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

All optical diode based on dipole modes of Kerr microcavity in asymmetric L-shaped photonic crystal waveguide

A design of all optical diode in $L$-shaped photonic crystal waveguide is proposed that uses the multistability of single nonlinear Kerr microcavity with two dipole modes. Asymmetry of the waveguide is achieved by difference in coupling of the dipole modes with the left and right legs of waveguide. By use of coupled mode theory we present domains in axis of light frequency and amplitude where an extremely high transmission contrast can be achieved. The direction of optical diode transmission can be governed by power and frequency of injecting light. The theory agrees with numerical solution of the Maxwell equations

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

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

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

S-matrix theory of single-channel ballistic transport through coupled quantum dots

We consider single-channel transmission through a double quantum dot system that consists of two single dots coupled by a wire of finite length L. In order to explain the numerically obtained results for a realistic double dot system we explore a simple model. It consists, as the realistic system, of two dots connected by a wire of length L. However, each of the two single dots is characterized by a few energy levels only, and the wire is assumed to have only one level whose energy depends on L. The transmission is described by using S-matrix theory. The model explains in particular the splitting of the resonant transmission peaks and the origin of the transmission zeros. The latter are independent of the length of the wire. When the transmission zeros of the single dots are of first order and both single dots are identical, those of the double dot are of second order. First-order transmission zeros cause phase jumps of the transmission amplitude by $\pi$, while there are no phase jumps related to second-order transmission zeros. In this latter case, a phase jump appears due to a resonance state whose decay width vanishes when crossing the energy of the transmission zero.Comment: 25 pages, 10 figure

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

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