Optical Bloch oscillations in waveguide arrays

We show that optical Bloch oscillations can emerge in waveguide arrays with linearly varying propagation constants. The existence of localized modes (Wannier-Stark states) with equidistant wave-number spacing (Wannier-Stark ladder) that do not undergo diffraction is analytically proved. The evolution of arbitrary initial excitations is described, and potential applications are suggested.     

Unidirectional optical Bloch oscillations in asymmetric waveguide arrays

We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.     

Plasmonic Bloch oscillations in cylindrical metal-dielectric waveguide arrays

This study investigates plasmonic Bloch oscillations (PBOs) in cylindrical metal-dielectric waveguide arrays (MDWAs) by performing numerical simulations and theoretical analyses. Optical conformal mapping is used to transform cylindrical MDWAs into equivalent chirped structures with permittivity and permeability gradients across the waveguide arrays, which is caused by the curvature of the cylindrical waveguide. The PBOs are attributed to the transformed structure. The period of oscillation increases with the wavelength of the incident Gaussian beam. However, the amplitude of oscillation is almost independent of wavelength.     

Surface optical Bloch oscillations in semi-infinite waveguide arrays

We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.     

Imaging of Bloch oscillations in erbium-doped curved waveguide arrays

We report a direct observation of Bloch-like dynamics of light in curved waveguide arrays manufactured in Er:Yb-doped phosphate glass by femtosecond laser writing. The green upconversion fluorescence emitted by excited erbium ions is exploited to image the flow of the guided pump light at approximately 980 nm along the array. Direct and clear evidence of periodic light breathing for single-waveguide excitation, closely related to Bloch oscillations, is reported.     

Bloch oscillations and Wannier-Stark ladder in the coupled LC circuits

We present a new scheme for realizing Bloch oscillations and Wannier-Stark ladder based on a lattice of coupled LC circuits. By converting the second order dynamical ODEs of the system into a first order Schrödinger-like equation, we propose an equivalent tight binding Hamiltonian to describe the circuit. We show that a synthesized electric field is produced by introducing a frequency mismatch into the resonant frequency of the adjacent LC resonators. The Wannier-Stark modes are the normal modes of the circuit and the Bloch oscillations can be observed in a coupled LC lattice. By addition of coupling capacitors between nodes of the circuit, we study the Bloch oscillation in the presence of long-range couplings. We also show that the circuit converts to a transmission line simulating synthetic electric fields in the continuum limit. The coupled LC circuit is, in some sense, amongst the simplest physical systems exhibiting Bloch oscillation and Wannier-Stark Ladder.     

Discrete diffraction in two-dimensional arrays of coupled waveguides in silica

The propagation of light in 5 x 5 and 7 x 7 cubic lattices of evanescently coupled waveguides is investigated for the first time, to the authors' knowledge. The results reveal ideal discrete diffraction and demonstrate the excellent quality of the waveguide arrays, which were manufactured in fused silica by femtosecond-laser-induced refractive-index modifications.     

Entanglement transfer via two arrays of coupled resonator waveguides

We propose a scheme for transferring entanglement through two independent arrays of coupled resonator waveguides,where a three-level atom is embedded in each resonator.We investigate the entanglement dynamics of the transferred state.The influence of initial states and applied lasers on the entanglement sudden death phenomenon is also discussed.Furthermore,we study the dynamics of pairwise quantum correlations measured by the quantum discord.     

Entanglement transfer via two arrays of coupled resonator waveguides

We propose a scheme for transferring entanglement through two independent arrays of coupled resonator waveguides, where a three-level atom is embedded in each resonator. We investigate the entanglement dynamics of the transferred state. The influence of initial states and applied lasers on the entanglement sudden death phenomenon is also discussed. Furthermore, we study the dynamics of pairwise quantum correlations measured by the quantum discord.     

Bloch oscillations in one-dimensional photonic crystal coupled microcavity composed of single-negative materials

We have studied the propagation properties of electromagnetic waves in one-dimensional photonic crystal coupled microcavity structure composed of single-negative materials. Two Wannier-Stark ladders can be obtained by employing only one type of microcavity. The dynamics behavior of a Gaussian pulse transmitting through the structure is simulated theoretically. We demonstrated for the first time that even in this multilayered structure completely made of single-negative materials, the optical Bloch oscillations and Zener tunneling can also be attained.     

Phase stability theory of Bloch eigenstates in active photonic lattices with coupled microlaser arrays

An generic model for the lattice dynamics of coupled microlaser arrays is employed for the lattice stability analysis. Nonlinear cross-cavity gain-coupling effects, characterizing active lattices, are included via the gain dependence on carrier depletion and cross-cavity hole burning. Passive near neighbor interactions (inter-cavity absorption and mirror reflection interference) are also included. The introduction of lattice-orthogonal modes simplifies the derivation of the coupled rate equations. The interaction phase among sites exhibits spontaneous long range “crystallization" into periodic Bloch states whereby the cavity radiation envelopes behave as laser “macro-atoms". The sign of the coupling coefficients as a function of geometry determines in- vs. out-of-phase locking and has practical implications for array design. Emphasis is placed on the stability analysis of Bloch states by including earlier omitted [1] effects of phase perturbations. The importance of the linewidth factor ι is uncovered: unconditional stability results for ι ≤1, otherwise a stability threshold exists for the coupling strength among sites. Choice of low ι gain material permits phase stability with high coupling strength, beneficial in overcoming manufacturing variations among array cavity parameters.     

Observation of anharmonic Bloch oscillations

We report on the experimental observation of Bloch oscillations of an optical wave packet in a lattice with second-order coupling. To this end, we employ zigzag waveguide arrays, in which the second-order coupling can be precisely tuned.     

A circular system of coupled waveguides and an optical analogue of bloch oscillations

The process of light propagation in a nonuniform system of tunnel-coupled waveguides is studied. The nonuniform system of waveguides is realized by making a circular system of waveguides on the inner wall of a supporting tube with the help of the SPCVD technology, which is designed for the synthesis of preforms of optical fibers. It is shown that the waveguide light beam propagates in such a system along a wavelike trajectory and partially radiates outwards at the crests of this trajectory. The oscillation period of the trajectory is measured, and it is shown that it is possible to input radiation into the waveguide mode by the process that is inverse to the process of light emission from the structure.     

Bloch oscillations of path-entangled photons

We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.     

Bloch oscillations in optical dissipative lattices

We show that Bloch oscillations are possible in dissipative optical waveguide lattices with a linearly varying propagation constant. These oscillations occur in spite of the fact that the Bloch wave packet experiences coupling gain and (or) loss. Experimentally, this process can be observed in different settings, such as in laser arrays and lattices of semiconductor optical amplifiers. In addition, we demonstrate that these systems can suppress instabilities arising from preferential mode noise growth.     

Photonic Bloch oscillations of correlated particles

A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.     

Bloch oscillations in a homogeneous nucleotide chain

It is shown that, at zero temperature, a hole placed in a homogeneous synthetic nucleotide chain with applied electric field demonstrates Bloch oscillations. The oscillations of the hole placed initially on one of the base pairs arise in response to disruption of the initial charge distribution caused by nucleotide vibrations. The finite temperature fluctuations result in degradation of coherent oscillations. The maximum permissible temperature for DNA “Bloch oscillator” occurrence is estimated.