All-optical light storage in bound states in the continuum and release by demand.

In the framework of the temporal coupled mode theory we consider bound states embedded in the continuum (BSC) of photonic crystal waveguide as a capacity for light storage. A symmetry protected BSC occurs in two off-channel microresonators positioned symmetrically relative to the waveguide. We demonstrate that the symmetry protected BSC captures a fraction of a light pulse due to the Kerr effect as the pulse passes by the microresonators. However the amount of captured light is found to be strongly sensitive to the parameters of the gaussian light pulse such as basic frequency, duration and intensity. In contrast to the above case the BSC resulted from a full destructive interference of two eigenmodes of a single microresonator accumulates a fixed amount of light dependent on the material parameters of the microresonator but independent of the light pulse. The BSCs in the Fabry-Perot resonator show similar effects. We also show that the accumulated light can be released by a secondary pulse. These phenomena pave a way for all-optical storage and release of light.

Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide.

We present a two-dimensional photonic crystal design of four defect dielectric rods, which form a microcavity with eigenfrequencies residing in the propagating band of a directional waveguide. In this system, a nonrobust bound state in the continuum (BSC) occurs as a result of full destructive interference of the monopole and quadrupole modes, with the same parity at certain values of the material parameters of the defect rods. Due to the Kerr effect, a robust BSC arises in a self-adaptive way without necessity to tune the material parameters. The absence of the superposition principle in that nonlinear system gives rise to coupling of the BSC with injected light, resulting in a novel transmission resonance.

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 through different couplings of the dipole modes with the left and right legs of the waveguide. Using coupled mode theory we demonstrate an extremely high transmission contrast. The direction of optical diode transmission can be controlled by power or frequency of injected light. The theory agrees with the numerical solution of the Maxwell equations.

Resonant angular conversion in a Fabry-Perot resonator holding a dielectric cylinder.

Light transmission through a Fabry-Perot resonator (FPR) holding a dielectric cylinder rod is considered. For the cylinder parallel to mirrors of the FPR and the mirrors mimicked by the δ functions we present an exact analytical theory. It is shown that light transmits only for resonant incident angles, α(m), similar to the empty FPR. However after transmission the light scatters into different resonant angles, α(m'), performing resonant angular conversion. We compare the theory with experiment in the FPR, exploring multilayer films as the mirrors and glass cylinder with diameter coincided with the distance between the FPR mirrors. The measured values of angular light conversion agree qualitatively with the theoretical results.

Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot.

We study the spectrum of an open double quantum dot as a function of different system parameters in order to receive information on the geometric phases of branch points in the complex plane (BPCP). We relate them to the geometrical phases of the diabolic points (DPs) of the corresponding closed system. The double dot consists of two single dots and a wire connecting them. The two dots and the wire are represented by only a single state each. The spectroscopic values follow from the eigenvalues and eigenfunctions of the Hamiltonian describing the double dot system. They are real when the system is closed, and complex when the system is opened by attaching leads to it. The discrete states as well as the narrow resonance states avoid crossing. The DPs are points within the avoided level crossing scenario of discrete states. At the BPCP, width bifurcation occurs. Here, different Riemann sheets evolve and the levels do not cross anymore. The BPCP are physically meaningful. The DPs are unfolded into two BPCP with different chirality when the system is opened. The geometric phase that arises by encircling the DP in the real plane, is different from the phase that appears by encircling the BPCP. This is found to be true even for a weakly opened system and the two BPCP into which the DP is unfolded.

Zeros in single-channel transmission through double quantum dots.

By using a simple model we consider single-channel transmission through a double quantum dot that consists of two single dots coupled by a wire of finite length L . 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 the length L . The transmission is described by using S matrix theory and the effective non-Hermitian Hamilton operator H(eff) of the system. The decay widths of the eigenstates of H(eff) depend strongly on energy. The model explains the origin of the transmission zeros of the double dot that is considered by us. Mostly, they are caused by (destructive) interferences between neighboring levels and are of first order. When, however, both single dots are identical and their transmission zeros are of first order, 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 occurs due to the fact that the width of one of the states vanishes when crossing the energy of the transmission zero. The parameter dependence of the widths of the resonance states is determined by the spectral properties of the two single dots.

Influence of branch points in the complex plane on the transmission through double quantum dots.

We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows one to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.

Wave function statistics for ballistic quantum transport through chaotic open billiards: statistical crossover and coexistence of regular and chaotic waves.

For ballistic transport through chaotic open billiards, we implement accurate fully quantal calculations of the probability distributions and spatial correlations of the local densities of single-electron wave functions within the cavity. We find wave-statistical behaviors intrinsically different from those in their closed counterparts. Chaotic-scattering wave functions in open systems can be quantitatively interpreted in terms of statistically independent real and imaginary random fields in the same way as for wave-function statistics of closed systems in the time-reversal symmetry-breaking crossover regime. We also discuss perceived statistical deviations, which are attributed to the coexistence of regular and chaotic waves and given analytical explanations.

Distribution of nearest distances between nodal points for the Berry function in two dimensions.

According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from numerical calculations for the Berry wave function.