Frequency-dependent Phase Shift Research Articles

A Time-Domain Perspective on the Structural and Electronic Response in Epitaxial Ferroelectric Thin Films on Silicon.

This operando study of epitaxial ferroelectric Pb(Zr0.48Ti0.52)O3 capacitors on silicon substrates studies their structural response via synchrotron-based time-resolved X-ray diffraction during hysteresis-loop measurements in the 2-200 kHz range. At high frequencies, the polarization hysteresis loop is rounded and the classical butterfly-like strain hysteresis acquires a flat dumbbell shape. We explain these observations from a time-domain perspective: The polarization and structural motion within the unit cell are coupled to the strain by the piezoelectric effect and limited by domain wall velocity. The solution of this coupled oscillator system is derived experimentally from the simultaneously measured electronic and structural data. The driving stress σFE(t) is calculated as the product of the measured voltage U(t) and polarization P(t). Unlike the electrical variables, σFE(t) and η(t) of the ferroelectric oscillate at twice the frequency of the applied electrical field. We model the measured frequency-dependent phase shift between η(t) and σFE(t).

Optical wavelength meter with machine learning enhanced precision

A photonic implementation of a wavelength meter typically applies an interferometer to measure the frequency-dependent phase shift provided by an optical delay line. This work shows that the information to be retrieved is encoded by a vector restricted to a circular cone within a 3D Cartesian object space. The measured data belong to the image of the object space under a linear orthogonal map. Component impairments result in broken orthogonal symmetry, but the mapping remains linear. The circular cone is retained as the object space, which suggests that the conventional conic section fitting for the wavelength meter application is a premature reduction of the object space from R3 to R2. The inverse map, constructed by a learning algorithm, compensates impairments such as source intensity fluctuation and errors in delay time, coupler transmission, and photoreceiver sensitivity while being robust to noise. The simple algorithm does not require initial estimates for all parameters except for a broad bracket of the delay; further, weak nonlinearity introduced by uncertain delay can be corrected by a robust golden search algorithm. The phase-retrieval process is invariant to source power and its fluctuation. Simulations demonstrate that, to the extent that the ten parameters of the interferometer model capture all significant impairments, a precision limited only by the level of random noise is attainable. Applied to measured data collected from a fabricated Si3N4 wavelength meter, greater than an order of magnitude improvement in precision compared with the conventional method is achieved.

Delay-Phase Precoding for Wideband THz Massive MIMO

Benefiting from tens of GHz of bandwidth, terahertz (THz) communication has become a promising technology for future 6G network. To deal with the serious propagation loss of THz signals, massive multiple-input multiple-output (MIMO) with hybrid precoding is utilized to generate directional beams with high array gains. However, the standard hybrid precoding architecture based on frequency-independent phase-shifters cannot cope with the beam split effect in THz massive MIMO caused by the large bandwidth and the large number of antennas, where the beams split into different physical directions at different frequencies. The beam split effect will result in a serious array gain loss across the entire bandwidth, which has not been well investigated in THz massive MIMO. In this paper, we first quantify the seriousness of the beam split effect in THz massive MIMO by analyzing the array gain loss it causes. Then, we propose a new precoding architecture called delay-phase precoding (DPP) to mitigate this effect. Specifically, the proposed DPP introduces a time delay network composed of a small number of time delay elements between radio-frequency chains and phase-shifters in the standard hybrid precoding architecture. Unlike <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">frequency-independent</i> phase shifts, the time delay network introduced in the DPP can realize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">frequency-dependent</i> phase shifts, which can be designed to generate frequency-dependent beams towards the target physical direction across the entire bandwidth. Due to the joint control of delay and phase, the proposed DPP can alleviate the array gain loss caused by the beam split effect. Furthermore, we propose a hardware structure by using true-time-delayers to realize frequency-dependent phase shifts for realizing the concept of DPP. A corresponding precoding algorithm is proposed to realize the precoding design. Theoretical analysis and simulations show that the proposed DPP can mitigate the beam split effect and achieve near-optimal rate with higher energy efficiency.

Phase Shifts Measured in Evanescent Acoustic Waves above the Solar Photosphere and Their Possible Impacts on Local Helioseismology

A set of 464 minutes of high-resolution high-cadence observations were acquired for a region near the Sun’s disk center using the Interferometric BI-dimensional Spectrometer installed at the Dunn Solar Telescope. Ten sets of Dopplergrams are derived from the bisector of the spectral line corresponding approximately to different atmospheric heights, and two sets of Dopplergrams are derived using an MDI-like algorithm and center-of-gravity method. These data are then filtered to keep only acoustic modes, and phase shifts are calculated between Doppler velocities of different atmospheric heights as a function of acoustic frequency. The analysis of the frequency- and height-dependent phase shifts shows that, for evanescent acoustic waves, oscillations in the higher atmosphere lead those in the lower atmosphere by an order of 1 s when their frequencies are below about 3.0 mHz, and lags behind by about 1 s when their frequencies are above 3.0 mHz. Nonnegligible phase shifts are also found in areas with systematic upward or downward flows. All these frequency-dependent phase shifts cannot be explained by vertical flows or convective blueshifts, but are likely due to complicated hydrodynamics and radiative transfer in the nonadiabatic atmosphere in and above the photosphere. These phase shifts in the evanescent waves pose great challenges to the interpretation of some local helioseismic measurements that involve data acquired at different atmospheric heights or in regions with systematic vertical flows. More quantitative characterization of these phase shifts is needed so that they can either be removed during measuring processes or be accounted for in helioseismic inversions.

Mechano-Optical Resonant Emission by Edge Angle Modulation of Wrinkled Graphene on Plasmonic Metal Gratings

Graphene coated on top of photonic-plasmonic metasurfaces can produce resonant radiative emission in the mid-infrared region. Narrowband emission peaks are observed through folding graphene into “origami” ridges over metal grating grooves, creating a complementary cavity mode above the trench. This geometrically tuned phenomenon of graphene surface plasmon excitation along the folded sheet enhances the emission when added to magnetic polariton (MP) resonance induced within the plasmonic grating groove. Our analytical models describe how this graphene surface plasmon polariton (SPPG) is a function of folded graphene geometric parameters, and most importantly, the graphene edge angle that distends from the grating surface. The frequency-dependent phase shift of SPPG is fitted to grating parameters, and a modified inductor-capacitor circuit model was developed for predicting MP resonance mode with graphene influence. It was found that the edge angle of wrinkled graphene blue-shifts the groove MP resonance and SPPG resonant emission peak in both wrinkled graphene alone and with the grating substrate. The understanding of geometrically modulated graphene adhered on plasmonic gratings impacts the design and capability of narrowband cavity emitters and contributes toward the development of mechanical-optical environmental sensors.

3D-printed meta-slab for focusing flexural waves in broadband

Focusing of elastic waves by meta-structures is of considerable significance in energy harvesting. However, meeting both high transmission and wide bandwidth for these meta-structures is a challenge. In this paper, we propose a 3D-printed meta-slab with shuttle-like subunits with gradually varying thickness to focus incident flexural waves in broadband. Shuttle-like subunits have high transmission performance and frequency-dependent phase shifts. Based on these subunits, the meta-slab is designed by the mechanism of phase compensation, which makes the focal position unchanged with the incident frequencies. The wave fields of the transmitted region are obtained by the phased array theory and measured by the experiments. Their results are consistent and demonstrate well the focus ability of the meta-slab. Our design effectively concentrates the energy of broadband flexural waves, providing a new approach for energy harvesting.

Squeezed light generation in cascaded optomechanical systems

We theoretically investigate the enhancement of the degree and bandwidth of squeezed states of light generated in cascaded optomechanical (OM) systems. With the obtained recursion relation of the generalized output quadratures, it is possible to realize cascaded OM systems operated simultaneously in a deamplification situation for the same quadrature with a frequency-dependent phase shift between cascaded systems. Due to the cumulative OM interaction, the degree of squeezing can be significantly improved and nearly independent of frequencies. Thus the squeezing frequency band is notably broadened. Moreover, the squeezing bandwidth can be further broadened through tuning the detunings between laser and cavity frequencies. Finally, the influence of optical losses on squeezing due to the inefficient transmission between cascaded systems is also taken into account, which degrades the squeezing via introducing uncorrelated vacuum noises. However, a better squeezed state is still achievable compared to that generated in single OM system.

Broadband Hybrid Precoding Scheme Based on Cyclic Delay in Terahertz Communications

The terahertz communication system with traditional hybrid precoding structure has the problem of beam diffusion. This problem leads to the serious loss of achievable rate and offsets the performance gain caused by bandwidth increase, so a broadband hybrid precoding scheme based on cyclic delay is proposed in this paper. Firstly, a broadband hybrid precoding framework based on cyclic delay is constructed. A delay element is placed at each antenna of the traditional full-connected hybrid precoding structure. Thus, a frequency-dependent phase shift is accomplished to compensate the beam diffusion. Then, the unit delay of delay element at each antenna is determined by maximizing the array gain of the sub-carriers, but there is a problem that the unit delay is not uniform. Finally, through the design of analog precoding, the unity of the unit delay can be realized, while maximizing the array gain of each sub-carrier. The simulation results show that the proposed scheme can achieve 100% array gain at any sub-carrier, and is suitable for solving the problem of beam diffusion under different bandwidth and different number of transmit antennas. Compared with the existing schemes, the achievable rate of the proposed scheme is very close to that of the full-digital precoding scheme, and has the advantage of high energy efficiency.

Millimeter-Wave Near-Field-Focused Full 2-D Frequency Scanning Antenna Array With Height-Modulated-Ridge Waveguide

A millimeter-wave near-field-focused (NFF) full 2-D frequency-scanning antenna array is presented in this article. The proposed antenna is achieved by combining an NFF ridged-waveguide slot array with a double-layer folded focused progressive feeding network. The linear ridged-waveguide slot array antenna is designed with a height-modulated ridge to focus on the power in one direction. The folded feeding line with different length is used to generate the desired focused phase and frequency-dependent progressive phase shift in the other direction. In this case, as the working frequency is swept in the considered range, the inherent frequency-dependent behavior of the linear NFF leaky-wave antenna (LWA) allows a single-scanning sweep in one direction, whereas the focused progressive feeding network ensures multiple-scanning sweeps in the other direction. A full 2-D electronic scanning with no coverage blindness in the scanning area is achieved. To the best of our knowledge, the proposed NFF antenna array is the first design to achieve the full 2-D scanning focus in the near-field (NF) region only by sweeping the frequency, which means that the testing information in the NF region can be directly obtained with a certain band of frequency. This type of antenna is a good candidate in NF fast-scanning applications, e.g., electromagnetic imaging/detecting systems.

Broadband Huygens’ Metasurface Based on Hybrid Resonances

Recently, a special class of Huygens' surfaces has been proposed which are capable of manipulation of transmitted wavefronts while exhibiting high transparency over a broad range of frequencies. In this work we propose and study a new meta-atom for achieving broadband transparency of Huygens' surfaces based on two mutually shifted split-ring resonators. The resonators were carefully optimized using a new developed analytical model so that their electric and magnetic responses was balanced to achieve unidirectional scattering of the incident field. Moreover, their mutual shift canceled their inductive coupling so that both the responses were resonant at the same frequency and the meta-atom exhibited no magneto-electric coupling. The analytical prediction of broadband transparency along with the frequency-dependent phase shift of the transmitted wave within the full coverage of $360\degree$ has been verified numerically and experimentally in the microwave range. The proposed metasurface can be used for symmetric high-efficient polarization conversion and beam-splitting, and opens the way for other interesting applications.

Surpassing the tuning speed limit of slow-light-based tunable optical delay via four-wave mixing Bragg scattering.

We demonstrate a tunable optical delay that surpasses the tuning speed limit of the conventional slow-light-based optical delay. A novel nonlinear optical coupler, implemented by the four-wave mixing (FWM) Bragg scattering process, is utilized to perform destructive interference of the slow-light delayed signal pulse and a nondelayed reference pulse. As a result, the Brillouin-induced frequency-dependent phase shift, as well as the group delay of the synthesized pulse, is amplified. The group delay amplification factor, determined by the coupling ratio of the nonlinear optical coupler, can be tuned through varying the FWM pump power to provide an ultrafast response. Our experimental result demonstrates that an initial 6.2ns Brillouin-induced optical delay can be amplified and rapidly tuned within the range of -5.2 to 27.2ns.

Wave Mechanics of the Vestibular Semicircular Canals

The semicircular canals are biomechanical sensors responsible for detecting and encoding angular motion of the head in 3D space. Canal afferent neurons provide essential inputs to neural circuits responsible for representation of self-position/orientation in space, and to compensatory circuits including the vestibulo-ocular and vestibulo-collic reflex arcs. In this work we derive, to our knowledge, a new 1D mathematical model quantifying canal biomechanics based on the morphology, dynamics of the inner ear fluids, and membranous labyrinth deformability. The model takes the form of a dispersive wave equation and predicts canal responses to angular motion, sound, and mechanical stimulation. Numerical simulations were carried out for the morphology of the human lateral canal using known physical properties of the endolymph and perilymph in three diverse conditions: surgical plugging, rotation, and mechanical indentation. The model reproduces frequency-dependent attenuation and phase shift in cases of canal plugging. During rotation, duct deformability extends the frequency bandwidth and enhances the high frequency gain. Mechanical indentation of the membranous duct at high frequencies evokes traveling waves that move away from the location of indentation and at low frequencies compels endolymph displacement along the canal. These results demonstrate the importance of the conformal perilymph-filled bony labyrinth to pressure changes and to high frequency sound and vibration.

Simple Broadband Circular Polarizer in Oversized Waveguide

In this paper, a possibility is shown to realize a simple waveguide polarizer producing nearly the same circular polarization over a broad frequency range up to an octave. It is based upon the combination of two smoothly squeezed oversized waveguides with different diameters. The principle is similar to an achromatic lens in optics, where two counteracting lenses with differently sloped wavelength dependencies of the refractive index are combined to compensate the dispersion in the desired wavelength range. Consequently, two different wavelengths of light are brought into focus at the same plane. A waveguide for the transmission of microwaves has a similar frequency dependence of the refractive index resulting in a frequency-dependent phase shift between two propagating waves polarized along the symmetry axes of a waveguide with an elliptical cross section. For this reason, an incident wave with a linear polarization between the axes of symmetry can be only converted into a circularly polarized wave over a limited frequency range. However, the diameter and the shape along two counteracting squeezed waveguides can be adjusted in such a way that the frequency dependence of the resultant phase shift is finally canceled out.

Broadband discrete-level excitations for improved extraction of information in bioimpedance measurements

The implementation of bioimpedance-based methods in implantable and wearable medical devices requires simple, cheap and low energy consuming measurement settings for enabling impedance spectroscopy at a wide range of frequencies. In the present paper, such a wideband bioimpedance measurement method is discussed, which embodies two-channel impedance measurement for monitoring of the frequency-dependent phase shift between the channels (phase spectrum). In addition, the improved resolution is achieved by employing comparative measurements by introducing the predetermined reference impedance into one of the measurement channels. The proposed and analyzed measurement system uses a binary excitation signal that simplifies signal generation and processing hardware and does not need sophisticated software—low-complexity devices can be designed this way. It is shown that in particular the binary chirp excitation has some essential advantages compared with its counterparts—the maximum length sequence and binary multifrequency excitations. The spectra of chirps of the binary chirp excitation, including their discrete-level modifications, are continuous and flat at the same time. Due to the independent scalability in time and frequency domains and very high chirping rate, the chirps are especially suitable as excitation signals for wideband spectroscopy of dynamic objects with changing impedances in devices such as implantable heart monitors, pacemakers and high-throughput microfluidic lab-on-chip-type devices for performing bioimpedance-based monitoring of cells and droplets.

Chimeralike States in an Ensemble of Globally Coupled Oscillators

We demonstrate the emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in nonlocally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that the chimera emerges because of effective bistability, which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling.

Non-Invasive Quadrature Modulator Balancing Method to Optimize Image Band Rejection

The design, simulation, and implementation of a non-ideal quadrature modulator balancing system based on the image rejection using correction factors with non-invasive and simple method is given. The novel balancing system proposed in this paper improves the performance of the quadrature modulator by eliminating the imperfections inherent in the RF systems. Furthermore, the proposed system improves DC offsets that can exist at the output of digital-to-analog converters in addition to frequency-dependent loss and phase shift of low-pass anti-aliasing filters by optimizing the image band rejection. The complete analytical model for a non-ideal quadrature modulator is developed and verified for several conditions. The method is non-invasive and requires only two sets of measurements to obtain the correction factors for amplitude and phase of I and Q signals. The proposed method eliminates the requirement for existing time consuming pre-calibration methods where the system is measured before operation and correction factors that depend on several parameters are stored in memory to be recalled during operation.

Fractional Describing Function Analysis of PWPF Modulator

Pulse-width pulse-frequency (PWPF) modulators are widely used in spacecraft thruster control. Their dynamic characteristic is still lack of effective analysis tools. This paper presents a fractional describing function method to describe the frequency characteristics of PWPF. A frequency-dependent gain and phase shift are clearly described by fractional-order expression, and the fractional-order behaviors depict the nonlinear properties of PWPF modulators. This fractional describing function method can also be applied to other kinds of modulators.

A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo

The main contribution of this paper is the development of a linearized model for describing the dynamic hysteresis behaviors of piezoelectrically actuated fast tool servo (FTS). A linearized hysteresis force model is proposed and mathematically described by a fractional order differential equation. Combining the dynamic modeling of the FTS mechanism, a linearized fractional order dynamic hysteresis (LFDH) model for the piezoelectrically actuated FTS is established. The unique features of the LFDH model could be summarized as follows: (a) It could well describe the rate-dependent hysteresis due to its intrinsic characteristics of frequency-dependent nonlinear phase shifts and amplitude modulations; (b) The linearization scheme of the LFDH model would make it easier to implement the inverse dynamic control on piezoelectrically actuated micro-systems. To verify the effectiveness of the proposed model, a series of experiments are conducted. The toolpaths of the FTS for creating two typical micro-functional surfaces involving various harmonic components with different frequencies and amplitudes are scaled and employed as command signals for the piezoelectric actuator. The modeling errors in the steady state are less than ±2.5% within the full span range which is much smaller than certain state-of-the-art modeling methods, demonstrating the efficiency and superiority of the proposed model for modeling dynamic hysteresis effects. Moreover, it indicates that the piezoelectrically actuated micro systems would be more suitably described as a fractional order dynamic system.

Relaxation mechanisms in magnetic colloids studied by stroboscopic spin-polarized small-angle neutron scattering

Stroboscopic small-angle neutron scattering by using polarized neutrons is presented as a technique for investigations of relaxation phenomena on a nanometer scale. Applying a cyclic perturbation to the sample by an oscillating magnetic field allows the polarization-dependent scattering cross-sections to be extracted as time-dependent response. The potential of this special type of ``physical'' contrast variation technique is demonstrated with three examples of ferrofluids of different particle sizes and viscosities. The dynamics of magnetic moment reorientations turned out to be governed by different time scales. For a temperature-dependent fraction of individual mobile particles, a frequency-dependent phase shift and damping of the intensity modulation have been precisely determined and quantitatively explained using a Debye-like relaxation model. The characteristic relaxation times, \ensuremath{\tau}, in the liquid state of all samples scale with the particle volume and viscosity confirming a Brownian-relaxation mechanism. For the remaining fraction of particles that form locally ordered domains the orientation distribution of the dynamically arrested static moments has been quantified by an order parameter ${S}_{1}$${}^{\mathrm{arr}}$, which is not accessible with nonpolarized neutrons. In a high viscous Co and a magnetite-based ferrofluid, ${S}_{1}$${}^{\mathrm{arr}}$ corresponds to maximal alignment of the static moments in the liquid state and to a gradual decrease at lower temperatures when the solvent is frozen. In a low viscosity Co-ferrofluid almost no preferred alignment of the arrested particle moments was observed. In the magnetite-based ferrofluid with the highest dipolar attraction energy an additional phase shift has been detected which increases with frequency and magnitude of the magnetic field. This indicates clearly that the set-up of local particle ordering in distorted hexagonal arrangement is delayed with respect to the moment alignment in the time varying magnetic field.

Matched-field processing and modal filtered range estimates of bowhead whale calls detected in the Alaskan Beaufort Sea

In 2010, a 15-element autonomous vertical array was deployed roughly 35 km north of Kaktovik alongside a distributed array of directional autonomous seafloor acoustic recorders (DASARs). Matched-field processing and geoacoustic inversion techniques were used to extract the range, depth, bottom sound speed profile, density, and attenuation from one close-range whale call. The inversion localized the call at 1.2 km range and 44 m depth in 55 m deep water. The inverted propagation model was used to derive the group and phase velocities of the normal modes in the region surrounding the array. The vertical array spanned sufficient aperture in the water column to permit isolation of the first and second mode arrivals from any given call. A range- and frequency-dependent phase shift was applied to each modal arrival to remove geometric dispersion effects. The modeled range that time-aligned the modal arrivals was selected as the range estimate. The modal filtering technique is demonstrated on additional whale calls produced at 17.3 km and 35 km range from the vertical array, with the range estimates independently confirmed by triangulating bearings of call detections on surrounding DASARs. [Work supported by the North Pacific Research Board, Shell Exploration and Production Company, and Greeneridge Sciences Incorporated.]