Zener tunneling in a binary array of coupled optical waveguides with transverse index gradient is shown to produce a sequence of regular or irregular beam splitting and beam recombination events superimposed to Bloch oscillations. These periodic or aperiodic Zener-Bloch oscillations provide a clear and visualizable signature in an optical system of coherent multiband dynamics encountered in solid-state or matter-wave systems
Bloch-Zener oscillations (BZO), i.e. the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external dc force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian systems such oscillations are rather generally aperiodic and only accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition from aperiodic to periodic as a NH parameter in the system is varied. Remarkably, the phase transition can be either smooth or sharp, contrary to other types of NH phase transitions which are universally sharp. A dis…
Quantum walks are processes that model dynamics in coherent systems. Their experimental implementations proved key to unveil novel phenomena in Floquet topological insulators. Here we realize a photonic quantum walk in the presence of a synthetic gauge field, which mimics the action of an electric field on a charged particle. By tuning the energy gaps between the two quasi-energy bands, we investigate intriguing system dynamics characterized by the interplay between Bloch oscillations and Landau-Zener transitions. When both gaps at quasi-energy values 0 and $π$ are vanishingly small, the Floqu…
The Lieb Lattice exhibits intriguing properties that are of general interest in both the fundamental physics and practical applications. Here, we investigate the topological Landau-Zener Bloch oscillation in a photonic Floquet Lieb lattice, where the dimerized helical waveguides is constructed to realize the synthetic spin-orbital interaction through the Floquet mechanism, rendering us to study the impacts of topological transition from trivial gaps to non-trivial ones. The compact localized states of flat bands supported by the local symmetry of Lieb lattice will be associated with other band…
Photonic lattices have been widely used for simulating quantum physics, owing to the similar evolutions of paraxial waves and quantum particles. However, nonparaxial wave propagations in photonic lattices break the paradigm of the quantum-optical analogy. Here, we reveal that nonparaxiality exerts stretched and compressed forces on the energy spectrum in the celebrated Aubry-Andre-Harper model. By exploring the mini-gaps induced by the finite size of the different effects of nonparaxiality, we experimentally present that the expansion of one band gap supports the adiabatic transfer of boundary…
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 wh…
A coupled Bloch-wave approach is employed to analyze active photonic-crystal (PhC) waveguides and cavities. Gain couples the otherwise independent counter-propagating Bloch modes. This coupling is shown to limit the maximum attainable slow-light enhancement of gain itself and to strongly affect the mode selection in PhC lasers.
Extraction of optical Bloch modes in a photonic-crystal waveguide
我们在光子晶体波导上进行相敏近场扫描光学显微镜。观察到的复杂的场模式进行了分析，通过空间傅里叶变换，揭示了几个指导TE和TM的模式。使用Ha等人提出的重建算法（Opt. Lett. 34（2009）），我们将测量的二维场图案分解为传播布洛赫模式的叠加。这为研究近场测量中的特定模式开辟了新的可能性。我们应用该方法研究了类TE导模的横向行为，当接近带边时，该导模在周围的光子晶体中延伸得更深。
We find the exact Bloch oscillations in zigzag arrays of curved optical waveguides under the influence of arbitrary long-range coupling. The curvature induces a linear transverse potential gradient in the equations of the light evolution. In the case of arrays with second-order coupling, steady states can be obtained as linear combinations of Bessel functions of integer index. The corresponding eigenvalues are equally spaced and form the well-known Wannier-Stark ladder, the spacing being independent of the second-order coupling. We also solve exactly the wave packet dynamics and compare it wit…
By applying a coupled-Bloch-mode approach, we have derived a simple expression for the transmission properties of photonic crystal (PhC) line-defect waveguides with a complex refractive index perturbation. We have provided physical insights on the coupling mechanism by analyzing the frequency dependence and relative strength of the coupling coefficients. We have shown the impact of the perturbation on the waveguide dispersion relation and how the gain-induced distributed feedback limits the maximum attainable slow-light enhancement of the gain itself. We have then applied our approach to analy…
Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e. a complex Bloch wavenumber, even when the periodic waveguide is lossless (no absorption loss). These so-called complex modes are physical solutions that can be excited by incident waves whenever the waveguide has discontinuities and defects. We show that the complex modes in an open dielectric periodic waveguide form bands, and the …
The behavior of electromagnetic waves in chirally twisted structures is a topic of enduring interest, dating back at least to the invention in the 1940s of the microwave travelling wave tube amplifier and culminating in contemporary studies of chiral metamaterials, metasurfaces, and photonic crystal fibers (PCFs). Optical fibers with chiral microstructures, drawn from a spinning preform, have many useful properties, exhibiting for example circular birefringence and circular dichroism. It has recently been shown that chiral fibers with N fold rotationally symmetric (symmetry group CN) transvers…
Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of the spatial Bloch oscillations on the emission of the dispersive radiation by …
We present a systematic comparison between guided modes supported by slab waveguides and Bloch Surface Waves (BSWs) propagating at the surface of truncated periodic multilayers. We show that, contrary to common belief, the best surface field enhancement achievable for guided modes in a slab waveguide is comparable to that observed for BSWs. At the same time, we demonstrate that, if one is interested in maximizing the electromagnetic energy density at a generic point of a dielectric planar structure, BSWs are often preferable to modes in which light is confined uniquely by total internal reflec…
The existence of a frozen mode in a periodic serpentine waveguide with broken longitudinal symmetry is demonstrated numerically. The frozen mode is associated with a stationary inflection point (SIP) of the Bloch dispersion relation, where three Bloch eigenmodes collapse on each other, as it is an exceptional point of order three. The frozen mode regime is characterized by vanishing group velocity and enhanced field amplitude, which can be very attractive in various applications including dispersion engineering, lasers, and delay lines. Useful and simple design equations that lead to realizati…
Coupled-resonator optical waveguides (CROWs), which play a significant role in modern photonics, achieve waveguiding through near-field coupling between tightly localized resonators. The coupling factor, a critical parameter in CROW theory, determines the coupling strength between two resonators and the waveguiding dispersion of a CROW. However, the original CROW theory proposed by Yariv et al. only demonstrated one value of coupling factor for a multipole resonance mode. Here, by imaging the tight-binding Bloch waves on a CROW consisting of designer-surface-plasmon resonators in the microwave…
We design a three-way silicon optical waveguide with the Bloch dispersion relation supporting a stationary inflection point (SIP). The SIP is a third order exceptional point of degeneracy (EPD) where three Bloch modes coalesce forming the frozen mode with greatly enhanced amplitude. The proposed design consists of a coupled resonators optical waveguide (CROW) coupled to a parallel straight waveguide. At any given frequency, this structure supports three pairs of reciprocal Bloch eigenmodes, propagating and/or evanescent. In addition to full-wave simulations, we also employ a so-called ''hybrid…
We show that a synthetic pseudospin-momentum coupling can be used to design quasi-one-dimensional disorder-resistant coupled resonator optical waveguides (CROW). In this structure, the propagating Bloch waves exhibit a pseudospin-momentum locking at specific momenta where backscattering is suppressed. We quantify this resistance to disorder using two methods. First, we calculate the Anderson localization length $ξ$, obtaining an order of magnitude enhancement compared to a conventional CROW for typical device parameters. Second, we study propagation in the time domain, finding that the loss of…
In physics, synthetic dimensions trigger great interest to manipulate light in different ways, while in technology, lithium niobate shows important capability towards on-chip applications. Here, based on the state-of-art technology, we propose and study a theoretical model of dynamically-modulated waveguide arrays with the Su-Schrieffer-Heeger configuration in the spatial dimension. The propagation of light through the one-dimensional waveguide arrays mimics time evolution of field in a synthetic two-dimensional lattice including the frequency dimension. By adding the effective gauge potential…
Evanescently coupled waveguides are a powerful platform to study and visualize the wave dynamics in tight-binding systems. Here, we investigate the propagation of surface plasmon polaritons in arrays of dielectric loaded surface plasmon polariton waveguides with a propagation constant gradient acting as an effective external potential. Using leakage radiation microscopy, we observe in real-space for single site excitation a periodic breathing of the wavepacket and an oscillatory motion in the case of Gaussian excitation of multiple waveguides. The corresponding momentum resolved spectra are co…
We present an exact analytical solution for a one-dimensional zigzag waveguide array with first and second neighbor interactions. It is found that the waveguide system possess a classical analog to the displaced squeezed number states. The exact solution was compared directly with the numerical solution showing a perfect agreement between both results. The implication of a linear index of refraction changing as a function of the site number is also studied. In this case, we show that the first neighbor interaction strongly influences the periodicity of Bloch oscillations.
We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching behavior of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input.
Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous qu…
