Optical Bloch Oscillations Research Articles

Observation of Period-Doubling Bloch Oscillations.

Bloch oscillations refer to the periodic oscillation of a wave packet in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wave packet traversing the first Brillouin zone once. Here, we demonstrate, both theoretically and experimentally, the optical Bloch oscillations where the wave packet must traverse the first Brillouin zone twice to complete a full cycle, resulting in a period of oscillation that is 2 times longer than that of usual Bloch oscillations. The unusual Bloch oscillations arise due to the band crossing of valley-Hall topological edge states at the Brillouin boundary for zigzag domain walls between two staggered honeycomb lattices with inverted on-site energy detuning, which are protected by the glide-reflection symmetry of the underlying structures. Our work sheds light on the direct detection of band crossings resulting from intrinsic symmetries that extend beyond the fundamental translational symmetry in topological systems.

Higher-order dynamic localization in sinusoidal modulated optical lattices with [formula omitted]-symmetry

The influence of complex lattices with PT-symmetry on dynamic localization (DL) in optics, particularly higher-order DL, has been examined in this study. We found an intriguing result: the order of DL is equal to the frequency of light passing through the first Brillouin zone's boundary during a half-period of DL oscillation. Additionally, the DL is still possible below the PT-symmetry breaking point, but beam power evolution differs from Bloch oscillation in PT-symmetry systems. Similar to damped vibration, the amplitude of beam power oscillation diminishes as propagation distance increases. The nonreciprocal beam propagation behavior is also found at the PT-symmetry breaking point, which is comparable to the optical Bloch oscillation in the PT-symmetry system.

Experimental demonstration of optical Bloch oscillation in electromagnetically induced photonic lattices

The optical Bloch oscillation (OBO) is an optical-quantum analogy effect that is significant for light field manipulations, such as light beam localization, oscillation and tunneling. As an intra-band oscillation, OBO was important for optical investigations in photonic lattices and atomic vapors over an extended period of time. However, OBO in reconfigurable platforms is still an open topic, even though tunability is highly desired in developing modern photonic techniques. Here we theoretically establish and experimentally demonstrate OBO in an electromagnetically induced photonic lattice with a ramping refractive index, established in a coherently-prepared three-level 85Rb atomic vapor under the electromagnetically induced transparency condition. This is achieved by interfering two coupling beams with Gaussian profiles and launching a probe beam that exhibits OBO within the resulting lattice. The induced reconfigurable photonic lattice possesses a transverse gradient, due to the innate edges of Gaussian beams, and sets a new stage for guiding the flow of light in periodic photonic environments. Our results should motivate better understanding of peculiar physical properties of an intriguing quantum-optical analogy in an atomic setting.

Bloch oscillations in arrays of helical waveguides

We study optical Bloch oscillations in the one- and two-dimensional arrays of helical waveguides with transverse refractive index gradient. Longitudinal rotation of waveguides may lead to notable variations of the width of the band of quasi-energies and even its complete collapse for certain radii of the helix. This drastically affects the amplitude and direction of Bloch oscillations. Thus, they can be completely arrested for certain helix radii or their direction can be reversed. If the array of helical waveguides is truncated and near-surface waveguide is excited, helix radius determines whether periodic Bloch oscillations persist or replaced by the irregular near-surface oscillations.

Optical Bloch Oscillations of a Dual Airy Beam

AbstractWe investigate the propagation of a dual Airy beam in Hermitian and non‐Hermitian waveguides, theoretically and numerically. Optical Bloch oscillations (OBOs) of the beam are demonstrated during propagation in both types of waveguides, and the numerical OBO period is found to be in accordance with the theoretical predictions. The two branches of the dual Airy beam do not display translational symmetry — the peaks will form in one branch only, due to the desynchronized Bragg reflection of the lobes. In the non‐Hermitian waveguides, the dual Airy beam will be damped or amplified during propagation — depending on the imaginary part of the complex potential, which may provide loss or gain to the beam. In the ‐symmetric‐like potential, the dual Airy beam may undergo amplification during propagation, but the total power will exhibit a stair‐like behavior. The non‐reciprocity is also exhibited by the dual Airy beam in such a potential. We believe that our research not only provides a new geometry for optical switches but also deepens the understanding of OBO in dual Airy beams.

Optical Bloch oscillation and Zener tunneling in the fractional Schr\xf6dinger equation

We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrödinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrödinger equation and the FSE, by adjusting the Lévy index, and expound the differences between the two. We find that the spreading of the OBO decreases in the fractional case, due to the diminishing band width. Increasing the transverse force, due to the linear potential, leads to the appearance of OZT, but this process is suppressed in the FSE. Our results indicate that the adjustment of the Lévy index can effectively control the emergence of OBO and OZT, which can inspire new ideas in the design of optical switches and interconnects.

The Optical Bloch oscillation in chirped one-dimensional superconducting photonic crystal

We exploit theoretically the propagation properties of electromagnetic waves in nanoscale one-dimensional superconducting photonic crystal. The Wannier Stark ladders can be formed in the photonic crystal by varying the thickness of the dielectric layers linearly across the structure. The dynamics behavior of a Gaussian pulse transmitting through the structure is simulated theoretically. We find that photons undergo Bloch oscillations inside tilted photonic bands and the Bloch oscillations are sensitive to the change of temperature in the range of 3–8K. It is demonstrated that our structure is possible to realize tunable optical Bloch oscillations by controlling the temperature of superconducting material.

Optical Bloch oscillation and Zener tunneling in an atomic system

Atomic media are important in optics research since they can be conveniently manipulated and controlled due to easy selection of atomic levels, laser fields, and the active adjustment of many system parameters. In this paper, we investigate optical Bloch oscillation, Zener tunneling, and Bloch–Zener oscillation in atomic media both theoretically and numerically. We use two coupling fields to prepare the dynamical optical lattice through interference. To induce a transverse force, we make the frequency difference between the two coupling fields increase linearly along the longitudinal coordinate. These phenomena have potential application for beam splitters and optical interconnects, and are helpful for investigating quantum analogies.

Trajectory variations of optical Bloch oscillations for Airy beams in transversely and longitudinally modulated photonic lattices.

We consider four types of modulated photonic lattices and numerically study the optical Bloch oscillations of Airy beams in these periodic structures. Our results demonstrate that in transversely modulated photonic lattices, the oscillation period increases and the amplitude reduces as the separation variation index increases. However, the increasing of the width variation index could lead to a consistent reduction of oscillation period and amplitude. On the other hand, in three kinds of longitudinally bent photonic lattices, the optical Bloch oscillation trajectories of Airy beams follow the waveguide shape perfectly within the whole propagation length. For another three kinds of refractive index longitudinally varied lattices, the optical Bloch oscillation period and amplitude are limited with the increasing of refractive index, contributing to the presentation of dramatically different Airy propagation trajectories. Our study proposes a new view to manipulate the Airy trajectory in periodic structures.

Non-diffracting optical Bloch oscillations in hexagonal photonic lattices.

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.

Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices.

We report on the existence of optical Bloch oscillations (OBOs) and Zener tunneling (ZT) of Airy beams in ionic-type photonic lattices with a refractive index ramp. Different from their counterparts in uniform lattices, Airy beams undergoing OBOs show an alternatively switched concave and convex trajectory as well as a periodical revival of input beam profiles. Moreover, the ionic-type photonic lattice established in photorefractive crystal exhibits a reconfigurable lattice structure, which provides a flexible way to tune the amplitude and period of the OBOs. Remarkably, it is demonstrated that the band gap of the lattice can be readily controlled by rotating the lattice inducing beam, which forces the ZT rate to follow two significant different decay curves amidst decreasing index gradient. Our results open up new possibilities for all-optical switching, routing and manipulation of Airy beams.

Ultracompact Superlattices for Multi-frequency Optical Bloch Oscillations Simultaneously

In this paper, we investigate the photonic transmission properties of a kind of one-dimensional optical superlattices composed of alternately stacked metal and dielectric films. A geometric thickness gradient of the dielectric layers, which is analog to an external electric field applied to the electronic crystals for observing electron Bloch oscillations, is introduced in the superlattices along the photonic propagation direction. Analytical results from the transfer matrix method reveal that three sets of photonic Wannier-Stark ladder with different frequency-space in terahertz level exist simultaneously from visible to near infrared frequency domain as the gradient is varied from 0.5 to 0.8, which indicates that the optical superlattices can support three different terahertz Bloch oscillations simultaneously. In particular, at a certain gradient, the Zener tunneling effect between two adjacent Wannier-Stark ladders is achieved. Finite-difference time-domain simulations on the dynamic evolution of photons propagation in the superlattices confirm the analytical predictions. The largest total thickness of the superlattices is around 8 μm, which is a quarter of that of superlattices composed of alternately stacked Bragg reflectors and dielectric microcavities.

Anomalous optical Bloch oscillations

Abstract Anomalous optical Bloch oscillation in waveguide arrays are investigated within the generalized Coupling Mode Model (CMM). This model takes into account the next neighbor interaction between the waveguides along with the nearest neighbor interaction. The exact analytical solution for the optical beam path is found. A criterion of the appearance of the anomalous Bloch oscillations against the standard Bloch oscillations background is discovered. A comparison between the analytical result and the numerical simulation reveals a good agreement.

Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient.

We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.

On the theory of the optical Bloch oscillations

The light Bloch oscillations in the array of optical waveguides are investigated based on the electrodynamics of continual approach. The array possesses a step-like refractive index profile. Usually, these oscillations are described in a phenomenological manner. However, the parameters entering the phenomenological equations are obtained either from additional numerical simulations or from experiments. The approach proposed here is based on multiple-scattering formalism. This approach allows us to justify the phenomenological description. The phenomenological approach is valid only if the interaction between the waveguides is weak and the nearest neighbor approximation is applicable. To describe the path of light, we calculate the local isofrequency curve. It is shown that the path represents Bloch oscillations. The results obtained are found to correlate with the experiments available.

On-chip optical isolation via unidirectional Bloch oscillations in a waveguide array

We propose to use the unidirectionality of the optical Bloch oscillation phenomenon achievable in a magneto-optic asymmetric waveguide array to achieve optical isolation. At the 1.55 μm telecommunication wavelength, our isolator design exhibits an isolation ratio of 36 dB between forward- and backward-propagating waves. The proposed design consists of a waveguide array made in a silicon-on-insulator substrate with a magnetic garnet cover layer. A key role is played by the transverse-magnetic mode nonreciprocal phase shift effect.

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.

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.

Bloch Oscillations of Surface Plasmon-Like Modes in Waveguide Arrays That Comprise Perforated Perfect Conductor Layers and Dielectric Layers

This study investigates the optical Bloch oscillations (OBOs) in waveguide arrays that consist of alternative perfect electric conductor (PEC) layers and dielectric layers by performing both numerical simulations and theoretical analyses. In PEC dielectric waveguide arrays (PDWAs), the PEC layers are perforated with square holes to support the surface plasmon-like (SPL) modes. The relative permittivities of the dielectric layers have a constant gradient across the waveguide arrays. The OBOs in the PDWAs arise because of the excitation and coupling of the SPL modes. The ray trajectories that are predicted using Hamiltonian optics are consistent with the simulated results. When the position of incidence is fixed, the period of oscillation varies as the reciprocal of the incident frequency. However, the amplitude of oscillation is almost independent of the frequency. For a fixed incident frequency, the amplitude and period of oscillation increases and decreases, respectively as the position of incidence moves toward the dielectric layers with higher relative permittivities.

On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures

The WKB equations for the dynamics of the surface plasmon polariton (SPP)wavepacket are studied. The dispersion law for the SPP in a metal–dielectricheterostructure with varying thickness of a dielectric grating is rigorously calculated andinvestigated using the scattering matrix method. Two channels of the SPP wavepacketoptical losses related to the absorption in a metal and to the SPP leakage areanalyzed. It is shown that change of the dielectric layer thickness acts on theSPP as an external force leading to evolution of its quasimomentum and to thewavepacket reversal or even to optical Bloch oscillations (BO). Properties of thesephenomena are investigated and discussed. Typical values of the BO amplitude areabout tens of microns and the period is around tens or hundreds of femtoseconds.