures

Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and exciton-polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generation photonic devices that make use of these features, it is first essential to model the all-optical control mechanisms in TMDCs. Herein, a simple model is proposed to quantify the performance of a 35$\,$\textmu m long Si$_3$N$_4$ waveguide-integrated all-optical MoSe$_2$ modulator. Using this model, a switching energy of 14.6$\,$pJ is obtained for a transverse-magnetic (TM) and transverse-electric (TE) polarised pump signals at $\lambda =\,$480$\,$nm. Moreover, maximal extinction ratios of 20.6$\,$dB and 20.1$\,$dB are achieved for a TM and TE polarised probe signal at $\lambda =\,$500$\,$nm, respectively, with an ultra-low insertion loss of $<0.3\,$dB. Moreover, the device operates with an ultrafast recovery time of 50$\,$ps, while maintaining a high extinction ratio for practical applications. These findings facilitate modeling and designing novel TMDC-based photonic devices., Comment: \copyright 2022 Optica Publishing Group. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

Acoustic resonant cavities play a vital role in modern acoustical systems. They have led to many essential applications for noise control, biomedical ultrasonics, and underwater communications. The ultrahigh quality-factor resonances are highly desired for some applications like high-resolution acoustic sensors and acoustic lasers. Here, we theoretically propose and experimentally demonstrate a new class of supercavity resonances in a coupled acoustic resonators system, arising from the merged bound states in the continuum (BICs) in geometry space. We demonstrate their topological origin by explicitly calculating their topological charges before and after BIC merging, accompanied by charges annihilation. Comparing with other types of BICs, they are robust to the perturbation brought by fabrication imperfection. Moreover, we found that such supercavity modes can be linked with the Friedrich-Wintgen BICs supported by an entire rectangular (cuboid) resonator sandwiched between two rectangular (or circular) waveguides, and thus more supercavity modes are constructed. Then, we fabricate these coupled resonators and experimentally confirm such a unique phenomenon: moving, merging, and vanishing of BICs by measuring their reflection spectra, which show good agreement with the numerical simulation and theoretical prediction of mode evolution. Finally, given the similar wave nature of acoustic and electromagnetic waves, such merged BICs also can be constructed in a coupled photonic resonator system. Our results may find exciting applications in acoustic and photonics, such as enhanced acoustic emission, filtering, and sensing., Comment: 16 pages, 5 figures

Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by making an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the well-known Gorini-Kossakowski-Lindblad-Sudarshan form (here called standard Lindblad form). Instead, it has a more general structure (here called generalized Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. Moreover, for systems weakly coupled to a reservoir, the presence of counter-rotating terms in the interaction Hamiltonian or the nonstationarity of the reservoir state guarantees that the master equation describing the system of interest will be of the generalized Lindblad form. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear systems, bosonic and fermionic, described by generalized Lindblad master equations. Our method is efficient and allows one to obtain analytical solutions for the steady state. Further, we include as a review some covariance matrix methods for which our results are particularly relevant, paying special attention to those related to the measurement of entanglement. Finally, we prove that the Duan criterion for entanglement is also applicable to fermionic systems., Comment: 14 pages, 2 figures

A general strategy for the realization of electric and magnetic quasi-trapped modes located at the same spectral position is presented. This strategy's application makes it possible to design metasurfaces allowing switching between the electric and magnetic quasi-trapped modes by changing the polarization of the incident light wave. The developed strategy is based on two stages: the application of the dipole approximation for determining the conditions required for the implementation of trapped modes and the creation of the energy channels for their excitation by introducing a weak bianisotropy in nanoparticles. Since excitation of trapped modes results in a concentration of electric and magnetic energies in the metasurface plane, the polarization switching provides possibilities to change and control the localization and distribution of optical energy at the sub-wavelength scale. We demonstrate a practical method for spectral tuning of quasi-trapped modes in metasurfaces composed of nanoparticles with a pre-selected shape. As an example, the optical properties of a metasurface composed of silicon triangular prisms are analyzed and discussed.

We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of $GaP$, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. We observe and explain intensive sharp spikes in scattering cross section just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell's equations and occurs very high. The models' advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed., Comment: 27 pages, 9 figures

Nonlinear light sources are central to a myriad of applications, driving a quest for their miniaturisation down to the nanoscale. In this quest, nonlinear metasurfaces hold a great promise, as they enhance nonlinear effects through their resonant photonic environment and high refractive index, such as in high-index dielectric metasurfaces. However, despite the sub-diffractive operation of dielectric metasurfaces at the fundamental wave, this condition is not fulfilled for the nonlinearly generated harmonic waves, thereby all nonlinear metasurfaces to date emit multiple diffractive beams. Here, we demonstrate the enhanced single-beam second- and third-harmonic generation in a metasurface of crystalline transition-metal-dichalcogenide material, offering the highest refractive index. We show that the interplay between the resonances of the metasurface allows for tuning of the unidirectional second-harmonic radiation in forward or backward direction, not possible in any bulk nonlinear crystal. Our results open new opportunities for metasurface-based nonlinear light-sources, including nonlinear mirrors and entangled-photon generation., Comment: 16 pages, 8 figures

The ability of extreme sound energy confinement with high-quality factor (Q-factor) resonance is of vital importance for acoustic devices requiring high intensity and hypersensitivity in biological ultrasonics, enhanced collimated sound emission (i.e. sound laser) and high-resolution sensing. However, structures reported so far demonstrated a limited quality factor (Q-factor) of acoustic resonances, up to several tens in an open resonator. The emergence of bound states in the continuum (BIC) makes it possible to realize high-Q factor acoustic modes. Here, we report the theoretical design and experimental demonstration of acoustic BICs supported by a single open resonator. We predicted that such an open acoustic resonator could simultaneously support three types of BICs, including symmetry protected BIC, Friedrich-Wintgen BIC induced by mode interference, as well as a new kind of BIC: mirror-symmetry induced BIC. We also experimentally demonstrated the existence of all three types of BIC with Q-factor up to one order of magnitude greater than the highest Q-factor reported in an open resonator., Comment: 14 pages, 5 figures

Two dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS2, WS2, MoSe2, and WSe2, have received extensive attention in the past decade due to their extraordinary physical properties. The unique properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance is limited by the relatively weak light-matter interactions due to their atomically thin form factor. Resonant nanophotonic structures provide a viable way to address this issue and enhance light-matter interactions in 2D TMDCs. Here, we provide an overview of this research area, showcasing relevant applications, including exotic light emission, absorption and scattering features. We start by overviewing the concept of excitons in 1L-TMDC and the fundamental theory of cavity-enhanced emission, followed by a discussion on the recent progress of enhanced light emission, strong coupling and valleytronics. The atomically thin nature of 1L-TMDC enables a broad range of ways to tune its electric and optical properties. Thus, we continue by reviewing advances in TMDC-based tunable photonic devices. Next, we survey the recent progress in enhanced light absorption over narrow and broad bandwidths using 1L or few-layer TMDCs, and their applications for photovoltaics and photodetectors. We also review recent efforts of engineering light scattering, e.g., inducing Fano resonances, wavefront engineering in 1L or few-layer TMDCs by either integrating resonant structures, such as plasmonic/Mie resonant metasurfaces, or directly patterning monolayer/few layers TMDCs. We then overview the intriguing physical properties of different types of van der Waals heterostructures, and their applications in optoelectronic and photonic devices. Finally, we draw our opinion on potential opportunities and challenges in this rapidly developing field of research., Comment: 101 pages, 25 figures

Infrared imaging is a crucial technique in a multitude of applications, including night vision, autonomous vehicles navigation, optical tomography, and food quality control. Conventional infrared imaging technologies, however, require the use of materials like narrow-band gap semiconductors which are sensitive to thermal noise and often require cryogenic cooling. Here, we demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas, using a nonlinear wave-mixing process. We experimentally show the up-conversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation. In this process, an infrared image of a target is mixed inside the metasurface with a strong pump beam, translating the image from infrared to the visible in a nanoscale ultra-thin imaging device. Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences., Comment: 32 pages, 13 figures

Optically resonant dielectric metasurfaces offer unique capability to fully control the wavefront, polarisation, intensity or spectral content of light based on the excitation and interference of different electric and magnetic Mie multipolar resonances. Recent advances of the wide accessibility in the nanofabrication and nanotechnologies have led to a surge in the research field of high-quality functional optical metasurfaces which can potentially replace or even outperform conventional optical components with ultra-thin feature. Replacing conventional optical filtering components with metasurface technology offers remarkable advantages including lower integration cost, ultra-thin compact configuration, easy combination with multiple functions and less restriction on materials. Here we propose and experimentally demonstrate a planar narrow-band-pass filter based on the optical dielectric metasurface composed of Si nanoresonators in array. A broadband transmission spectral valley (around 200~nm) has been realised by combining electric and magnetic dipole resonances adjacent to each other. Meanwhile, we obtain a narrow-band transmission peak by exciting a high-quality leaky mode which is formed by partially breaking a bound state in the continuum generated by the collective longitudinal magnetic dipole resonances in the metasurface. Our proposed metasurface-based filter shows a stable performance for oblique light incidence with small angles (within 10 deg). Our work imply many potential applications of nanoscale photonics devices such as displays, spectroscopy, etc., Comment: 6

The review is devoted to a discussion of new (and often unexpected) aspects of the old problem of elastic light scattering by small metal particles, whose size is comparable to or smaller than the thickness of the skin layer. The main focus is put on elucidating the physical grounds for these new aspects. It is shown that, in many practically important cases, the scattering of light by such particles, despite their smallness, may have almost nothing in common with the Rayleigh one. The so-called, anomalous scattering and absorption, as well as Fano resonances, including unconventional (associated with the excitation of longitudinal electromagnetic oscillations) and directional Fano resonances, observed only in a small solid angle, are discussed in detail. The review contains a Mathematical Supplement, which includes a summary of the main results of the Mie theory and a discussion of some general properties of the scattering coefficients. In addition to purely academic interest, the phenomena considered in this review can find wide applications in biology, medicine, pharmacology, genetic engineering, imaging of ultra-small objects, ultra-high-resolution spectroscopy, information transmission, recording, and processing, and many other applications and technologies. The reported study was funded by RFBR, project number 19-11-00001 and the project of the Russian Science Foundation No. 19-72-30012, within the framework of which all the original calculations given in this publication were performed., Comment: a review paper, 27 pages, in Russian

Modern nanophotonics has witnessed the rise of "electric anapoles", destructive interferences of electric dipoles and toroidal electric dipoles, actively exploited to cancel electric dipole radiation from nanoresonators. However, the inherent duality of Maxwell's equations suggests the intriguing possibility of "magnetic anapoles", involving a nonradiating composition of a magnetic dipole and a magnetic toroidal dipole. Here, we predict, fabricate and observe experimentally via a series of dark field spectroscopy measurements a hybrid anapole of mixed electric and magnetic character, with all the dominant multipoles being suppressed by the toroidal terms in a nanocylinder. We delve into the physics of such exotic current configurations in the stationary and transient regimes and predict a number of ultrafast phenomena taking place within sub-ps times after the breakdown of the hybrid anapole. Based on the preceding theory, we design a non-Huygens metasurface featuring a dual functionality: perfect transparency in the stationary regime and controllable ultrashort pulse beatings in the transient.

If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative description of these effects may be a very difficult problem. We suggest a simple tractable model to describe these phenomena. The model is based on approximation of the actual Fourier spectrum of the system by that composed of the superposition of the spectra of uncoupled harmonic oscillators (normal modes). The physical nature of the underlying system is employed to select the proper approximation. This reduces the dynamics of the system to tractable dynamics of just a few driven oscillators. The method is simple and may be applied to many types of resonances. As an illustration, the approach is employed to describe the sharp intensive spikes observed in the recent numerical simulation of short light pulses scattered by a cylinder in the proximity of destructive Fano interference [Phys. Rev. A., vol. 100, 053824 (2019)] and exhibits excellent agreement with the numerics., Comment: 5 pages, 2 figures

We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves, making the obstacle lose its intrinsic responses in a broadband spectrum. The associated coherent beams generate a finite and static region, inside which the corresponding electric field intensity and Poynting vector vanish. As a solution to go beyond the sum-rule limit, our methodology is also irrespective of inherent system properties, as well as extrinsic operating wavelength, providing a non-invasive control on the wave-obstacles interaction for any kinds of shape.

A key concept underlying the specific functionalities of metasurfaces, i.e. arrays of subwavelength nanoparticles, is the use of constituent components to shape the wavefront of the light, on-demand. Metasurfaces are versatile and novel platforms to manipulate the scattering, colour, phase or the intensity of the light. Currently, one of the typical approaches for designing a metasurface is to optimize one or two variables, among a vast number of fixed parameters, such as various materials' properties and coupling effects, as well as the geometrical parameters. Ideally, it would require a multi-dimensional space optimization through direct numerical simulations. Recently, an alternative approach became quite popular allowing to reduce the computational cost significantly based on a deep-learning-assisted method. In this paper, we utilize a deep-learning approach for obtaining high-quality factor (high-Q) resonances with desired characteristics, such as linewidth, amplitude and spectral position. We exploit such high-Q resonances for the enhanced light-matter interaction in nonlinear optical metasurfaces and optomechanical vibrations, simultaneously. We demonstrate that optimized metasurfaces lead up to 400+ folds enhancement of the third harmonic generation (THG); at the same time, they also contribute to 100+ folds enhancement in optomechanical vibrations. This approach can be further used to realize structures with unconventional scattering responses., Comment: 29 pages, 7 figures

High index dielectric nanostructure supports different types of resonant modes. However, it is very challenging to achieve high-Q factor in a single subwavelength dielectric nanoresonator due to non-hermtian property of the open system. Here, we present a universal approach of finding out a series of high-Q resonant modes in a single nonspherical dielectric nanocavity by exploring quasi-bound state in the continuum. Unlike conventional method relying on heavy computation (ie, frequency scanning by FDTD), our approach is built upon leaky mode engineering, through which many high-Q modes can be easily achieved by constructing avoid-crossing (or crossing) of the eigenvalue for pair leaky modes. The Q-factor can be up to 2.3*10^4 for square subwavelength nanowire (NW) (n=4), which is 64 times larger than the highest Q-factor (Q=360) reported so far in single subwavelength nanodisk. Such high-Q modes can be attributed to suppressed radiation in the corresponding eigenchannels and simultaneously quenched electric(magnetic) at momentum space. As a proof of concept, we experimentally demonstrate the emergence of the high-Q resonant modes (Q=380) in the scattering spectrum of a single silicon subwavelength nanowire., Comment: 8 pages, 5 figures

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., Comment: 13 pages, 2 figures; infinite potential range emphasized. arXiv admin note: text overlap with arXiv:1904.03227

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., Comment: The Heisenberg condition has been reduced down to analytic relation (35) for the cylindrical Bessel functions (7 pages, 1 figure)

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.

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.

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., Comment: 18 pages, 5 figures

All-dielectric nanophotonics attracts ever increasing attention nowadays due to the possibility to control and configure light scattering on high-index semiconductor nanoparticles. It opens a room of opportunities for the designing novel types of nanoscale elements and devices, and paves a way to advanced technologies of light energy manipulation. One of the exciting and promising prospects is associated with the utilizing so called toroidal moment being the result of poloidal currents excitation, and anapole states corresponding to the interference of dipole and toroidal electric moments. Here, we present and investigate in details via the direct Cartesian multipole decomposition higher order toroidal moments of both types (up to the electric octupole toroidal moment) allowing to obtain new near- and far-field configurations. Poloidal currents can be associated with vortex-like distributions of the displacement currents inside nanoparticles revealing the physical meaning of the high-order toroidal moments and the convenience of the Cartesian multipoles as an auxiliary tool for analysis. We demonstrate high-order nonradiating anapole states (vanishing contribution to the far-field zone) accompanied by the excitation of intense near-fields. We believe our results to be of high importance for both fundamental understanding of light scattering by high-index particles, and a variety of nanophotonics applications and light governing on nanoscale.

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., Comment: 6 pages, 1 figure

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 Schr\"odinger 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., Comment: 49 pp, 18 figures; connection with Heun equation emphasized, a couple of new references added, discussion refined, a comparison with the Rabi models emphasized

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., Comment: 29 pages, 7 figures and comments welcomed

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., Comment: 4 pages, 6 figures

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., Comment: 8 pages, 4 figures

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., Comment: 7 pages, 4 figures and comments are welcome

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., Comment: Comments are welcome! :-)

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., Comment: Submit for publication, comments are welcome