Bloch bound states in the radiation continuum in a periodic array of dielectric rods

We consider an infinite periodic array of dielectric rods in vacuum with the aim to demonstrate three types of a Bloch bound states in the continuum (BSC), symmetry protected with a zero Bloch vector, embedded into one diffraction channel with nonzero Bloch vector, and embedded into two and three diffraction channels. The first and second types of the BSC exist in a wide range of material parameters of the rods, while the third occurs only at a specific value of the radius of the rods. We show that the second type supports the power flux along the array. In order to find BSC we put forward an approach based on the expansion over the Hankel functions. We show how the BSC reveals itself in the scattering function when the singular BSC point is approached along a specific path in the parametric space.Comment: 12 pages, 10 figure

Robust bound states in the continuum in Kerr microcavity embedded in photonic crystal waveguide

We present a two-dimensional photonic crystal design with a microcavity of four defect dielectric rods with eigenfrequencies residing in the propagating band of directional waveguide. In the linear case for tuning of material parameters of defect rods the nonrobust bound state in the continuum (BSC) might occur. The BSC is a result of full destructive interference of resonant monopole and quadrupole modes with the same parity. % to trap light interior of the microcavity. A robust BSC arises in a self-adaptive way without necessity to tune the parameters of the microcavity with the Kerr effect. Lack of the superposition principle in nonlinear systems gives rise to coupling of the BSC with injecting light. That forms a peculiar shape of isolated transmittance resonance around BSC frequency. We show if injecting light is switched off the BSC storages light that opens a way for light accumulation

Near-bound states in the radiation continuum in circular array of dielectric rods

We consider E polarized bound states in the radiation continuum (BICs) in circular periodical arrays of $N$ infinitely long dielectric rods. We find that each true BIC which occurs in an infinite linear array has its counterpart in the circular array as a near-BIC with extremely large quality factor. We argue analytically as well as numerically that the quality factor of the symmetry protected near-BICs diverges as $e^{\lambda N}$ where $\lambda$ is a material parameter dependent on the radius and the refraction index of the rods. By tuning of the radius of rods we also find numerically non-symmetry protected near-BICs. These near-BICs are localized with exponential accuracy outside the circular array but fill the whole inner space of the array carrying orbital angular momentum.Comment: 14 pages, 14 figure

Electromagnetic analog of Rashba spin-orbit interaction in wave guides filled with ferrite

We consider infinitely long electromagnetic wave guide filled with a ferrite. The wave guide has arbitrary but constant cross-section $. We show that Maxwell equations are equivalent to the Schr\"odinger equation for single electron in the two-dimensional quantum dot of the form D with account of the Rashba spin-orbit interaction. The spin-orbit constant is determining by components of magnetic permeability of the ferrite. The upper component of electron spinor function corresponds to the z-th component electric field, while the down component$\chi$ related to the z-th component of magnetic field by relation (30).Comment: 6 pages, 1 figur

Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity

We report bound states in the radiation continuum (BSCs) in a single infinitely long dielectric rod with periodically stepwise modulated permittivity alternating from $\epsilon_1$ to $\epsilon_2$. For $\epsilon_2=1$ in air the rod is equivalent to a stack of dielectric discs with permittivity $\epsilon_1$. Because of rotational and translational symmetries the BSCs are classified by orbital angular momentum $m$ and the Bloch wave vector $\beta$ directed along the rod. For $m=0$ and $\beta=0$ the symmetry protected BSCs have definite polarization and occur in a wide range of the radius of the rod and the dielectric permittivities. More involved BSCs with $m\neq 0, \beta=0$ exist only for a selected radius of the rod at a fixed dielectric constant. The existence of robust Bloch BSCs with $\beta\neq 0, m=0$ is demonstrated. Asymptotic limits to a homogeneous rod and to very thin discs are also considered.Comment: 15 pages, 15 figure

Symmetry breaking in binary chain 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 different from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior

Light trapping above the light cone in one-dimensional array of dielectric spheres

We demonstrate bound states in the first TE and TM diffraction continua (BSC) in a linear periodic array of dielectric spheres in air above the light cone. We classify the BSCs according to the symmetry specified by the azimuthal number $m$, the Bloch wave vector $\beta$ directed along the array, and polarization. The most simple symmetry protected TE and TM polarized BSCs have $m=0$ and $\beta=0$ and occur in a wide range of the radius of the spheres and dielectric constant. More complicated BSCs with $m\neq 0$ and $\beta=0$ exist only for a selected radius of spheres at a fixed dielectric constant. We also find robust Bloch BSCs with $\beta\neq 0, m=0$. We present also the BSCs embedded into two and three diffraction continua. We show that the BSCs can be easily detected by the collapse of Fano resonance for scattering of electromagnetic plane waves by the array.Comment: 17 pages, 10 figure

Fibers based on propagating bound states in the continuum

We show that a circular periodic array of $N$ dielectric cylinders supports nearly bound states in the continuum (BICs) propagating along the cylinders. These propagating nearly BICs with extremely large $Q$ factors of order $exp(\lambda N)$ are surrounded by resonant modes weakly leaking into the radiation continuum. We present leaky zones in the vicinity of different types of BICs: symmetry protected nearly BICs with the resonant width proportional to the squared propagation constant $\Gamma \sim k_z^2$, non-symmetry protected nearly BICs with finite propagation constant $k_c$ with $\Gamma\sim (k_z-k_c)^2$ and non-symmetry protected nearly BICs with $\Gamma\sim k_z^4$. The latter propagating nearly BICs can serve for transmission of electromagnetic signal paving a way to novel type of optical fibers. We also demonstrate weakly leaking resonant modes which carry orbital angular momentum.Comment: 6 pages, 9 figure

Temporal oscillations of light transmission through dielectric microparticles subjected to optically induced motion

We consider light-induced binding and motion of dielectric microparticles in an optical waveguide that gives rise to a back-action effect such as light transmission oscillating with time. Modeling the particles by dielectric slabs allows us to solve the problem analytically and obtain a rich variety of dynamical regimes both for Newtonian and damped motion. This variety is clearly reflected in temporal oscillations of the light transmission. The characteristic frequencies of the oscillations are within the ultrasound range of the order of $10^{5}$ Hz for micron size particles and injected power of the order of 100 mW. In addition, we consider driven by propagating light dynamics of a dielectric particle inside a Fabry-Perot resonator. These phenomena pave a way for optical driving and monitoring of motion of particles in waveguides and resonators.Comment: 8 pages, 11 figure

Effect of gate-driven spin resonance on the conductance of a one-dimensional quantum wire

We consider quasiballistic electron transmission in a one-dimensional quantum wire subject to both time-independent and periodic potentials of a finger gate that results in a coordinate- and time-dependent Rashba-type spin-orbit coupling. A spin-dependent conductance is calculated as a function of external constant magnetic field, the electric field frequency, and the potential strength. The results demonstrate the effect of the gate-driven electric dipole spin resonance in a transport phenomenon such as spin-flip electron transmission.Comment: 7 figure