Periodic Time Modulation Research Articles

Quasiperiodic Emissions: Fine Structure Corresponding to a Bouncing Wave

AbstractQuasiperiodic (QP) emissions are whistler‐mode electromagnetic waves observed in the Earth's inner magnetosphere whose intensity has a nearly periodic time modulation with typical modulation periods on the order of minutes. Some events exhibit, on top of the main modulation period, an additional fine inner modulation with modulation periods on the order of seconds. We use high‐resolution multi‐component electromagnetic wave data obtained by the Van Allen Probes spacecraft to investigate one such event. Detailed wave analysis demonstrates that the fine inner modulation is due to a wave packet bouncing back and forth between the hemispheres. The presence of a density duct is important for the formation of the event, as demonstrated by the increased ratio of wave power propagating away from the equator (a tentative source region) within the duct. The main QP modulation period corresponds to the plasma number density modulation observed just outside the plasmasphere.

Accurate 2-D DoA Estimation Based on Active Metasurface With Nonuniformly Periodic Time Modulation

A novel direction of arrival (DoA) estimation method based on amplifier-integrated active metasurface is proposed to find multisource directions by a single-channel system. Nonuniformly periodic time modulation (NPTM) on the metasurface reduces the hardware complexity by taking full advantage of the spectral resources. As a result, only partial metasurface elements are required to achieve 2-D DoA estimation, while the remaining elements can be redesigned and encoded to control electromagnetic waves. Thus, adaptive beamsteering can be expected to realize in a full-duplex way. Moreover, the amplifiers in the metasurface can function as modulation units to generate the required harmonics and enhance signal quality. The nonideality of the modulated square wave due to the active devices is allowed without affecting the estimation accuracy. An active metasurface prototype composed of 5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 5 elements is fabricated and measured in the microwave anechoic chamber for multisource direction finding. The measured maximum error is 0.31 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> , which is high accuracy compared with the state-of-the-art works. Thus, the proposed method has application values in the Internet of Things (IoT), wireless communications, and radar.

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

An Interpolation-Based Time-Modulated Antenna Array for Beam Scanning at Carrier Frequency

The formula of the Fourier series for a periodic function indicates that traditional periodic time modulation only provides amplitude weighting at the carrier frequency of a time-modulated array (TMA). Therefore, beam scanning through time modulation technique could only be realized at harmonic frequencies. In order to achieve low sideband levels (SBLs) in harmonic beam scanning, a large number of modulation statuses are required in TMAs, which significantly increases the cost and complexity of the entire system. The intent of this work is to develop a novel TMA with array-interpolation aperture and ON–OFF time modulation to achieve beam scanning at the carrier frequency. By performing interpolation computation at the antenna array level, high-precision beam scanning with low SBLs can be realized with pseudorandom ON–OFF time modulation and a static 1-bit phase control. As compared with the state-of-the-art designs, the proposed TMA requires much fewer modulation statuses, and it significantly facilitates beam-scanning control. A forward design strategy is presented to analytically determine the time modulation sequences and the static 1-bit phase statuses for specified beam scanning angles and sidelobe levels (SLLs). Numerical and experimental results well demonstrate the effectiveness of the proposed TMA.

On the fine inner structure of whistler mode quasiperiodic emissions

Whistler mode quasiperiodic (QP) emissions are electromagnetic waves at frequencies between about 0.5 and 4 kHz observed in the Earth’s inner magnetosphere, which are characterized by their nearly periodic time modulation of the wave intensity. Although they have been studied using both ground-based and satellite instruments for already a few decades, their origin remains unclear. Recent studies of these emissions revealed that, on top of the main modulation period, some of the events exhibit an additional fine inner intensity modulation. We use high-resolution electromagnetic wave measurements obtained by the low-altitude DEMETER spacecraft to systematically study the presence/absence of such fine inner structure and the corresponding fine inner modulation periods. Altogether, as many as 251 events are analyzed. Out of these, the clear fine inner modulation is observed for 71 events, only unclear fine inner modulation is observed for 63 events, and the fine inner modulation is completely absent for 117 events. We show that the fine inner structure tends to occur primarily for QP events with shorter modulation periods. The fine inner modulation periods are on the order of few seconds, corresponding to bounce times of whistler mode waves in between the hemispheres. They typically stay quite constant within a single event, and they tend to be lower at larger geomagnetic latitudes (L-shells). Interestingly, the fine inner modulation periods are positively correlated with the main QP modulation periods. The results obtained are of interest for understanding possible mechanisms responsible for the generation of QP events.

Topological Properties of Floquet Winding Bands in a Photonic Lattice.

The engineering of synthetic materials characterized by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterized by a winding number. The winding emerges from the breakup of inversion symmetry, and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enriches the variety of topological phases available in lattices subject to Floquet driving and suggests the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.

Jamming of ISAR Imaging With Time-Modulated Metasurface Partially Covered on Targets

The phase information of the echo is essential for inverse synthetic aperture radar (ISAR) imaging. Time-modulated metasurface (TMM) generates time-varying reflection phase that can modulate the phase of echo, thus enabling jamming of ISAR imaging, which has great potential for real applications. In practice, covering the whole target with TMM is difficult to achieve. Consequently, the echo model of a radar target partially covered with a TMM is developed, which extends the model of ISAR jamming with TMM fully covering to a more general and near-realistic case in this letter. Then, the echoes of each component of the target are obtained by electromagnetic simulation, and the time-varying reflection phase of the 1-bit TMM is obtained by experimental testing. Finally, using the abovementioned data, we validate that ISAR image of the component covered metasurface can be blurred using random time modulation sequence. Meanwhile, duplicated components can be produced in the ISAR image using periodic time modulation sequence. Experimental results of range profile jamming confirm the validity of the conclusions in this letter. The partial defocusing or duplicating of the radar target in the ISAR image can reduce the recognized possibility and enhance the jamming performance, effectively.

Chaotic-Enabled Phase Modulation in Time-Modulated Arrays for Secure Transmission

The “time” factor in time-modulated arrays (TMAs) offers a new degree of freedom for securing wireless communication. However, the widely used periodic time modulation introduces limited randomness for eavesdropping receivers, and thus gives weak security. To meet this challenge, this work proposes a TMA with chaotic-enabled phase modulation (CPM) for secure transmission. The proposed CPM technique offers the chaos features of high randomness, unpredictability, and initial condition sensitive characteristic, to increase the information uncertainty for eavesdropping receivers. An optimization-based time sequence design approach is introduced to design optimal CPM time sequences for secure transmission in a given direction. Thus, a variety of security strategies including beam scanning, directional modulation (DM), and chaotic encryption are simultaneously enabled by the optimized CPM time sequence. Moreover, the CPM is a radio frequency (RF)-domain security technique without requiring any baseband modulation modules, which exhibits a simplified hardware architecture. Numerical analysis and experimental results are presented to illustrate the effectiveness of the proposed CPM technique. The results indicate that the security is improved by lowering the bit error rate (BER) between the legitimate receiver and the transmitter, and reducing the mutual information between eavesdropping receivers and the transmitter.

Power leakage minimization in time‐modulated linear antenna array with optimized switching strategies employing modified harmony search algorithm

Time-modulated linear antenna array (TMLAA) with periodic time modulation of antenna elements radiates infinite inevitable harmonic beams. The infinite harmonic sideband radiation is a wastage of power unless the power is exploited. This paper aims to minimize inevitable power wastage in the harmonic beams radiated from TMLAA by employing an optimized periodic timing sequence. The optimization of the timing sequence is conducted employing harmony search (HS) to suppress the power wastage, However, conventional HS achieves an acceptable sidelobe level (SLL) below – 30 dB. Nevertheless, a modified harmony search algorithm (MHSA) is proposed to attain more power in the desired fundamental beam. The algorithm is validated using an array of 4-, 10-, and 16-element uniform half-wavelength spacing TMLAA. The optimization is conducted on the ON and OFF time instants and the real current of the elements. The simulation results exhibit that HS and MHSA perform potentially alike to suppress the SLL of fundamental below –30 dB. However, the further suppression of the sideband levels employing MHSA justifies the modification proposed in this work. The MHSA performance in terms of radiation parameters is compared with the HS and also with previous works to show the potentiality of the modification.

Surface-wave coupling in double Floquet sheets supporting phased temporal Wood anomalies

Abstract We investigate symmetry-selective surface-mode excitation in a general periodically time-modulated double-layer system, where the modulation of the two layers has a constant phase difference. By deriving a semi-analytic transfer matrix formalism of a Drude-dispersive double-layer structure with periodic time-modulation, we calculate the scattering amplitudes and the corresponding transmission coefficient. Our results show that the phase-difference between the modulation of the two sheets plays an essential role in significantly enhancing and selectively exciting either the even or odd surface mode with high efficiency. We verify our calculations with full-wave time-domain simulations, showing that efficient switching between the surface-wave excitation of the two distinct modal channels can be achieved, even under illumination from a single off-resonant Gaussian pulse, by controlling the phase difference between the two modulations. Our results pave the way towards ultrafast, symmetry-selective mode excitation and switching via temporal modulation.

Time-Modulated Transmissive Programmable Metasurface for Low Sidelobe Beam Scanning.

Programmable metasurfaces have great potential for the implementation of low-complexity and low-cost phased arrays. Due to the difficulty of multiple-bit phase control, conventional programmable metasurfaces suffer a relatively high sidelobe level (SLL). In this manuscript, a time modulation strategy is introduced in the 1-bit transmissive programmable metasurface for reducing the SLLs of the generated patterns. After the periodic time modulation, harmonics are generated in each reconfigurable unit and the phase of the first-order harmonic can be dynamically controlled by applying different modulation sequences onto the corresponding unit. Through the high-speed modulation of the real-time periodic coding sequences on the metasurface by the programmable bias circuit, the equivalent phase shift accuracy to each metasurface unit can be improved to 6-bit and thus the SLLs of the metasurface could be reduced remarkably. The proposed time-modulated strategy is verified both numerically and experimentally with a transmissive programmable metasurface, which obtains an aperture efficiency over 34% and reduced SLLs of about −20 dB. The proposed design could offer a novel approach of a programmable metasurface framework for radar detection and secure communication applications.

Ratchet effect in frequency-modulated waveguide-coupled emitter arrays

We study theoretically the spatial distribution of the polarizations in the array of resonant electromagnetic dipole emitters coupled to a one-dimensional waveguide. The ratchet effect manifests itself in the spatial asymmetry of the distribution of the emitter occupations along the array under symmetrical pumping from both sides. The occupation asymmetry is driven by the periodic modulation in time of the emitter resonance frequencies. We find numerically and analytically the optimal conditions for maximal asymmetry. We also demonstrate that the ratchet effect can be enhanced due to the formation of topological electromagnetic edge states, enabled by the frequency modulation. Our results apply to the classical structures with coupled resonators or arrays of semiconductor quantum wells as well as the quantum setups with waveguide-coupled natural or artificial atoms.

Conjugate Observations of Quasiperiodic Emissions by the Van Allen Probes Spacecraft and Ground‐Based Station Kannuslehto

AbstractWhistler mode waves observed in the Earth's inner magnetosphere at frequencies between about 0.5 and 4 kHz which exhibit a nearly periodic time modulation of the wave intensity are called quasiperiodic (QP) emissions. Conjugate measurements of QP events at several different locations can be used to estimate their spatial extent and spatiotemporal variability. Results obtained using conjugate QP measurements provided by the ground‐based station Kannuslehto (L≈5.5) and the Van Allen Probes spacecraft (L shells between about 1.1 and 6.5) between September 2012 and November 2017 are presented. Altogether, 26 simultaneously detected events were analyzed. The event modulation periods and frequency‐time structures were generally the same at all observation points. Spatial separations of the spacecraft and the ground‐based station during conjugate observations are typically within about 40° in azimuth and from about 1 to 3 in L shell. RBSP consistently observes events at lower L shells than Kannuslehto, with the event occurrence primarily inside of the plasmasphere. Ratios of Poynting fluxes observed by the spacecraft and on the ground are used to evaluate event intensity variations related to the spacecraft position. It is found that the intensity decreases considerably both at low L shells and outside of the plasmasphere. Finally, an event containing a gap in its frequency‐time structure related to a sudden change of its properties is analyzed in detail.

Whistler Mode Quasiperiodic Emissions: Contrasting Van Allen Probes and DEMETER Occurrence Rates

AbstractQuasiperiodic emissions are magnetospheric whistler mode waves at frequencies between about 0.5 and 4 kHz which exhibit a nearly periodic time modulation of the wave intensity. We use large data sets of events observed by the Van Allen Probes in the equatorial region at larger radial distances and by the low‐altitude DEMETER spacecraft. While Van Allen Probes observe the events at all local times and longitudes, DEMETER observations are limited nearly exclusively to the daytime and significantly less frequent at the longitudes of the South Atlantic Anomaly. Further, while the events observed by Van Allen Probes are smoothly distributed over seasons with only mild maxima in spring/autumn, DEMETER occurrence rate has a single pronounced minimum in July. The apparent inconsistency is explained by considering a nondipolar Earth's magnetic field and significant background wave intensities which in these cases prevent the quasiperiodic events from being identified in DEMETER data.

Floquet dynamics in the quantum measurement of mechanical motion

The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically, employing multiple probe tones, we perform sideband asymmetry measurements, a macroscopic quantum effect, on a silicon optomechanical crystal sideband-cooled to 40% ground-state occupation. We show that the Floquet dynamics, resulting from the presence of multiple pump tones, gives rise to an artificially modified motional sideband asymmetry by redistributing thermal and quantum fluctuations among the initially independently scattered thermomechanical sidebands. For pump tones exhibiting large frequency separation, the dynamics is suppressed and accurate quantum noise thermometry demonstrated. We develop a theoretical model based on Floquet theory that accurately describes our observations. The resulting dynamics can be understood as resulting from a synthetic gauge field among the Fourier modes, which is created by the phase lag of the Kerr-type response. This novel phenomenon has wide-ranging implications for schemes utilizing several pumping tones, as commonly employed in backaction-evading measurements, dissipative optical squeezing, dissipative mechanical squeezing and quantum noise thermometry. Our observation may equally well be used for optomechanical Floquet engineering, e.g. generation of topological phases of sound by periodic time-modulation.

A High-Sensitivity and Low-Power Circuit for the Measurement of Abnormal Blood Cell Levels

This paper describes a technique to detect blood cell levels based on the time-period modulation of a relaxation oscillator loaded with an Inter-Digitated Capacitor (IDC). A digital readout circuit has been proposed to measure the time-period difference between the two oscillators loaded with samples of healthy and (potentially) unhealthy blood. A prototype circuit was designed in 65-nm CMOS technology and post-layout simulations show 15.25-aF sensitivity. The total circuit occupies 2,184-[Formula: see text]m2 silicon area and consumes 216[Formula: see text][Formula: see text]A from a 1-V power supply.

Floquet engineering in superconducting circuits: From arbitrary spin-spin interactions to the Kitaev honeycomb model

We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio frequency regime so that the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.

Flat bands and dynamical localization of spin-orbit-coupled Bose-Einstein condensates

Flat bands and dynamical localization of binary mixtures of Bose-Einstein condensates, with spin-orbit coupling subjected to a deep optical lattice which is shaking in time and to a periodic time modulation of the Zeeman field, are investigated. In contrast with usual dynamical localization in the absence of spin-orbit coupling, we find that to fully suppress the tunneling in the system the optical lattice shaking is not enough, and a proper tuning of the spin-orbit term, achievable via the Zeeman field modulation, is also required. This leads to a sequence of Zeeman parameter values where energy bands become flat, the tunneling in the system is suppressed, and the dynamical localization phenomenon occurs. Exact wave functions at the dynamical localization points show that the binary mixture localizes on a dimer with the two components occupying different sites. This type of localization occurs in exact form also for the ground state of the system at the dynamical localization points in the presence of nonlinearity and remains valid, although in approximate form, for a wide range of the Zeeman parameter around these points. The possibility of observing the above phenomena in real experiments is also briefly discussed.

Stability of solitons in time-modulated two-dimensional lattices

We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose–Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint of the variational approximation and systematic simulations. For solitons in the semi-infinite gap, well-defined stability patterns are produced under the action of the attractive nonlinearity, clearly exhibiting the presence of resonance frequencies. The analysis is reported for several time-modulation formats, including the case of in-phase modulations of both quasi-1D sublattices, which build the 2D square-shaped OL, and setups with asynchronous modulation of the sublattices. In particular, when the modulations of two sublattices are phase-shifted by $$\delta =\pi /2$$ , the stability map is not improved, as the originally well-structured stability pattern becomes fuzzy and the stability at high modulation frequencies is considerably reduced. Mixed results are obtained for anti-phase modulations of the sublattices ( $$\delta =\pi $$ ), where extended stability regions are found for low modulation frequencies, but for high frequencies the stability is weakened. The analysis is also performed in the case of the repulsive nonlinearity, for solitons in the first finite bandgap. It is concluded that, even though stability regions may be found, distinct stability boundaries for the gap solitons cannot be identified clearly. Finally, the stability is also explored for vortex solitons of both the “square-shaped” and “rhombic” types (i.e., off- and on-site-centered ones).

Observation of ionospherically reflected quasiperiodic emissions by the DEMETER spacecraft

AbstractQuasiperiodic (QP) electromagnetic emissions are whistler mode waves at typical frequencies of a few kHz characterized by a periodic time modulation of their intensity. The DEMETER spacecraft observed events where the QP emissions exhibit a sudden change in the wave vector and Poynting vector directions. The change happens in a short interval of latitudes. We explain this behavior by ionospheric reflection and present a ray‐tracing simulation which matches resulting wave vector directions. We also attempt to locate the source region of these emissions and conclude that they are most probably generated at the inner boundary of the plasmapause which also acts as a guide during the propagation of the QP emissions.