Chiral optical solitons in an electrically active multiferroic guiding structure.

A stack of a dielectric planar waveguide with a Kerr-type nonlinearity, sandwiched between two oxide-based helical multiferroic layers is shown to support electrically-controlled chiral solitons. These findings follow from analytical and full numerical simulations. The analytical scheme delivers explicit material parameters for the guided mode soliton and unveils how the soliton propagation characteristics are controlled by tuning the multiferroic helicity and amplitude of the injected electromagnetic wave. Silicon and CS2 are considered as the optical media in the guiding region enclosed by the multiferroic slabs. CS2 has very similar nonlinearity characteristics to silicon but in the linear regime it exhibits a smaller refractive index in the THz frequency range. The scattering simulations are performed using our developed numerical code based on the rigorous coupled wave method and the results for the dispersion curve for the guided mode agree very well with the analytical formula that we derive in this work. The results demonstrate a case of nonlinear pulse generation with field-controlled, nontrivial topological properties.

Tunable chiral photonic cavity based on multiferroic layers.

Realization of externally tunable chiral photonic sources and resonators is essential for studying and functionalizing chiral matter. Here, oxide-based stacks of helical multiferroic layers are shown to provide a suitable, electrically-controllable medium to efficiently trap and filter purely chiral photonic fields. Using analytical and rigorous coupled wave numerical methods we simulate the dispersion and scattering characteristics of electromagnetic waves in multiferroic heterostructures. The results evidence that due to scattering from the spin helix texture, only the modes with a particular transverse wavenumber form standing chiral waves in the cavity, whereas all other modes leak out from the resonator. An external static electric field enables a nonvolatile and energy-efficient control of the vector spin chirality associated with the oxide multilayers, which tunes the photonic chirality density in the resonator.

Thickness-dependent slow light gap solitons in three-dimensional coupled photonic crystal waveguides.

The thickness-dependent multimodal nature of three-dimensional (3D) coupled photonic crystal waveguides is investigated with the aim of realizing a medium for controlled optical gap soliton formation in the slow light regime. In the linear case, spectral properties of the modes (dispersion diagrams), location of the gap regions versus the thickness of the 3D photonic crystal, and the near-field distributions at frequencies in the slow light region are analyzed using a full-wave electromagnetic solver. In the nonlinear regime (Kerr-type nonlinearity), we infer an existence of crystal-thickness-dependent temporal solitons with stable pulse envelope and use the solitonic pulses for driving quantum transitions in localized quantum systems within the photonic crystal waveguide. The results may be useful for applications in optical communications, multiplexing systems, nonlinear physics, and ultrafast spectroscopy.

Photonic Signatures of Spin-Driven Ferroelectricity in Multiferroic Dielectric Oxides.

We study the dispersion and scattering properties of electromagnetic modes coupled to a helically ordered spin lattice hosted by a dielectric oxide with a ferroelectric polarization driven by vector spin chirality. Quasianalytical approaches and full-fledged numerics evidence the formation of a chiral magnonic photonic band gap and the presence of gate-voltage dependent circular dichroism in the scattering of electromagnetic waves from the lattice. Gating couples to the emergent ferroelectric polarization and hence, to the underlying vector-spin chirality. The theory relies on solving simultaneously Maxwell's equations coupled to the driven localized spins taking into account their spatial topology and spatial anisotropic interactions. The developed approach is applicable to various settings involving noncollinear spins and multiferroic systems with potential applications in noncollinear magnetophotonics.

Functional all-optical logic gates for true time-domain signal processing in nonlinear photonic crystal waveguides.

We present a conceptual study on the realization of functional and easily scalable all-optical NOT, AND and NAND logic gates using bandgap solitons in coupled photonic crystal waveguides. The underlying structure consists of a planar air-hole type photonic crystal with a hexagonal lattice of air holes in crystalline silicon (c-Si) as the nonlinear background material. The remaining logical operations can be performed using combinations of these three logic gates. A unique feature of the proposed working scheme is that it operates in the true time-domain, enabling temporal solitons to maintain a stable pulse envelope during each logical operation. Hence, multiple concatenated all-optical logic gates can be easily realized, paving the way to multiple-input all-optical logic gates for ultrafast full-optical digital signal processing. In the suggested setup, there is no need to amplify the output signal after each operation, which can be directly used as a new input signal for another logical operation. The feasibility and efficiency of the proposed logic gates as well as their scalability is demonstrated using our original rigorous theoretical formalism together with full-wave computational electromagnetics.

Effective negative specific heat by destabilization of metastable states in dipolar systems.

We study dipolarly coupled three-dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low-energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

Theory of soliton propagation in nonlinear photonic crystal waveguides.

Propagation of the temporal soliton in Kerr-type photonic crystal waveguide is investigated theoretically and numerically. An expression describing the evolution of the envelope of the soliton based on the full-wave modal analysis, taking into account all space-harmonics, is rigorously obtained. The nonlinear coefficient is derived, for the first time, based on a modification of the refractive indices for each space-harmonic due to the Kerr-type nonlinearity. For illustrating the general formulation and results, we performed extensive computational electromagnetics simulations for the propagation of gap solitons in an experimentally feasible photonic crystal waveguides, endorsing the correctness and usefulness of the proposed formalism.

Realization of true all-optical AND logic gate based on nonlinear coupled air-hole type photonic crystal waveguides.

In this manuscript we propose an easily scalable true all-optical AND logic gate for pulsed signal operation based on band-gap transmission within nonlinear realistic air-hole type coupled photonic crystal waveguides (C-PCW). We call it "true" all-optical AND logic gate, because all AND gate topologies operate with temporal solitons that maintain a stable pulse envelope during the optical signal processing along the different C-PCW modules yielding ultrafast full-optical digital signal processing. We directly use the registered (output) signal pulse as new input signal between multiple concatenated nonlinear C-PCW modules (i.e. AND gates) to setup a multiple-input true all-optical AND logic gate. Extensive full-wave computational electromagnetic analysis proves the correctness of our theoretical studies and the proposed operation principle of the multiple-input AND logic gate is vividly demonstrated for realistic C-PCWs.

Landau-Zener tunneling of solitons.

We consider Landau-Zener tunneling of solitons in a weakly coupled two-channel system, for this purpose we construct a simple mechanical system using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows us to consider soliton propagation and Landau-Zener tunneling between the chains. It is shown that soliton tunneling characteristics become drastically dependent on its amplitude in nonlinear regime. The validity of the developed tunneling theory is justified via comparison with direct numerical simulations on oscillator ladder system.

Fractional lattice charge transport.

We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value.

Landau-Zener Bloch Oscillations with Perturbed Flat Bands.

Sinusoidal Bloch oscillations appear in band structures exposed to external fields. Landau-Zener (LZ) tunneling between different bands is usually a counteracting effect limiting Bloch oscillations. Here we consider a flat band network with two dispersive and one flat band, e.g., for ultracold atoms and optical waveguide networks. Using external synthetic gauge and gravitational fields we obtain a perturbed yet gapless band structure with almost flat parts. The resulting Bloch oscillations consist of two parts-a fast scan through the nonflat part of the dispersion structure, and an almost complete halt for substantial time when the atomic or photonic wave packet is trapped in the original flat band part of the unperturbed spectrum, made possible due to LZ tunneling.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder.

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.

Instabilities and relaxation to equilibrium in long-range oscillator chains.

We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.e., by varying initially the excitation amplitude of the lowest mode, which is the control parameter, instabilities occur in narrow amplitude intervals. Only for sufficiently large values of the amplitude, the system enters a permanently unstable regime. These findings also clarify the long-standing problem of the relaxation to equilibrium in the short-range FPU model. Because of the weaker localization in mode space of this latter model, the transfer of energy is retarded and relaxation occurs on a much longer timescale.

Negative refraction and spatial echo in optical waveguide arrays.

The special symmetry properties of the discrete nonlinear Schrödinger equation allow a complete revival of the initial wave function employed in the context of stationary propagation of light in a waveguide array. As an inverting system, we propose a short array of almost isolated waveguides, which cause a relative π phase shift in the neighboring waveguides. By means of numerical simulations of the model equations, we demonstrate what we believe is a novel mechanism for the negative refraction of spatial solitons.

Delocalization and spreading in a nonlinear Stark ladder.

We study the evolution of a wave packet in a nonlinear Stark ladder. In the absence of nonlinearity all normal modes are spatially localized giving rise to an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. For large strength of nonlinearity we observe single-site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For moderate nonlinearities an immediate subdiffusion takes place. Finally, for small nonlinearities we find linear Stark localization as a transient, with subsequent subdiffusion. For single-mode excitations and weak nonlinearities, stability intervals are predicted and observed upon variation in the dc bias strength, which affects the short- and the long-time dynamics.

Stochastic resonance in the Fermi-Pasta-Ulam chain.

We consider a damped beta-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly responds to the modulating frequency of the forcing signal. Multiple peaks appear in the signal-to-noise ratio, signaling the phenomenon of stochastic resonance. The presence of multiple peaks is explained by the existence of many stable and metastable states that are found when solving this boundary value problem for a semicontinuum approximation of the model. Stochastic resonance is shown to be generated by transitions between these states.

Tristability in the pendula chain.

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a regime which produces an output frequency at an odd fraction of the driving frequency. The stationary state is then obtained with numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kinklike motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.

Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays.

Considering the coherent nonlinear dynamics between two weakly linked optical waveguide arrays, we find the first example of coexistence of Josephson oscillations with a novel self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated nonlinear Schrödinger equation. The effect is illustrated and confirmed by numerical simulations. This property allows us to conceive an optical switch based on the variation of the refractive index of the linking central waveguide.

Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index.

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave "acceleration" and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schrödinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.

The anti-FPU problem.

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.