Phase Difference Δφ Research Articles

Self-propelled heaving and pitching flexible fin in a quiescent flow

A self-propelled flexible fin with heaving and pitching motions in a quiescent flow has been simulated by using the penalty immersed boundary method. The flexible fin can move freely in the horizontal direction and the body of the flexible fin moves passively along with the active head motion. The position of the head of the fin was described as a harmonic heaving oscillation in the vertical direction, while the inclination angle of the head was prescribed as a harmonic oscillation with a moving clamped condition for the heaving and pitching fin. The cruising speed and the swimming efficiency of the self-propelled fin were determined as functions of the bending stiffness (γ), the heaving amplitude (Ah), the pitching amplitude (Ap), the flapping frequency (f) and the phase difference (Δϕ) between Ah and Ap. We optimized the cruising speed and the swimming efficiency with respect to γ, f, Ah, Ap and Δϕ. For a certain range of Ap, the swimming efficiency of the heaving and pitching fin is larger than that of a heaving-only fin.

Interferometric properties of standing spin waves and the application to a phase comparator

We numerically studied the material and structural parameter dependence of interferometric properties of the standing spin wave resonance (SSWR) by micromagnetic simulations and demonstrate the feasibility of practical application to an integrated phase comparator. The micromagnetic configuration of the synthesized SSWR emitted from the two microwave currents flowing through the parallel strip lines depends on the phase difference Δϕ between them. Resultantly, the Δϕ is converted to the related output voltage with an overlaid phase detector, inductively coupled to the magnetic strip. Among the investigated various material systems, low damping (α ∼ 0.001) metallic ferromagnets are found to exhibit superior device performance due to the reduced viscous dissipation.

Dynamic Speckle-Interferometry of Microscopic Processes in Thin Biological Objects

Speckle dynamics in a thin biological object illuminated through a diffusor box is studied both theoretically and experimentally. A model that allows for random time variations in the phase difference Δφ of pairs of waves transmitted through the object is used in the theoretical part of this study. Formulas for the time-averaged intensity of the radiation at a certain point of observation and a temporal autocorrelation function of the radiation intensity are deduced. The relationship between the characteristics of the random variable Δφ and the parameters of the speckle dynamics is discussed. The case of occurrence of a quasiperiodic variation in the radiation intensity is separately considered. The theoretical results are used for interpretation of the data obtained in the experiments on studying the metabolic activity of cells cultivated on a glass substrate.

Phase determination of crystal structure factor using measured rocking curves

AbstractWe report on a novel phase determination method of crystal structure factor using phase difference Δφ between the interference fringes of the diffracted intensities and those of the transmitted intensities. It is an advantage that the phase of crystal structure factor can be determined using the anomalous scattering only at one wavelength. We demonstrate the method by applying to GaAs 200 reflection near K‐absorption edges of Ga and As.

Optical properties of homeotropically aligned flexoelectric nematic layers deformed by direct current electric field

Optical properties of homeotropically aligned flexoelectric nematic layers deformed by dc electric fields were analyzed by calculating the phase difference ΔΦ between ordinary and extraordinary light rays passing through a layer placed between crossed polarizers. A phase difference arises when the bias voltage U exceeds the threshold value UT. Close to the threshold, ΔΦ increases linearly with U. The possibility of using this effect to detect the flexoelectric properties of the nematic was explored by simulated experiments. The method considered in this paper is based on measurement of the slope of the linear section of the voltage dependence of ΔΦ, which depends on the sum of the flexoelectric coefficients and which differs from a well-known theoretical slope that ignores flexoelectric properties. The difference between the slopes reveals the flexoelectric properties of the nematic. The effectiveness of the proposed method is discussed.

Comparitive Study of Coaxial Bragg Resonators

A coaxial Bragg resonator can be performed in four kinds of structures: it is constructed by inserting a regular waveguide between two selective Bragg reflectors (being called the upstream reflector and downstream reflector, respectively), or it consists of only two Bragg reflectors without regular waveguide section between them, where connection of these two reflectors is smooth with phase difference Δϕ = 0 or is step-changed with corrugation phase difference Δϕ = +π or −π, respectively. The present paper is devoted to a comparative study for the response of reflectivity and quality factor on frequency in these four kinds of coaxial Bragg resonators, including the influences of the location and corrugation-phase difference of the step-changed connection of the two reflectors. Results show that a coaxial Bragg resonator possesses most attractive properties when the corrugation-phase difference is Δϕ = +π at the point of connection and the upstream reflector is longer than the downstream reflector.

All-Optical Half-Adder Using All-Optical XOR and AND Gates for Optical Generation of “Sum” and “Carry”

In this article, a numerical simulation study using the symmetric planar three-core non-linear directional coupler, operating with a short light pulse (2 ps), for the implementation of an all-optical half-adder is presented. The half-adder is the key building block for many digital processing functions such as shift register, binary counter, and serial parallel data converters. Optical couplers are an important component for application in optical fiber telecommunication systems and all integrated optical circuits because of very high switching speeds (as high as the femto-second range). In this numerical simulation, the symmetric planar three-core non-linear directional coupler presents a planar symmetrical structure with three cores in a parallel equidistant arrangement, three logical inputs (CP, A, and B), and two output logic functions (C and S). The CP(ΔΦ) input is a control pulse with a phase difference ΔΦ = Δθπ (0 ≤ Δθ ≤ 2) between inputs A and B (logical inputs of the half-adder) and one amplitude discriminator circuit. The half-adder uses two output logic functions of Sum(S) and Carry(C), which can be demonstrated by using XOR and AND gates, respectively. For the half-adder, the phase [ΔΦMIN, ΔΦMAX] intervals are studied, allowing the operation of the device as a half-adder. For the selected range of CP(ΔΦBETTER), the extinction ratio was studied, the compression factors for both Sum(S) and Carry(C) outputs of the symmetric planar three-core non-linear directional coupler.

Numerical investigation of influence of ionic space charge and flexoelectric polarization on measurements of elastic constants in nematic liquid crystals

AbstractDeformations of nematic layers caused by magnetic field allow determination of the elastic constants of liquid crystal. In this paper, we simulated numerically the deformations of planar and homeotropic nematic layers. The flexoelectric properties of the nematic and presence of ions were taken into account. Our aim was to show the influence of flexoelectricity on the results of the real measurement of the elastic constants k33 and k11. In these simulations, we calculated the optical phase difference ΔΦ between the ordinary and extraordinary rays of light passing through the layer placed between crossed polarizers as a function of the magnetic field induction B. One of the elastic constants can be calculated from the magnetic field threshold for deformation. The ratio k33/k11 can be found by means of fitting theoretical ΔΦ(B) dependence to the experimental results. The calculations reveal that the flexoelectric properties influence the deformations induced by the external magnetic field. In the case of highly pure samples, this may lead to false results of measurement of the elastic constants ratio k33/k11. This influence can be reduced if the nematic material contains ions of sufficiently high concentration. These results show that the flexoelectric properties may play an important role, especially in well purified samples.

Piezoresponse force microscopy of ferroelectric thin films: Frequency dependence of phase imaging

The objective of this work is an evaluation of quantitative measurements of piezoresponse force microscopy for nanoscale characterization of ferroelectric films. To this end, we investigate how the piezoresponse phase difference ΔΦ between c domains depends on the frequency ω of the applied ac field much lower than the cantilever first resonance frequency. The main specimen under study was a 102nm thick film of Pb(Zr0.2Ti0.8)O3. For the sake of comparison, a 100nm thick PbTiO3 film was also used. From our measurements, we conclude a frequency dependent behavior ΔΦ∼ω−1, which can only be partially explained by the presence of adsorbates on the surface.

Retro‐directive array with beam steering capability, made by coupled, self‐oscillating mixers

AbstractA novel, phase‐conjugator array for active, retro‐directive operation has been made by use of three dual‐gate, self‐oscillating mixers (SOM's), mutually locked by use of 6 dB hybrid couplers. The coupling network incorporates the load of the oscillators. Reduced LO penetration has been achieved at the RF and IF and ports by trapping the LO signal within the dc bias lines of each SOM. Injection of two external signals at the LO frequency, each at a marginal SOM, with phase difference ΔΦ between them, allows for retransmission at angles other than the angle of arrival of the incident signal. Measured results are presented for a retro‐directive array designed for nominal operation at 900 MHz. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1303–1309, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22447

Influence of refraction on plasma density measurements

The plasma density profile in the T-11M tokamak is measured with a multichannel Cotton-Mouton polarimeter and also with a time-of-flight refractometer. Both instruments operate at frequencies in the range of 140 GHz. Since, in this case, the trajectory of the probing microwave beam deviates from a straight line, the maximum refraction angle being as large as ∼0.25 rad, the measurement results should be corrected for refraction. In order to solve this problem, a computer code has been developed for calculating the trajectories of both O-and X-mode probing beams. In calculations, it is assumed that the plasma is cold and that the inequality ω ≫ 2πνp (where ω is the probing frequency and νp is the collision frequency) is satisfied. The wavelength λ is assumed to be much less than the plasma inhomogeneity scale length, so the calculations are performed in the geometric optics approximation. The dependences of the phase difference ΔΦ (for the Cotton-Mouton polarimeter) and the propagation time of a microwave pulse (for the time-of-flight refractometer) on the linear plasma density 〈nl〉 are calculated. For comparison, similar dependences are calculated for a conventional interferometer operating at the same frequency. It is shown that, in the latter case, the influence of refraction on the measurement results is about three times less. The dependences obtained are presently being used in measurements of 〈nl〉 by means of the Cotton-Mouton polarimeter and the time-of-flight refractometer with allowance for the density profiles recovered by abelianizing the data from the multichannel polarimeter (a series of iterative Abel inversion procedures are performed for each instant of time). The code can also be used to find corrections for refraction when performing interferometric measurements in other devices.

Ordered-mesoporous-silica-thin-film-based chemical gas sensors with integrated optical polarimetric interferometry

A technology to make integrated optical chemical gas sensors using sol-gel surfactant-templated mesoporous thin films was demonstrated. The sensor was prepared by dip coating of an ordered mesoporous silica thin film onto a tapered thin TiO2 layer sputtered on top of a tin-diffused glass waveguide. The sensor employs single-beam polarimetric interferometry to detect molecular adsorption in the mesoporous silica film because the adsorption can lead to a change of the phase difference (Δϕ) between the fundamental transverse electric (TE0) and magnetic (TM0) modes propagating in the waveguide. The sensor is sensitive to humidity and NH3 gas at room temperature (RT). The sensitivity of Δϕ>180° was detected for 40min exposure of the sensor to 2ppm of NH3 in dry air. The sensor was recoverable from the HN3 exposure but its recovery was too slow to cause a detectable Δϕ per unit time. The slow response and recovery of the sensor were ascribed to slow diffusion of gaseous molecules in the laterally oriented tube-like pores of the silica film.

Phase dynamics in cerebral autoregulation

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index gamma = (sin delta phi)2 + (cos delta phi)2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 +/- 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.

Critical current in a system of two superconductors connected by a short small-diameter normal metal bridge

It is shown that states with phase increments δϕ>π can form in superconductor-narrowing (normal metal)-superconductor systems. If the conditions a≪l≪ξ(0), where a is the cross-sectional size of the narrowing, l is the length of narrowing, and ξ(0) is the correlation radius at zero temperature, are satisfied, there is a region of parameters (a, l, ξ(0), T) in which the critical current is attained in solutions with a phase difference δϕ>π.

Spectra of dual overwritten fiber Bragg grating

The perturbation to the refractive index induced by dual overwritten fiber Bragg grating (FBG) is analyzed, and the coupled-mode equations are obtained. The spectral characteristics that can be achieved in dual overwritten fiber gratings are investigated by numerical simulation. It is found that the spectral characteristics are affected significantly by period difference ΔΛ, primary phase difference Δφ and grating length L. Moreover, multiwavelength reflection and strong second harmonics will occur in dual written FBG when the nonlinear UV-induced index perturbation exists, which is very useful for multichannel wavelength-division multiplexing. The results concluded in this paper are conducive to the fabrication and applications of dual overwritten FBGs.

Optimization of laser intracavity second-harmonic generation by a linear dispersion element

Changing the relative phase Δϕ between the fundamental and harmonic waves produces periodic power modulation of a laser intracavity second-harmonic generated wave. The periodic power modulations of the two counterpropagating second-harmonic waves are at exactly opposite phases. This behavior is different from that in the case of intracavity second-harmonic generation in a passive cavity. A phenomenological numerical model developed for a laser consists of double-pass second-harmonic generation. The steady-state plane-wave model incorporates second-order nonlinear interaction, laser gain, and linear dispersion that contribute to the phase difference Δϕ. The model predictions are in good agreement with the experimental results. The model is useful for optimization of laser intracavity second-harmonic generation, and it may be applied to different types of intracavity nonlinear interaction.

Micron and sub-micron aerosol sizing with a standard phase-Doppler anemometer

In this paper the extended application range of the standard phase-Doppler anemometer (PDA) to particle diameters below the commonly accepted lower limit of about 5–10 μm is described. The problems that accompany measurements on smaller particles are small scattering cross-sections and ambiguous relations between the measured phase difference ΔΦ and the particle diameter d . A simple, but flexible optical set-up for the transmitting part of a standard PDA system, and a numerical algorithm, which allows careful data evaluation from ambiguous ΔΦ ( d ) relations, help to manage these problems. Measurements on aqueous suspensions of micron and sub-micron sized dielectric and metalic monospheres, as well as on polydisperse aerosols, are presented and evaluated by means of the proposed algorithm.

Micron and sub-micron aerosol sizing with a standard phase-Doppler anemometer

In this paper the extended application range of the standard phase-Doppler anemometer (PDA) to particle diameters below the commonly accepted lower limit of about 5–10 μm is described. The problems that accompany measurements on smaller particles are small scattering cross-sections and ambiguous relations between the measured phase difference ΔΦ and the particle diameter d. A simple, but flexible optical set-up for the transmitting part of a standard PDA system, and a numerical algorithm, which allows careful data evaluation from ambiguous ΔΦ( d) relations, help to manage these problems. Measurements on aqueous suspensions of micron and sub-micron sized dielectric and metalic monospheres, as well as on polydisperse aerosols, are presented and evaluated by means of the proposed algorithm.

Synchronization of cubic distortion spontaneous otoacoustic emissions

A spontaneous otoacoustic emission spectrum may contain equally spaced emission peaks. Then, two peaks, at frequencies, f1 and f2, respectively, apparently generate a distortion product at fd=2 f1−f2 [or 2 f2−f1]. For the three emission peaks of nine of such triplets (in six emission spectra), the phases φ1(t), φ2(t) and φd(t) were computed, respectively. The phase difference Δφ(t)=φd−(2φ1−φ2) [or Δφ=φd−(2φ2−φ1)] tends to lock at a plateau value φlock (modulo 2π), but occasional jumps up or down n×2π to a neighboring plateau. Apparently, the emission at position 2 f1−f2 [or 2 f2−f1] synchronizes to the cubic distortion product generated by the primaries f1 and f2, but occasionally slips out of the synchronized regime. This behavior is consistent with a model consisting of a self-sustained oscillator in the presence of weak noise, driven by a periodic force.

Phase-sensitive reentrance into the normal state of mesoscopic SNS structures

Normal (N) metallic (Ag) mesoscopic conductors with two superconducting (S) faces (Al), arranged mirror-symmetrically relative to the streamlines of the current, periodically switch into the normal state as the superconducting phase difference Δϕ between the NS boundaries approaches the values Δϕ =(2n+1)π, n=0,1,2,..., irrespective of temperature and applied voltage. For Δϕ =2nπ and low applied voltages the conductance passes through a maximum and approaches the normal value as temperature decreases (reentrance). As the voltage subsequently increases, the conductance increases and passes through a maximum. As the phase difference moves away from the values Δϕ=2nπ, the maxima shift in the direction of low temperatures and voltages. The latter result shows unequivocally that in our metal structures it is necessary to take into account the next-order corrections to the “weak” proximity effect approximation.