Mapping the electronic transitions of protonation sites in peptides using soft X-ray action spectroscopy.

Near-edge X-ray absorption mass spectrometry (NEXAMS) around the nitrogen and oxygen K-edges was employed on gas-phase peptides to probe the electronic transitions related to their protonation sites, namely at basic side chains, the N-terminus and the amide oxygen. The experimental results are supported by replica exchange molecular dynamics and density-functional theory and restricted open-shell configuration with single calculations to attribute the transitions responsible for the experimentally observed resonances. We studied five tailor-made glycine-based pentapeptides, where we identified the signature of the protonation site of N-terminal proline, histidine, lysine and arginine, at 406 eV, corresponding to N 1s → σ*(NHx+) (x = 2 or 3) transitions, depending on the peptides. We compared the spectra of pentaglycine and triglycine to evaluate the sensitivity of NEXAMS to protomers. Separate resonances have been identified to distinguish two protomers in triglycine, the protonation site at the N-terminus at 406 eV and the protonation site at the amide oxygen characterized by a transition at 403.1 eV.

Quantum Manifestation of the Classical Bifurcation in the Driven Dissipative Bose-Hubbard Dimer.

We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose-Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.

Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton.

We consider Tamm plasmon polariton in a subwavelength grating patterned on top of a Bragg reflector. We demonstrate dynamic control of the phase and amplitude of a plane wave reflected from such metagrating due to resonant coupling with the Tamm plasmon polariton. The tunability of the phase and amplitude of the reflected wave arises from modulation of the refractive index of a transparent conductive oxide layer by applying the bias voltage. The electrical switching of diffracted beams of the ±1st order is shown. The possibility of doubling the angular resolution of beam steering by using asymmetric reflected phase distribution with integer and half-integer periods of the metagrating is demonstrated.

Temperature-Dependent Electronic Ground-State Charge Transfer in van der Waals Heterostructures.

Electronic charge rearrangement between components of a heterostructure is the fundamental principle to reach the electronic ground state. It is acknowledged that the density of state distribution of the components governs the amount of charge transfer, but a notable dependence on temperature is not yet considered, particularly for weakly interacting systems. Here, it is experimentally observed that the amount of ground-state charge transfer in a van der Waals heterostructure formed by monolayer MoS2 sandwiched between graphite and a molecular electron acceptor layer increases by a factor of 3 when going from 7 K to room temperature. State-of-the-art electronic structure calculations of the full heterostructure that accounts for nuclear thermal fluctuations reveal intracomponent electron-phonon coupling and intercomponent electronic coupling as the key factors determining the amount of charge transfer. This conclusion is rationalized by a model applicable to multicomponent van der Waals heterostructures.

Critical coupling vortex with grating-induced high Q-factor optical Tamm states.

We investigate optical Tamm states supported by a dielectric grating placed on top of a distributed Bragg reflector. It is found that under certain conditions the Tamm state may become a bound state in the continuum. The bound state, in its turn, induces the effect of critical coupling with the reflectance amplitude reaching an exact zero. We demonstrate that the critical coupling point is located in the core of a vortex of the reflection amplitude gradient in the space of the wavelength and angle of incidence. The emergence of the vortex is explained by the coupled mode theory.

Refractive index sensing with optical bound states in the continuum.

We consider refractive index sensing with optical bounds states in the continuum (BICs) in dielectric gratings. Applying a perturbative approach we derived the differential sensitivity and the figure of merit of a sensor operating in the spectral vicinity of a BIC. Optimisation design approach for engineering an effective sensor is proposed. An analytic formula for the maximal sensitivity with an optical BIC is derived. The results are supplied with straightforward numerical simulations.

Fano feature induced by a bound state in the continuum via resonant state expansion.

We consider light scattering by an anisotropic defect layer embedded into anisotropic photonic crystal in the spectral vicinity of an optical bound state in the continuum (BIC). Using a resonant state expansion method we derive an analytic solution for reflection and transmission amplitudes. The analytic solution is constructed via a perturbative approach with the BIC as the zeroth order approximation. The solution is found to describe the collapsing Fano feature in the spectral vicinity of the BIC. The findings are confirmed via comparison against direct numerical simulations with the Berreman transfer matrix method.

Nonlinear response from optical bound states in the continuum.

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced triggering optical bistability. Using coupled mode approach we derive a nonlinear equation for the amplitude of the resonant mode associated with the bound state. We show that such an equation for the isolated resonance can be easily solved yielding bistable solutions which are in quantitative agreement with the full-wave solutions of Maxwell's equations. The coupled mode approach allowed us to cast the the problem into the form of a driven nonlinear oscillator and analyze the onset of bistability under variation of the incident wave. The results presented drastically simplify the analysis nonlinear Maxwell's equations and, thus, can be instrumental in engineering optical response via bound states in the continuum.

Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab.

We consider reflection of the Laguerre-Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre-Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos-Hänchen and the Imbert-Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos-Hänchen shift up to one half of the beam radius, both negative and positive.

Light enhancement by quasi-bound states in the continuum in dielectric arrays.

The article reports on light enhancement by structural resonances in linear periodic arrays of identical dielectric elements. As the basic elements both subwavelength spheres and rods with circular cross section have been considered. In either case it has been demonstrated numerically that high-Q structural resonant modes originated from bound states in the continuum enable near-field amplitude enhancement by factor of 10-25 in the red-to-near infrared range in lossy silicon. The asymptotic behavior of the Q-factor with the number of elements in the array is explained theoretically by analyzing quasi-bound states propagation bands.

Topological Bound States in the Continuum in Arrays of Dielectric Spheres.

We consider Bloch bound states in the radiation continuum in periodic arrays of dielectric spheres. It is demonstrated that the bound states are associated with phase singularities of the quasimode coupling strength. That makes the bound states topologically protected and, therefore, robust against any variation of parameters preserving the periodicity and rotational symmetry about the array axis. It is shown that under variation of parameters the bound states can only be destroyed by either annihilation of the topological charge or by migration to the sector of the parametric space where the second radiation channel is open.

Light guiding above the light line in arrays of dielectric nanospheres.

We consider light propagation above the light line in arrays of spherical dielectric nanoparticles. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance of 60 wavelengths at the frequencies close to the bound states in the radiation continuum. A semi-analytical estimate for decay rates of the guided waves is found to match the numerical data to a good accuracy.

Gate controlled resonant widths in double-bend waveguides: bound states in the continuum.

We consider quantum transmission through double-bend [Formula: see text]- and Z-shaped waveguides controlled by the finger gate potential. Using the effective non-Hermitian Hamiltonian approach we explain the resonances in transmission. We show a difference in transmission in the short waveguides that is the result of different chirality in Z and [Formula: see text] waveguides. We demonstrate that the potential selectively affects the resonant widths resulting in the occurrence of bound states in the continuum.

Symmetry breaking in binary chains with nonlinear sites.

We consider a system of two or four nonlinear sites coupled with binary chain waveguides. When a monochromatic wave is injected into the first (symmetric) propagation channel, the presence of cubic nonlinearity can lead to symmetry breaking, giving rise to emission of antisymmetric wave into the second (antisymmetric) propagation channel of the waveguides. We found that in the case of nonlinear plaquette, there is a domain in the parameter space where neither symmetry-preserving nor symmetry-breaking stable stationary solutions exit. As a result, injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies differing from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior.

A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures.

Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behavior due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems that are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modeled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations that can be solved for the mean energies in the short wavelength subsystems.

Statistics of nodal points of in-plane random waves in elastic media.

We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.

Quantum stress in chaotic billiards.

This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u+iv . With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T_{alphabeta} . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T_{alphabeta}(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

Bound states in elastic waveguides.

We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C(4upsilon). Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A2. The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.

Electric circuit networks equivalent to chaotic quantum billiards.

We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.