Coupling to an endfaced multi-clad optical fibre from a misaligned gaussian beam or a separated multi-clad fibre

The excitation of a multi-clad optical fibre by a misaligned gaussian beam is analysed using a least-squares boundary residual modal technique and a Born approximation. The modal technique is used to analyse the axial coupling via a gap between two aligned fibres. Comparison is made with a method based on a gaussian approximation for the fibre fields. Results of the modal technique confirm the accuracy of the Born approximation when corrected for Fresnel reflection. However, the modal technique is more precise than the other methods when serious mismatch exists and is efficient for treating the gap problem, where the Born approximation is not applicable.     

Partially coherent sources which produce the same far-field intensity distribution as a laser

It is shown that certain partially coherent model sources whose intensity distribution and degree of coherence are both gaussian will generate the same far-field intensity distributions as a completely coherent laser source.     

用于光束整形的多功能衍射相位板的设计

提出一种设计多功能衍射相位板的随机搜索和模拟退火混合设计方法利用这种方法,通过采用多个评价函数,可设计出在不同观察面上同时产生所需光强分布的衍射相位板设计用于高斯光束整形的多功能衍射相位板可以在焦面上产生高能量利用率、小旁瓣的光强分布,同时在离焦面上获得具有良好顶部均匀性的光强分布该方法提高了衍射器件的设计灵活性,对于设计同一块器件在光路的不同位置产生所需的光强分布提供了新的思路,在激光武器、激光加工和激光手术等领域有广阔的应用潜力.     

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.     

Equilibrium states for a plane incompressible perfect fluid

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.Research partially supported by C.N.R., G.N.F.M.     

Angular correlation of neutrons from thermal-neutron fission of 235U

The neutron-neutron angular correlation for neutrons with energies ? 1 MeV emitted in thermal-neutron-induced fission of ²³⁵U has been measured. The correlation could be adequately described by a simple model, assuming isotropic neutron emission in the fully accelerated fragment frames together with a 20% isotropic scission component and using binomial distributions to simulate the neutron multiplicity (instead of the usual gaussian form) for each fission fragment. The results give no indication of enhanced polar emission.     

A simple filter for detecting low-rank submatrices

We present a simple algorithm for detecting low-rank submatrices from within a much larger matrix. This algorithm relies on a basic geometric property of high-dimensional space: random 2-d projections of eccentric gaussian distributions are typically concentrated in opposite quadrants of the plane.     

Propagating modes of a lens-like medium

The wave equation for a weakly guiding medium having a cylindrical symmetry and parabolic index distribution has been solved exactly. Simple power series are obtained for the field distributions of the modes, which illustrate the type of fields that will be found in graded core fibres away from the core cladding discontinuity. These results are discussed and compared to the modes predicted for other types of fibres.     

Overlap function analysis of p-p elastic scattering data at ISR energies

Recent data from the CERN-ISR are analysed in terms of a gaussian overlap function in impact parameter space. It is found that the upward concavity in the angular distributions is accurately reproduced. Phenomenological implications are discussed.     

The forward and backward projection of acoustic fields from axisymmetric ultrasonic radiators using impulse response and Hankel transform techniques

A generalized impulse response formulation to evaluate the harmonic pressure field of ultrasonic planar vibrators having axisymmetric nonuniform surface velocity distributions is presented. The harmonic pressure is expressed as a Fourier transform of a generalized impulse response which is a function of the spatially nonuniform velocity of the vibrator. A backward projection method is then developed to reconstruct the normal surface velocity of axisymmetric vibrators from harmonic field pressures using an angular spectrum or Hankel transform formulation. The numerical accuracy of the backward projection technique is evaluated using the impulse response formulation to evaluate the pressure fields for several velocity distributions on disk vibrators. Experiments were performed to reconstruct the velocity distributions over the surface of a uniformly driven piezoelectric ceramic disk and ceramic ring using farfield measurements of the complex pressure. The experimental results were in good agreement with theoretical results based on the electrode patterns of the transducers.     

Density-matrix formalism for partially coherent optical fields propagating in slightly inhomogeneous media

The integral of motion method and the density matrix formalism are used to describe the propagation of partially coherent radiation in slightly inhomogeneous media. Expressions for the parameters of partially coherent gaussian beams in media with general square-law refractive-index distributions are obtained using operator algebra. New equations for the correlation function are formulated and beam invariants are obtained.     

The effect of cladding loss in graded-index fibres

We present quantitative results for the effect of cladding absorption on the transmitted power and impulse response of a typical multimode, graded-index fibre that is excited by a Lambertian source. Power attenuation is due to the absorbing cladding material and the radiation loss of the tunnelling rays. Graded-index fibres are shown to be far less susceptible to the effect of cladding absorption than step-index fibres.     

Binding energy,occupancy and spin-cutoff factor calculated by statistical spectroscopy with configuration-isospin skewness and excess terms

Binding energy, occupancy and spin-cutoff factor are calculated from configuration-isospin density distributions. Corrections to gaussian shapes are needed since the low-lying configurations have predominantly positive skewness and high-lying ones negative skewness. Mass 28 nuclei in the (ds)¹² model space and masses 16 to 20 in the complete p-ds model space are used as examples.     

New aspects in bandwidth measurements considering the effects of DMD

This paper focuses on the effects of differential mode delay (DMD) on the bandwidth of multimode optical fibres. First an analytical solution for the computation of the differential mode time delay is presented. The electrical field of each mode is calculated by the numerical solution of the Helmholtz equation. Based on this solution the modal power distribution as well as the fibre's impulse response under different launching conditions can be obtained.Next, the refractive-index profile of two fibres is modelled on the basis of DMD measurements. It is shown that these measurements provide enough information to predict the fibre's propagation characteristics under different launch conditions (excitation conditions).     

Pulse dispersion in partially-excited graded-index fibres

Simple analytical results are obtained for the mode distribution and impulse response of graded index fibres under a variety of excitation conditions relevant to practical systems. It is found that the choice of an optimum refractive index profile depends quite strongly on the source distribution of or, that one can significantly improve the impulse response of a particular profile by appropriate choice of launching conditions. Furthermore the r.m.s. pulse width is not necessarily reduced simply by partially filling the numerical aperture of the fibre.     

Finite-range nucleon-nucleon interaction in the radiative capture of fast nucleons

The direct-semidirect model for nucleon radiative capture has so far been formulated assuming a zero-range nucleon-nucleon interaction. An extension of the theory to finite-range forces is proposed here. The usual δ-function in the interaction is replaced by a range-dependent gaussian function and then the radial form factor in the particle-vibration coupling (responsible for excitation of the E1 and E2 giant resonance states) is derived. Calculations are performed for the ¹⁴²(p, γ) reaction in the 5–30 MeV energy region. A detailed analysis provides indications on effects related to the interaction range as regards both the E1 and E2 integrated cross sections and the forward-backward asymmetry of the γ-ray angular distributions. Sensitivity to the interaction range shows connections with the proton final-level spin.     

Real time measurements of rough object vibration by imaging of Gaussian illumination

A real time method for measuring the vibration of rough surface using image of gaussian illumination is suggested. Theoretical prediction is done by assumption of gaussian distribution of image intensity. Experiments confirming the usefulness of the method have been performed.     

Field distributions at57Fe in Zn2-Y and their fitting with the transmission integral

Conclusions Introduction of lorentzian or gaussian distributions of fields in the exact transmission integral leeds to integrals which can be solved. With this more general function it was possible to interpret even such broadened lines as in the spectra of Zn₂-Y. Because of the detected broadening the Zn₂-Y is a good polarizator. After transition through such a crystal even the wings of a unpolarized unbroadened linie are polarized. So this ferrite is a good candidate for a fast switch in linear polarisation experiments.     

Geometric optics analysis of non-circular,graded-index fibres

The cross-sections of practical optical fibres do not have perfect circular symmetry. The appropriate mathematical representation of the refractive index profile is discussed and it is shown that the basic power law profile in circular fibres should be replaced by a grading functionF which is a homogeneous function of thex andy coordinates. Multimode optical fibres of this type are analysed using geometric optics. General properties of ray paths are described. The fundamental quantities of interest in fibre optics (power acceptance, ray transit time, impulse response) are shown to depend on the degree of homogeneity ofF but not on its specific form. Thus, fibres need not have circular symmetry in order to retain the desirable properties of the circular power law fibres. Ray paths and classifications are analysed in detail for elliptical, parabolic-index fibres. Splicing losses are examined and are shown to be not drastically dependent on deviations from circular symmetry.