Spatio-temporal Transfer Function Research Articles

On-chip spatiotemporal optical vortex generation using an integrated metal–dielectric resonator

We theoretically demonstrate the possibility of generating a spatiotemporal optical vortex (STOV) beam in a dielectric slab waveguide. The STOV is generated upon reflection of a spatiotemporal optical pulse from an integrated metal–dielectric structure consisting of metal strips “buried” in the waveguide. For describing the interaction of the incident pulse with the integrated structure, we derive its “vectorial” spatiotemporal transfer function (TF) describing the transformation of the electromagnetic field components of the incident pulse. We show that if the TF of the structure corresponds to the TF of a spatiotemporal differentiator with a π/2 phase difference between the terms describing temporal and spatial differentiation, then the envelope of the reflected pulse will contain an STOV in all nonzero components of the electromagnetic field. The obtained theoretical results are in good agreement with the results of rigorous numerical simulation of the STOV generation using a three-strip metal–dielectric integrated structure. We believe that the presented results pave the way for the research and application of STOV beams in the on-chip geometry.

Electromagnetic Spatiotemporal Differentiation Meta‐Devices

AbstractSpatiotemporal optical computing devices that can perform mathematical operations in both spatial and temporal domains can provide unprecedented measures to build efficient and real‐time information processing systems. It is particularly important to realize the comprehensive functions in a compact design for better integration with electronic components. In this work, an analog spatiotemporal differentiator in microwaves based on an asymmetrical metasurface that has a phase singularity in the spatiotemporal domain is experimentally demonstrated. It is shown that this structure can give rise to a spatiotemporal transfer function required by an ideal first‐order differentiator in both spatial and temporal domains by tailoring the unidirectional excitation of spoof surface plasmon polaritons (SSPPs). The spatial edge detection is performed utilizing a metallic slit, and the temporal differentiation capability of the device is examined by Gaussian‐like temporal pulses of different widths. It is further confirmed that the differentiator demonstrated here can detect sharp changes in spatiotemporal pulses even with intricate profiles and theoretically estimated the resolution limits of the spatial and temporal edge detection. It is also shown that the pulse input after passing the spatiotemporal differentiator implemented here could carry a transverse orbital angular momentum (OAM) with a fractal topology charge.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones—Part I: Spatiotemporal Transfer Function and Graphical Guide

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent "effective" sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Time domain model and experimental validation of non-contact surface wave scanner

This paper presents a time-domain model for the prediction of acoustic field in an air-coupled, non-contact, ultrasonic surface wave scanner, which includes an air-coupled Emitter, the Propagation space, and an air-coupled Receiver (EPR). The computation is divided into three steps, with each step being modeled in the time domain by its spatio-temporal transfer function. The latter are then used in turn, to find the pulse response of the overall system.The model takes the finite size of the aperture receiver, the attenuation in both air and the tested solid sample, as well as the electric response of the emitter-receiver set he into account. The attenuation is characterized by a causal time-domain Green’s function, allowing wideband attenuation of a lossy medium, obeying the power law αω=α0ωη,0⩽η⩽2, to be used. The model is implemented numerically using a Discrete Representation approach. It is then validated quantitatively by comparing the predicted acoustic field with experiment. The prediction error for three typical field features, the system’s impulse response, the on-axis field distribution, and the directivity pattern, is globally smaller than 3%.In order to obtain this high level of accuracy in the model, the parameters characterizing the solid sample used during the experiment were measured experimentally, with a specifically developed experimental setup.Overall, the proposed model is approximately 100 times faster than 3D FEM with an equivalent spatio-temporal resolution. In parallel, a simplified model is proposed, which neglects the attenuation in air and assumes the emitter inclination angle to be perfectly adjusted. This approach makes it possible to further shorten the computational time by a factor of about ten, whilst maintaining good accuracy. Thanks to its computational efficiency, the proposed model can be used to formulate various recommendations concerning the scanner settings, in particular the inclination angles of the emitter and receiver, and their distance from the sample.

Neural field theory of perceptual echo and implications for estimating brain connectivity.

Neural field theory is used to predict and analyze the phenomenon of perceptual echo in which random input stimuli at one location are correlated with electroencephalographic responses at other locations. It is shown that this echo correlation (EC) yields an estimate of the transfer function from the stimulated point to other locations. Modal analysis then explains the observed spatiotemporal structure of visually driven EC and the dominance of the alpha frequency; two eigenmodes of similar amplitude dominate the response, leading to temporal beating and a line of low correlation that runs from the crown of the head toward the ears. These effects result from mode splitting and symmetry breaking caused by interhemispheric coupling and cortical folding. It is shown how eigenmodes obtained from functional magnetic resonance imaging experiments can be combined with temporal dynamics from EC or other evoked responses to estimate the spatiotemporal transfer function between any two points and hence their effective connectivity.

Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics

This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function and geometrical isomorphism between the space-time domain and the mode-frequency domain are developed, whereof the H∞-norm is extended to be 2D-H∞ norm in mode-frequency domain. On grounds of this small-gain theorem, robust performance of any Sturm-Liouville plant can be formulated as robust stability of a feedback connection, whereupon feedback syntheses can be performed via modal-spectral μ-loopshaping.

A 2-D Signal Processing Model to Predict the Effect of Mutual Coupling on Array Factor

A semi-analytical method for modeling the effects of electromagnetic mutual coupling in uniform linear array (ULA) of N antennas is proposed. The coupling is described as a two-dimensional (2-D) spatiotemporal transfer function derived from S-parameter measurements. The proposed 2-D transfer function enables prediction of the distortions in array factor due to coupling, and thereby enables the potential design of coupling-compensation algorithms. The method is verified with simulations in the 1.5-2.0-GHz range on both an N=7-element ULA using CST Microwave Studio using 50- Ω terminations and a N=3-element ULA in FEKO but with non-50 Ω impedance obtained from measurements of a CMOS low noise amplifier (LNA). Coupling effect on array factor of delay-sum-type beamformer was examined. The proposed model matches within an error of 4%-12% and 4%-10% with respect to the results from two full-wave electromagnetic simulators CST Microwave Studio and FEKO, respectively, in the frequency range 1.75-2 GHz.

Visualization of superluminal pulses inside a white light cavity using plane wave spatio temporal transfer functions

In a white light cavity (WLC), the group velocity is superluminal over a finite bandwidth. For a WLC-based data buffering system we recently proposed, it is important to visualize the behavior of pulses inside such a cavity. The conventional plane wave transfer functions, valid only over space that is translationally invariant, cannot be used for the space inside WLC or any cavity, which is translationally variant. Here, we develop the plane wave spatio temporal transfer function (PWSTTF) method to solve this problem, and produce visual representations of a Gaussian input pulse incident on a WLC, for all times and positions.

Functional Mechanisms Shaping Lateral Geniculate Responses to Artificial and Natural Stimuli

Functional models of the early visual system should predict responses not only to simple artificial stimuli but also to sequences of complex natural scenes. An ideal testbed for such models is the lateral geniculate nucleus (LGN). Mechanisms shaping LGN responses include the linear receptive field and two fast adaptation processes, sensitive to luminance and contrast. We propose a compact functional model for these mechanisms that operates on sequences of arbitrary images. With the same parameters that fit the firing rate responses to simple stimuli, it predicts the bulk of the firing rate responses to complex stimuli, including natural scenes. Further improvements could result by adding a spiking mechanism, possibly one capable of bursts, but not by adding mechanisms of slow adaptation. We conclude that up to the LGN the responses to natural scenes can be largely explained through insights gained with simple artificial stimuli.

Post-Onset Behaviour of the Pure Katabatic Flow

An analytic improvement of the classic Prandtl model for pure katabatic flows is obtained. The one-dimensional unsteady problem employs gradually-varying eddy diffusivity K(z) fixed in time. A new solution is found for thefourth-order governing equation that couples the momentum and heat transfer in an approximate but still systematic way. The solution for wind and temperature perturbations is a generalization of the Prandtl solution allowing for: (1) Local andcumulative K(z) effects, (2) gradual evolution from the initial, discontinuous- towardthe steady-state profiles and (3) the given two-dimensional background potential temperature gradient, the surface slope and its potential temperature deficit atthe surface. The solution that is based on a relaxation equation compares adequatelywith its numerical counterpart soon after the estimated flow onset. It is a product ofthe steady-state solution with a spatio-temporal transfer function. The results can beuseful for data analyses, especially for the scale estimations of inclined stable boundarylayers and for surface flux calculations.

Spatiotemporal transfer function of human accommodation

We have investigated the spatiotemporal transfer function of human "reflex" accommodation. An accommodative mechanism that is sensitive to an intermediate temporal rate of retinal image contrast change is proposed as the basis of the fine focus control hypothesis. To test the proposed mechanism accommodative responses were monitored by a dynamic infrared optometer while the subject focused on sinusoidal gratings (0.98-10.5 c/deg) which were moving sinusoidally at temporal frequencies in the range of 0.05-0.80 Hz over a 0.50 or 2.00 D peak-to-peak amplitude. The accommodative responses were best at 3 and 5 c/deg at both amplitudes of target motion. This result does not support the proposed mechanism or the fine focus control hypothesis for "reflex" accommodation. Fitting the data with first-order response functions showed little evidence of prediction. In addition, a second experiment found that the profile of the accommodative gain function is not altered by instruction at spatial frequencies above 5 c/deg in this type of dynamic accommodation experiment. The use of sinusoidally moving accommodative blur targets, particularly with careful instruction, seems to discourage voluntary accommodation in investigations of "reflex" control mechanisms of accommodation.

A spatio-temporal model of ganglion cell receptive field in the cat retina

A spatio-temporal model of ganglion cell receptive fields is proposed on the basis of receptive field characteristics of cat retinal ganglion cells reported in our previous paper. The model consists of the linear and nonlinear mechanisms in the ganglion cell receptive field. The linear mechanism is assumed to be composed of antagonistic center and surround mechanisms. Then, by integrating these mechanisms we construct a spatio-temporal impulse response function of ganglion cell receptive field. Here we assume that spatio-temporal impulse response function may be factored into spatial and temporal terms. By Fouriertransforming the spatio-temporal impulse response function, we can obtain the spatio-temporal transfer function. Contrast sensitivity characteristics of X-and Y-cells in the cat retina may be explained by the transfer function.

Spatiotemporal transfer function: recent developments

Many electro-optical systems exhibit a performance which is governed by both temporal and spatial response characteristics. The analysis of such systems may be facilitated by the use of the spatiotemporal transfer function introduced earlier. Here we formulate the conditions when this is necessary, present some experimental results, and apply the theory to the display of a moving object.

The response of the Limulus retina to moving stimuli: a prediction by Fourier synthesis.

The Limulus retina responds as a linear system to light stimuli which vary moderately about a mean level. The dynamics of such a system may conveniently be summarized by means of a spatiotemporal transfer function, which describes the response of the system to moving sinusoidal gratings. The response of the system to an arbitrary stimulus may then be calculated by adding together the system's responses to suitably weighted sinusoidal stimuli. We have measured such a spatiotemporal transfer function for the Limulus eye. We have then accurately predicted, in a parameter-free calculation, the eye's response to various stimulus patterns which move across it at several different velocities.

The spatiotemporal transfer function of the Limulus lateral eye.

The dynamics of the Limulus retina may be well described by the spatiotemporal transfer function, which measures the response of the eye to moving sinusoidal gratings. We consider a model for this system, which incorporates an excitatory generator potential, and self- and lateral inhibitory processes. Procedures are described which allow estimation of parameters for the model consistent with the empirical transfer function data. Transfer functions calculated from the model show good agreement with laboratory measurements, and may be used to predict accurately the response of the eye to arbitrary moving stimuli. The model allows convenient interpretation of the transfer function measurements in terms of physiological processes which underly the response of the Limulus retina.