Coherent Square Research Articles

Propagation of Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam in uniaxial crystal

The evolution behavior of the intensity profile, beam spreading, and spectral degree of coherence of the Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam propagating in uniaxial crystal are studied. The expression of the cross spectral density of the beam in uniaxial crystal is obtained based on Huygens-Fresnel integration, and the expressions of spectral coherence and root mean square (rms) beam width are derived. The beam spot is circular or elliptical while the ordinary and extraordinary refractive indices of the crystal are equal or unequal, respectively. The ellipticity of the light spot is affected by the Lorentz parameters. The larger the ratio of ordinary to extraordinary refractive index in uniaxial crystal is, the larger the spectral coherence of beam and rms beam waist width is. The spectral coherence increases with the increase of the Gaussian beam waist and the decrease of the Lorentz parameters. The rms beam width of the beam increases with the increase of the Gaussian beam width and Lorentz partial parameters. With the increase of the transmission distance, the influence of the light source parameters on the rms beam width gradually weakens. The total number of terms of multi-Gaussian correlated Schell-Model (MGSM) source and the spatial coherence lengths add additional degree of freedom for adjusting the spot pattern inside crystal.

Evolution properties of a complex coherent square Gaussian-Schell-model beam in a uniaxial crystal orthogonal to the optical axis.

The analytical formulas for spectral density, degree of coherence, and effective beam widths of complex coherent square Gaussian-Schell-model (GSM) beams in a uniaxial crystal orthogonal to the optical axis are derived. Based on these analytical formulas, the evolution properties are investigated by a set of numerical examples. It is demonstrated that the complex coherent square GSM beams spread at different rates in the directions parallel and orthogonal to the optical axis due to the anisotropic crystal, but the self-shift effect of the light field is almost unaffected by the fact that the uniaxial crystal is anisotropic. The effect of anisotropy of the uniaxial crystal on the effective width of the beam in the x direction and that in the y direction is completely opposite. The results provide a way for the modulation of the complex coherent square GSM beams and enrich the propagation theory of uniaxial crystal.

Coherent Square Pulses Generation Based on Continuous Wave Phase Modulation

Coherent Square Pulses Generation Based on Continuous Wave Phase Modulation

Two-dimensional coherent VCSEL arrays with configurable beam emissions

An accurate far-field intensity distribution model of coherent VCSEL array is established based on Fraunhofer diffraction theory, of which the calculated far-field pattern can be configured by tuning the phase distribution of the array. In experiment, configurable beam emissions are achieved in two-dimensional coherent square 2 × 2 VCSEL arrays and triangular 3-element VCSEL arrays by engineering the phase distribution of the array through simply constructing the array structure. Single-lobe beam, double-lobe beam, and four-lobe beam are obtained in these arrays. Besides, beam shape manipulation is also realized by adjusting the ratio of horizontal dimension to vertical dimension of the array. The experimental results are in good agreement with the calculated results from the established theoretical model.

Complex coherent square Gaussian Schell-model beams

A class of random sources with complex multi-Gaussian coherence states producing a square flat topped far field with transverse self-shifting properties is introduced. The beams generated by such sources are called complex coherent square Gaussian Schell-model beams (GSM). The analytic propagating formulas of the cross-spectral density function of such beams propagating in isotropic random medium are derived. With the help of the analytic formulas, the evolutions of statistical characteristics for such beams in linear medium are illustrated numerically and interpreted physically. The effect of turbulence parameters on the beam propagation properties is stressed.

Electronic properties of atomically coherent square PbSe nanocrystal superlattice resolved by Scanning Tunneling Spectroscopy

Rock-salt lead selenide nanocrystals can be used as building blocks for large scale square superlattices via two-dimensional assembly of nanocrystals at a liquid-air interface followed by oriented attachment. Here we report Scanning Tunneling Spectroscopy measurements of the local density of states of an atomically coherent superlattice with square geometry made from PbSe nanocrystals. Controlled annealing of the sample permits the imaging of a clean structure and to reproducibly probe the band gap and the valence hole and conduction electron states. The measured band gap and peak positions are compared to the results of optical spectroscopy and atomistic tight-binding calculations of the square superlattice band structure. In spite of the crystalline connections between nanocrystals that induce significant electronic couplings, the electronic structure of the superlattices remains very strongly influenced by the effects of disorder and variability.

Loop Models and K-Theory

This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the Grassmannian. We interpret various concepts from integrable systems ($R$-matrix, partition function on a finite domain) in geometric terms. As a byproduct, we provide explicit formulae for $K$-classes of various coherent sheaves, including structure and (conjecturally) square roots of canonical sheaves and canonical sheaves of conormal varieties of Schubert varieties.

Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems

In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average symbol error probability of both coherent M-ary phase-shift keying and square M-ary quadrature amplitude modulation schemes. It is shown that all the obtained theoretical results include those that are already known for double Rayleigh channels as a special case. In addition, simplified expressions for the Hoyt $\times $ Rayleigh, Rayleigh $\times $ one-sided Gaussian, and double one-sided Gaussian channels are presented. Moreover, the applicableness of the proposed model to measured real-world propagation channels is examined and discussed by comparing the derived CDF and LCR with published measurement data collected in inter-vehicular propagation environments. Numerical and simulation results are also provided to confirm the validity of the derivations.

An EEMD-PCA approach to extract heart rate, respiratory rate and respiratory activity from PPG signal.

The pulse oximeter's photoplethysmographic (PPG) signals, measure the local variations of blood volume in tissues, reflecting the peripheral pulse modulated by cardiac activity, respiration and other physiological effects. Therefore, PPG can be used to extract the vital cardiorespiratory signals like heart rate (HR), respiratory rate (RR) and respiratory activity (RA) and this will reduce the number of sensors connected to the patient's body for recording vital signs. In this paper, we propose an algorithm based on ensemble empirical mode decomposition with principal component analysis (EEMD-PCA) as a novel approach to estimate HR, RR and RA simultaneously from PPG signal. To examine the performance of the proposed algorithm, we used 45 epochs of PPG, electrocardiogram (ECG) and respiratory signal extracted from the MIMIC database (Physionet ATM data bank). The ECG and capnograph based respiratory signal were used as the ground truth and several metrics such as magnitude squared coherence (MSC), correlation coefficients (CC) and root mean square (RMS) error were used to compare the performance of EEMD-PCA algorithm with most of the existing methods in the literature. Results of EEMD-PCA based extraction of HR, RR and RA from PPG signal showed that the median RMS error (quartiles) obtained for RR was 0 (0, 0.89) breaths/min, for HR was 0.62 (0.56, 0.66) beats/min and for RA the average value of MSC and CC was 0.95 and 0.89 respectively. These results illustrated that the proposed EEMD-PCA approach is more accurate in estimating HR, RR and RA than other existing methods.

Soft-Decision Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection for Differential QAM Dispensing with Channel Estimation in the Face of Rapidly Fading Channels

Turbo detection performed by exchanging extrinsic information between the soft-decision QAM detector and the channel decoder is beneficial for the sake of exploring the bit dependency imposed both by modulation and by channel coding. However, when the soft-decision coherent QAM detectors are provided with imperfect channel estimates in rapidly fading channels, they tend to produce potentially unreliable LLRs that deviate from the true probabilities, which degrades the turbo detection performance. Against this background, in this paper, we propose a range of new soft-decision multiple-symbol differential sphere detection (MSDSD) and decision-feedback differential detection (DFDD) solutions for differential QAM (DQAM), which dispense with channel estimation in the face of rapidly fading channels. Our proposed design aims for solving the two inherent problems in soft-decision DQAM detection design, which have also been the most substantial obstacle in the way of offering a solution for turbo detected MSDSD aided differential MIMO schemes using QAM: 1) how to facilitate the soft-decision detection of the DQAM’s amplitudes, which—in contrast to the DPSK phases—do not form a unitary matrix, and 2) how to separate and streamline the DQAM’s soft-decision amplitude and phase detectors. Our simulation results demonstrate that our proposed MSDSD aided DQAM solution is capable of substantially outperforming its MSDSD aided DPSK counterpart in coded systems without imposing a higher complexity . Moreover, our proposed DFDD aided DQAM solution is shown to outperform the conventional solutions in literature. Our discussions on the important subject of coherent versus noncoherent schemes suggest that compared to coherent square QAM relying on realistic imperfect channel estimation, MSDSD aided DQAM may be deemed as a better candidate for turbo detection assisted coded systems operating at high Doppler frequencies.

Restricted Isometry Property of Random Subdictionaries

We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size $m \times N$. A matrix is said to have a statistical restricted isometry property (StRIP) of order $k$ if most submatrices with $k$ columns define a near-isometric map of ${\mathbb R}^k$ into ${\mathbb R}^m$. As our main result, we establish sufficient conditions for the StRIP property of a matrix in terms of the mutual coherence and mean square coherence. We show that for many existing deterministic families of sampling matrices, $m=O(k)$ rows suffice for $k$-StRIP, which is an improvement over the known estimates of either $m = \Theta(k \log N)$ or $m = \Theta(k\log k)$. We also give examples of matrix families that are shown to have the StRIP property using our sufficient conditions.

Electronic structure of atomically coherent square semiconductor superlattices with dimensionality below two

The electronic structure of recently synthesized square superlattices with atomic coherence composed of PbSe, CdSe, or CdTe nanocrystals (NCs) attached along {100} facets is investigated using tight-binding calculations. In experimental realizations of these systems [W. H. Evers et al., Nano Lett. 13 2317 (2013)], NC facets are atomically bonded, resulting in single-crystalline sheets, which, due to their nanogeometry, have an effective dimensionality below two. We predict electronic structures composed of successive bands formed by strong coupling between the wave functions of nearest-neighbor NCs. This coupling is mainly determined by the number of atoms at the NC bonding plane. The band structures deviate markedly from that of the corresponding two-dimensional (2D) quantum well; the 2D case can be recovered, however, if the effects of the nanogeometry are gradually reduced. The width of the bands can reach hundreds of meV, ascribing highly promising transport properties to square superlattices. The band edges are located at k=0 except for PbSe superlattices, where their position in k space surprisingly depends on the parity of the number of {100} atomic planes in the NCs. Our calculations demonstrate that semiconductors with dimensionality below two have a strong potential for (opto-)electronic, photovoltaic, and spintronic applications.

部分相干方形平顶电磁脉冲光束经相位调制透镜的聚焦特性

部分相干方形平顶电磁脉冲光束经相位调制透镜的聚焦特性

Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks, and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length ${L}_{\ensuremath{\varphi}}$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network-dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ (model A). At low temperature, decoherence is limited by electron-electron interaction, and can be modeled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.

Stretch reflexes and joint dynamics in rheumatoid arthritis

In clinically diagnosed rheumatoid arthritis (RA), studies were conducted to investigate the reflex and passive tissue contribution to measured increases in joint stiffness in the resting upper limb and during constant contractions of an attached muscle. The tonic stretch reflex was induced by a servo-controlled sinusoidal stretch perturbation of the metacarpophalangeal joint of RA patients, and age- and sex-matched controls. The resulting reflexes and mechanical changes in the RA affected joint were explored. Surface electromyographic (EMG) measurements were obtained from first dorsal interosseus muscle. Reflex gain (EMG/joint angle amplitude ratio), phase difference (reflex delay after stretch), coherence square (proportion of EMG variance accounted for by joint angle changes), joint mechanical gain (torque-joint angle amplitude ratio) and mechanical phase difference (torque response delay after stretch) were determined. RA patients showed decreased reflex gain that was partly due to coexistent severe muscle weakness, as determined from maximum voluntary contraction and grip pressure estimates. The decreased reflex gain was most evident at high stretch frequency suggesting a disproportionate loss of the large diameter afferent response and also increased reflex delay in the patients. These changes ensemble suggest significant loss of neural drive to the motor unit population. Patients also showed increased joint stiffness (measured as torque gain) in the contracting muscle, but there was no evidence of reflex activity or increased stiffness at rest. This suggests that the increased joint stiffness in RA was due to changes in the mechanical properties of the active muscle-joint system rather than changes in reflex properties.

Performance degradation of source matching in optical CDMA due to source coherence effects

In this paper we study the performance of source matching technique for an optical code division multiple access (OCDMA) system in the presence of source coherence effects and square law detection process. We use a binary-asymmetric channel (BAC) model for an OCDMA system employing an all-optical passive correlator receiver. Source coherence effects lead to relative-intensity-noise (RIN) and phase-induced-intensity-noise (PIIN), which are included in our analysis. Previous studies only considered multiple access interference (MAI) noise, resulting in a Z-channel (where errors only occur for the transmission of data bit zero) model, and neglected RIN and PIIN. The presence of RIN and PIIN leads to errors occurring for both transmitted data bits one and zero, thus a BAC model. We show that source matching gain depends on the normalized source coherence time, defined as the ratio of the optical source coherence time to the bit duration. Our analysis shows that, while MAI limited analysis predicts that increasing the number of users increases the source matching gain, when taking into account RIN and PIIN, source matching gain is both bit rate and source type dependent, and tends to zero for very high numbers of users.

STRATEGY AND MOTIVATION IN THE GUNPOWDER PLOT

ABSTRACTThis article seeks to develop our understanding of the 1605 Gunpowder Plot by asking a number of elementary questions. Were the plotters terrorists in any meaningful sense? Were they religious fanatics, as the Jacobean state understandably chose to portray them after the event? Was their plan built on a misguided fantasy of widespread support for a Catholic insurrection, or does the Plot perhaps have a practical coherence that lies obscured by the drama of the projected strike against Westminster? How does evidence for coherent planning square with the strong desire for revenge, running through so much of the surviving testimony? Through answers to these questions, we begin to see the Gunpowder plotters as men engaged in a calculated and demonstrably pragmatic attempt to engineer a change in regime. Their planning was robust, and to the point, while the emotional power of revenge was channelled creatively by the ringleaders. The article concludes that the odds against success were long, but not impossible.

Exact performance analysis of M-ary QAM with MRC diversity in Rician fading channels

The exact expression of symbol error rate (SER) is derived for coherent square M-ary quadrature amplitude modulation (M-QAM) using Lth order maximal-ratio combining (MRC) diversity in Rician fading channels with an arbitrary fading parameter. The accuracy of the SER estimates evaluated by this expression is verified through comparison with the results evaluated by numerical integration.

Coherent state lattices and square integrability of representations

In this paper, we discretize the continuous theory of coherent states on a general semidirect product group G = V x S, where V is a vector space and S subset of GL(V) is a semisimple connected Lie group. We show that it is always possible to construct a discrete frame associated with a unitary irreducible representation of G, which is square integrable modulo an affine admissible section. We also prove the converse result that the existence of a discrete frame associated with a unitary representation U of G, indexed by a homogeneous space Gamma, implies the square integrability of U on Gamma.

Tetrakionia.Überlegungen zu einem Denkmaltypus tetrarchischer Zeit im Osten des römischen Reiches

This article focuses on a specific group of public monuments, generally called tetrapyla but also known as tetrakionia, which were a widespread and significant phenomenon in the urban layout of a number of Roman cities throughout the Near East. Some new thoughts and ideas as to their dating and function are presented here. Situated at the intersection of the major thoroughfares within the street grid and often placed in the middle of a kind of circular piazza tetrakionia formed an integral part of the urbanistic system of Roman provincial cities in the Near East. Aside from a prominent location, the basic characteristic feature of this type of monumental structure was to be composed of four single pillars, identical in size and shape. Though standing apart from each other, they were arranged in a coherent square plan. Each of the four pillars consisted of a massive pedestal or podium with a baldacchino-like superstructure, an open construction comprising four columns and an entablature, and thus forming a...