We study both theoretically and numerically the topological edge states in synthetic photonic lattice with finitely periodic gauge potentials. The effective gauge fields are implemented by tailoring the phase alternatively and periodically, which finally results in symmetric total reflection at two boundaries of the one-dimensional synthetic lattice. Further tuning the nearest-neighbor coupling anisotropically, topological edge states occur at the two boundaries. Our work provides a new way to study the topological physics of one-dimensional coupled waveguide arrays with synthetic photonic lattice.
Transmission of light through an optically ultrathin metal film with a thickness comparable to its skin depth is significant. We demonstrate experimentally nearly-zero transmission of light through a film periodically modulated by a one-dimensional array of subwavelength slits. The suppressed optical transmission is due to the excitation of surface plasmon polaritons and the zero-transmission phenomenon is strongly dependent on the polarization of the incident wave.
We theoretically investigate light propagation in two periodically modulated nonlinear waveguides with certain propagation constant detuning between two guides. By slowly varying the amplitude of modulation, we can steer the light to the desired output waveguide when equal amounts of lights are launched into each waveguide. We also reveal that the light propagation dynamics depends sensitively on the detuning between two guides. Our findings can be explained qualitatively by means of adiabatic navigation of the extended nonlinear Floquet states.
A numerical study of the features of the scattering of incident radiation at a periodically modulated hyperbolic metamaterial boundary was carried out. We have found optimal - sawtooth-shaped profile of the interface which provides minimal reflection. It is shown that at a certain orientation of the optical axes of the metamaterial, a subwave localization of the field occurs at the saw-tooth interface. An approximate analytical expression for the eigenmode was found. A generalization of the numerical method is implemented for calculating fields, based on the application of the Green's second i…
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-o…
We provide an analytic solution to the coupled-mode equations describing the steady-state of a single periodically-modulated optical resonator driven by a monochromatic input. The phenomenology of this system was qualitatively understood only in the adiabatic limit, i.e. for low modulation speed. However, both in and out of this regime, we find highly non-trivial effects for specific parameters of the modulation. For example, we show complete suppression of the transmission even with zero detuning between the input and the static resonator frequency. We also demonstrate the possibility for com…
The analysis of optical pulse generation by phase modulation of narrowband continuous-wave light, and subsequent propagation through a group-delay-dispersion circuit, is usually performed in terms of the so-called bunching parameter. This heuristic approach does not provide theoretical support for the electrooptic flat-top-pulse generation reported recently. Here, we perform a waveform synthesis in terms of the Fresnel images of the periodically phase-modulated input light. In particular, we demonstrate flat-top-pulse generation with a duty ratio of 50% at a quarter of the Talbot condition for…
We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{ö}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for…
We report bound states in the radiation continuum (BSCs) in a single infinitely long dielectric rod with periodically stepwise modulated permittivity alternating from $ε_1$ to $ε_2$. For $ε_2=1$ in air the rod is equivalent to a stack of dielectric discs with permittivity $ε_1$. Because of rotational and translational symmetries the BSCs are classified by orbital angular momentum $m$ and the Bloch wave vector $β$ directed along the rod. For $m=0$ and $β=0$ the symmetry protected BSCs have definite polarization and occur in a wide range of the radius of the rod and the dielectric permittivities…
We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows to induce a Moiré-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers.
Spatially localized and periodic field patterns in periodically modulated optical parametric amplifiers and oscillators are studied. In the degenerate case (equal signal and idler beams) we elaborate the systematic method of construction of the stationary localized modes in the amplifiers, study their properties and stability. We describe a method of constructing periodic solutions in optical parametric oscillators, by adjusting the form of the external driven field to the given form of either signal or pump beams.
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time ($\mathcal{PT}$) symmetric waveguides, their linear spectrum is partially complex, thus light exponentially grows or decays upon propagation, and this growth or delay is not altered by nonlinearity. However, several classes of non-$\mathcal{PT}$-symmetric waveguides are also identified to possess all-real linear spectrum. In the nonlinear reg…
Nonlinear dynamics of intra-cavity-field for periodically pump-modulated dual-coupled Kerr micro-ring cavities
College of Physics, Hangzhou Dianzi University（杭州电子科技大学物理学院）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Hangzhou Dianzi University（杭州电子科技大学浙江省量子态调控与光场操纵重点实验室）
We theoretically report an analog of photon-assisted tunneling (PAT) in a periodically driven lattice array without a static biased potential by studying a three-channel waveguide system. This analog of PAT can be achieved by only periodically modulating the top waveguide and adjusting the distance between the bottom and its adjacent waveguide. It is numerically shown that the PAT resonances also exist in the five-channel waveguide system and probably exist in the waveguide arrays with other odd numbers of waveguides, but they will become weak as the number of waveguides increases. With origin…
We predict the enhanced transmissivity of modulated slabs of layered superconductors for terahertz radiation due to the diffraction of the incident wave and the resonance excitation of the eigenmodes. The electromagnetic field is transferred from the irradiated side of a slab of layered superconductor to the other one by excited waveguide modes (WGMs) which do not decay deep into the slab, contrary to metals, where the enhanced light transmission is caused by the excitation of the evanescent surface waves. We show that a series of resonance peaks (with $T \sim 1$) can be observed in the depend…
One-way edge states at the surface of photonic topological insulators are of significant interest for communications, nonlinear and quantum optics. Moreover, when reciprocity is broken in a photonic topological insulator, these states provide protection against disorder, which is of particular importance for slow light applications. Achieving such a one-way edge state, however, requires the construction of a two-dimensional structure. Here, we show how unidiriectional Floquet bands can arise in purely one-dimensional, adiabatically-modulated dynamic systems, in contrasts with the higher dimens…
A rigorous coupled-wave analysis of birefringent holographic gratings with periodically-modulated dielectric tensor along an in-plane direction and tensor variations in the thickness direction
Photonic crystals and metamaterials are two overarching paradigms for manipulating light. Combining the two approaches leads to hypercrystals: hyperbolic dispersion metamaterials that undergo periodic modulation and mix photonic-crystal-like aspects with hyperbolic dispersion physics. So far, there has been limited experimental realization of hypercrystals due to various technical and design constraints. Here, we create nanoscale hypercrystals with lattice constants ranging from 25 nm to 160 nm and measure their collective Bloch modes and dispersion with scattering nearfield microscopy. We dem…
We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that …
Lithium niobate on insulator (LNOI) is extensively researched for potential applications in telecommunication, sensing and quantum technology. Low-loss waveguides in LNOI have been demonstrated in recent years, with further works investigating their nonlinear optical properties via electric field poling. The fabrication imperfections and minimum feature size of inverted ferroelectric domains currently limit the efficiency and application of nonlinear processes in LNOI. This work looks into focused ion beam poling and demonstrates its potential to overcome the limitations of electric field poli…
Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (…
Akin to zero-mode anomalies, such as the chiral anomaly of edge states in quantum Hall effect, in this work, a pi-mode anomaly is proposed in a 1+1 dimensional periodically-driven topological/normal insulator (TI/NI) heterostructure. Usually, when coupling in a background gauge field, the zero modes on domain walls would provide an anomalous current term that is eventually canceled by additional boundary contributions from the topological bulk, via the Callan-Harvey mechanism. This anomaly cancellation associated with the generalization of bulk-boundary correspondence is called anomaly inflow.…
We study two-component solitons and their symmetry-breaking bifurcations (SBBs) in linearly coupled photonic systems with a spatially inhomogeneous strength of the coupling. One system models an inverted virtual photonic crystal, built by periodically doping the host medium with atoms implementing the electromagnetically induced transparency (EIT). In this system, two soliton-forming probe beams with different carrier frequencies are mutually coupled by the EIT-induced effective linear interconversion. The system is described by coupled nonlinear Schrödinger (NLS) equations for the probes, wit…
We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear refractive index attains its maxima, we found that nonlinear surface waves exist and can be made stable only within a limited band of input energy flows, and for lattice depths exceeding a lower threshold.
We develop a general theoretical framework to dynamically engineer quantum correlations in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate, that when the resonance frequencies of the two qubits are periodically modulated with a $π$ phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations …
We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponds to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-mod…
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution ($t$$\to$$+\infty$) due to relaxation processes. The presented derivation simultaneously contains a simple computational algorithm non-using both Floquet and Fourier theories, i.e. our method automatically guarantees a full account of all frequency components. The description is accompanied by the examples demonstrating a simplicity and high eff…
