Parallel-beam impulse response of multimode fibres: numerical results

Impulse responses are calculated for parallel-beam injection into fibres having-type profiles with a varying from 1 to 8. The responses obtained exhibit characteristic features which can guide the interpretation of experimental investigations of such fibres. The ray model is used and leaky-mode attenuation is taken into account. Finally, the dependence of the transmitted power on the injection angle is investigated, suggesting a possible functional relation to the index profile.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Numerical evaluation of the impulse response of multimode optical fibers

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ≳ 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Numerical evaluation of the impulse response of multimode optical fibers

Abstract

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ? 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Estimation of the impulse response of ultra-wide-band systems

The time and frequency algorithms of impulse response recovery in linear ultra-wide-band systems by a finite set of digital data presenting the input and output signals are proposed. The results of approbation of these algorithms by numerical simulation in the presence of additive Gaussian noise in the output signal are given. It is shown that the systems with noise-like signals at the input have the largest noise immunity in the estimation of impulse response. Institute for High-Current Electronics of the Russian Academy of Sciences, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1195–1206, September, 1998.     

Propagation constants and delay parameters of near parabolic optical fibres

The normalized propagation constants and delay parameters of near parabolic index fibres are obtained by first order perturbation theory. Departures from the parabolic variation in the form of gaussian dip or bump, periodic changes and polynomial functions are combined in a single term allowing the generalization of existing results. The relevant parameters for each of these special cases are also obtained separately in a closed form.     

Time impulse response and time frequency response of optical pupils

We define the time impulse response of optical pupils and relate this function to the optical characteristics of the pupils. Then we link the time impulse response to the spatial impulse response of the pupil.     

Investigation of the impulse response of an image inversion interferometer

Based on the proposal of Wicker and Heintzmann “Interferometric resolution improvement for confocal microscopes” [1] we demonstrate in principle the functionality of an image inversion interferometer (III) experimentally, which can be described by an appropriate frequency transfer function. Thereby, the FWHM of the impulse response narrows around 30% compared to the PSF of a classical system. The experimental data yield a FWHM of the impulse response of 0.83 μm as compared to the theoretical value of 1.21 μm at by a wide field detection (NA=0.25) without an interferometer.     

Causal impulse response for circular sources in viscous media

The causal impulse response of the velocity potential for the Stokes wave equation is derived for calculations of transient velocity potential fields generated by circular pistons in viscous media. The causal Green's function is numerically verified using the material impulse response function approach. The causal, lossy impulse response for a baffled circular piston is then calculated within the near field and the far field regions using expressions previously derived for the fast near field method. Transient velocity potential fields in viscous media are computed with the causal, lossy impulse response and compared to results obtained with the lossless impulse response. The numerical error in the computed velocity potential field is quantitatively analyzed for a range of viscous relaxation times and piston radii. Results show that the largest errors are generated in locations near the piston face and for large relaxation times, and errors are relatively small otherwise. Unlike previous frequency-domain methods that require numerical inverse Fourier transforms for the evaluation of the lossy impulse response, the present approach calculates the lossy impulse response directly in the time domain. The results indicate that this causal impulse response is ideal for time-domain calculations that simultaneously account for diffraction and quadratic frequency-dependent attenuation in viscous media.     

Ambiguities in the implementation of the impulse approximation for the response of many-fermion systems

Within the impulse approximation, the response of a many-body system at large momentum transfer can be directly related to ground state properties. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the spectral function, the alternative definition in terms of the momentum distribution involves a more extended use of the same assumptions.     

An investigation of the impulse functions for the nonlinear BOLD response in functional MRI

Functional MRI (fMRI) based on blood oxygenation level dependent (BOLD) contrast can be used to detect hemodynamic responses to a broad range of stimuli. It however remains unclear in what fashion the BOLD response is a linear system, and how the impulse function differs with stimulation of varying duration. To address this question, fMRI using visual stimulation with a wide range of duration (0.5-12 s) was performed in six human volunteers. A strong linear correlation was shown on the full width at half maximum (r = 0.998) of the BOLD response curves and the area under the curves (r = 0.999) to the duration of stimulation. However, comparing the errors of the measured and predicted response curves, our results showed a poorer linearity at stimuli of shorter duration. By examining the impulse functions derived from different stimuli, based on the assumption that a linear convolution relationship existed, a higher differentiation was shown in the experiments with shorter stimuli (<3 s). Compared to the area under the impulse function derived from 12 s stimulation, with that obtained from 0.5, 1, 2, 3, 4, 8 s stimuli resulted in differences of 66.2, 33.5, 15.1, 5.4, 0.9, 7.9%, respectively. This study suggests a higher degree of nonlinearity in the BOLD signal changes due to stimuli of shorter duration, in agreement with earlier work.     

Experimental determination of the impulse response of cascade arcsusing a correlation technique

Low-current cascade arcs are one of the simplest configurations for investigating the behaviour of low-temperature arcs. In cascade experiments, arc conditions may be strictly controlled, in which case the results become reproducible, allowing detailed measurements of high resolution to be made. The response of cascade arcs to a small change in the current gives insights into the physical processes taking place in an arc, such as ionization/recombination, diffusion and energy transfer between the electrons and the heavy particles. In this work, a new method of measuring time constants is described, in which correlation techniques utilising a pseudo-random binary sequence are employed to deduce the impulse response of the arc. This type of experiment provides a useful check on the validity of the collision models used for the reaction processes in the arc plasma and it is planned to investigate other gases in the future. In this paper, the experimental arrangement and the data analysis are discussed and experimental results are presented     

Extensions of the scattering-object function and the pulser-receiver impulse response in the field II formalism

The pulse-echo impulse-response format in the Field II formalism is generalized to separately located transmitter and receiver. To first order in sound velocity and density perturbations, identical results for the scattering-object function are obtained for the Morse-Ingard and the Chernov formulation in both the temporal and frequency domains: f(s)=-[2Delta(c/c)+(Delta(rho/rho))(1-cos(theta))] where for ultrasonic pulse-echo or transmission modality, cos(theta) approximately -1 or +1, respectively.     

The measurement of the free field impulse response of microphones in a laboratory environment

A method is presented of measuring the free field frequency and impulse response of microphones by using a pulse technique in an ordinary laboratory environment. The pressure transient generated by exciting a loudspeaker with a narrow pulse is detected at some point in the loudspeaker's far field by a “reference” microphone whose response is assumed flat over the frequency range of interest. The microphone to be tested is then substituted in exactly the same position and its response to the transient measured. The outputs of the two microphones are accurately sampled and deconvolved by using a discrete Fourier transform technique to give the magnitude and phase parts of the “test” microphone's frequency response, and hence, via the discrete Fourier transform, its response to a delta function of pressure propagating in the free field. The computed impulse responses are presented and the accuracy of the method discussed.To illustrate the use of the method, the free field frequency response and free field correction curves of a one inch instrumentation microphone are measured. The method is then used to measure the pressure which occurs at the centre of the flat end-face of a long a cylinder when excited by an impulse of acoustic pressure propagating in the free field from various angles of incidence.     

Reliability of estimating the room volume from a single room impulse response

The methods investigated for the room volume estimation are based on geometrical acoustics, eigenmode, and diffuse field models and no data other than the room impulse response are available. The measurements include several receiver positions in a total of 12 rooms of vastly different sizes and acoustic characteristics. The limitations in identifying the pivotal specular reflections of the geometrical acoustics model in measured room impulse responses are examined both theoretically and experimentally. The eigenmode method uses the theoretical expression for the Schroeder frequency and the difficulty of accurately estimating this frequency from the varying statistics of the room transfer function is highlighted. Reliable results are only obtained with the diffuse field model and a part of the observed variance in the experimental results is explained by theoretical expressions for the standard deviation of the reverberant sound pressure and the reverberation time. The limitations due to source and receiver directivity are discussed and a simple volume estimation method based on an approximate relationship with the reverberation time is also presented.     

Analytical derivation of the impulse response for the bounded 2-D diffusion channel

This letter focuses on the derivation of the hitting probabilities of diffusing particles absorbed by an agent in a bounded environment. In particular, we analogously consider the impulse response of a molecular communication channel in a 2-D and 3-D environment. In 2-D, the channel involves a point transmitter that releases molecules to a circular absorbing receiver that absorbs incoming molecules in an environment surrounded by a circular reflecting boundary. Considering this setup, the joint distribution of the molecules on the circular absorbing receiver with respect to time and angle is derived. Using this distribution, the channel characteristics are examined. Then, we extend this channel model to 3-D using a cylindrical receiver and investigate the channel properties. We also propose how to obtain an analytic estimate for the unbounded 2-D channel from our derived solutions, as no analytic derivation for this channel is present in the literature. Throughout the letter, we perform particle-based simulations to compare the analytic results and lay evidence for our findings.     

一种精确计算换能器空间脉冲响应的快速方法

空间脉冲响应被认为是最有效的瞬态声场计算方法,针对空间脉冲响应直接计算时需要很高的采样频率,导致数据量大、计算效率差的问题,推导了空间点与其在换能器平面的投影点脉冲响应之间的关系,提出了一种计算脉冲响应的快速算法,探讨了计算采样频率和插值采样频率对计算精度和计算效率的影响,研究发现,采用1000 MHz采样频率能够保证精度要求,采用500 MHz作为插值时的采样频率是较优的选择。该方法与直接求解相比,可提高计算效率18倍。     

Bit-error rate evaluation for non-linear propagation in optical fibres

The influence of soliton time jitter on the bit-error rate in long-distance single-mode optical fibre transmission lines was studied. It was assumed that mutual interactions between two adjacent solitons were prevented by periodic amplification. It was found that the upper bit rate bound of practically acceptable non-linear transmission is about 50 Gbit s^–1. Above a bit rate of 50 Gbit s^–1 the advantage of non-linear (soliton) transmission, related to dispersion-free linear transmission, disappears.     

动态电路冲激响应初始值的一种简易求法

给出了求解动态电路冲激响应初始值和动态奇异电路响应初始值的一种简易方法.在电路换路后,其电容电压或电感电流的初始状态一般不产生跃变,但有时也可能产生跃变,当一时难于确定时,可先将电路化为其s域模型,并将0-值带进换路后的电路模型,再应用拉氏变换的初值定理,即可在s域解决t域响应的初始状态0 值的问题.该方法广泛适用于各种电路.