If optical methods are long time ago used in metrology, coming of laser sources has improved drastically the impact of optics in metrology. The progressive existence of more and more industrial optoelectronic components on the market is responsible of the actual introduction of optical technics in industrial processings like interferometric control, wide-ranging optical sensors , visual inspection..... Further partial coherence and guiding properties of the light field, non linear optical comportment of the medium offer also interesting metrological applications. The aim of this paper is not to give a full description of all the optical methods used in metrology, but to draw some general specific properties and ideas illustrated by representative applications.

Within the general problem of pulse propagation in single-mode optical fibers, the possibility has been shown of the existence of different light sources and modulating signal pulses that produce the same power after light travels a distance z along the single-mode fiber. The relationship and other general properties that should be satisfied by such sources and signals have been determined. These results may offer new possibilities for the optical transmission of information in high capacity communication channels.

The nonlocal dispersion relation for electromagnetic surface waves on a metal-vacuum surface, obtained within the framework of the semiclassical infinite-barrier model, is reviewed. Limiting ourselves to the hydrodynamic approach, which allows collective excitations in the electron gas only, we have for the first time determined and identified the branches of the nonlocal dispersion relation, completely. Also, we address the question of how to treat the stationary energy flow associated with electromagnetic surface waves in the nonlocal regime.

The numerical modeling to a boundary value problem and the numerical discretisation of interconnection problems of two slab waveguides are discussed. In the case of the interconnection of optical fibers, the problem is reduced to the solution of an iterative series of boundary value problems of the type representing the slab waveguides problem.

A fiber-optic correlation processing system is constructed to examine the fluctuation characteristics of optical waves guided in an externally perturbed birefringent fiber. Optical heterodyne detection processes by use of a laser beam with orthogonal linearly polarized two-frequency components are capable of producing the correlation output of the fluctuating guided HE11 modes. A high-speed phase demodulator is designed to produce the fluctuating phase whose correlation can be computed. By use of these techniques and devices, the dynamic fluctuation-characteristics of the guided modes can be examined for any fluctuation statistics. In the demonstrative experiment each guided wave is stable in intensity and its state of polarization is well preserved for axial vibration but not stable for lateral vibration.

An outline of applications of inverse scattering theory to the design problems of planar and circular waveguides is given. A method for the synthesis of planar waveguides with discontinous refractive-index profiles based on truncated potentials technique is presented. This method is then used to construct refractive-index profiles of single-mode planar waveguides with prescribed propagation constant.

The scattering of visible and infrared plane waves into surface waves is studied by using photographic analysis. The surface waves are excited at either dielectric or geometric discontinuities on the surface. The standing-wave field which is generated by interference between the plane and the surface waves is recorded in a suitable layer covering the surface. When the plane wave is chosen to be incident normally on the surface it serves as a reference wave with constant phase along the surface. In this case both the amplitude and the phase of the interference pattern are entirely due to the surface wave, and thus provide a direct mapping of the surface wavetrain. As for a recording material we use photoresist for visible and PMMA for infrared radiaton, respectively. The wave images are analysed by using a phase contrast microscope in the latter or a scanning electron microscope in the former case. From the photographs the type of excited mode - bulk wave, guided wave or surface wave - can be readily identified. Furthermore the phase of scattering, the velocity of propagation and the attenuation length are directly obtained.

The purpose of this talk is first to summarize a paper to be published in Radio Science in the near future. When both the resistivity and the thickness of a conducting film tend to zero, the properties of the infinitely thin resulting film depend on how the two vanishing parameters are linked during the limiting process. It is worth noting that a model, in which a surface current gives rise to the Joule effect, is perfectly conceivable, In the same way, when both the resistivity and the thickness of a rod tend simultaneously to zero, the properties of the infinitely conducting and infinitely thin strip that we get at the limit are difficult to describe. For example, they may depend on the shape of the cross section of the initial rod... We also present the results of a very simple numerical study that anyone can verify with his own microcomputer. Maybe practical people will prefer this study to theoretical considerations.

In this note, we consider the scattering of s-polarized electromagnetic waves by a cylindrical scatterer lying on the vicinity of a surface separating two homogeneous dielectric media. The scatterer is an inhomogeneous zone of arbitrary shape described by its dielectric constant ε(x,z). The upper and lower media are assumed to have a complex homogeneous, isotropic, linear and local dielectric constant. So far, this problem has received considerably less attention than the corresponding periodic problem. An extensive study using the differential approach has been reported. In this study, an integral equation is used to find the electric field in the inhomogeneous zone. Numerical aspects of the treatment such as evaluation of the Green function will be considered in some detail. From the knowledge of the field within the scatterer, standard calculation gives the far field. Thus, it is possible to compute the diffraction pattern and the extinction cross-section of the scatterer. The numerical results are checked by using the classical criteria of the conservation of energy (optical theorem) and reciprocity. For instance, the relative difference between the total scattered flux and the diminution of the flux in the specular direction is currently less than 10-5; in addition, the reciprocity relations are always verified up to 4 figures.

Parallel transmission of signals through single multimode fiber is analyzed. As a signal carrier is used single fiber mode or group of such modes. All transmission stages, i.e. coupling, propagation and decoupling are analyzed and possible number of channels is calculated.

Electromagnetic wave propagation along the layers in semiconductor-dielectric periodic structures in the presence of transverse dc magnetic fields is considered. Dispersion characteristics in the range of frequencies below 1013 s-1 for InSb/Al203 structures are presented.

By using a new numerical method based on the extinction theorem boundary condition. we obtain scattered intensities from both random and periodic perfectly conductive rough surfaces. Lambertian scattering and enhanced backscattering are predicted for random surfaces having Normal statistics and a Gaussian correlation function. Differences between distributions of scattered intensities for T.E. and T.M. waves are studied. Also, the behaviour of the backscattering peak with λ and θ0 is discussed. We show as well that, the blaze effect for the antispecular order, obtained from deep reflection gratings with arbitrary profiles, is closely connected with the effect of enhanced backscattering observed in random rough surfaces. In addition, we prove that when the illuminated structure has a center of symmetry, the intensity in the specular direction is also enhanced.

It is generally accepted, that optical methods are the most promising for the in-process measurement of surface finish. These methods have the advantages of being non-contacting and fast data acquisition. In the Micro-Engineering Centre at the University of Warwick, an optical sensor has been devised which can measure the rms roughness, slope and wavelength of turned and precision ground surfaces. The operation of this device is based upon the Kirchhoff-Fresnel diffraction integral. Application of this theory to ideal turned surfaces is straightforward, and indeed the theoretically calculated diffraction patterns are in close agreement with patterns produced by an actual optical instrument. Since it is mathematically difficult to introduce real surface profiles into the diffraction integral, a computer program has been devised, which simulates the operation of the optical sensor. The program produces a diffraction pattern as a graphical output. Comparison between computer generated and actual diffraction patterns of the same surfaces show a high correlation.

We investigate the influence of the finite conductivity of metals on scattering from two dimensional rough surfaces. The particular case of a random rough surface illuminated with a laser beam is considered. With this aim, we have implemented a beam simulation method, in order to overcome the very difficult problem which occurs when the number of asperities illuminated by the laser beam is increased. A rigorous integral theory, very close to that implemented to diffraction gratings, has been used. Numerical results show the influence of the width and the height of the asperities on the absorption of light.

From very simple theoretical considerations, it is shown that the physical optics approximation can be improved by taking into account the shape of the surface of the diffracting object. The theory has been numerically implemented for both polarizations, as well for perfectly conducting surfaces as for metallic or dielectric objects

The diffusion approximation of transport theory can only be applied to light propagation in random media if the absorption cross section is small compared with the effective scattering cross section. In order to obtain more general results, the Boltzmann transport equation was solved numerically in a separate study for the plane symmetry in an unbounded medium for Rayleigh-Gans scattering. Values for the absorption and backscattering coefficients K and S were obtained in this way for the whole range of absorption cross sections. The diffusion pattern within the medium is a part of the rigorous solution of the transport equation. The average photon path length per unit length in the positive direction proves to be different from that in the negative direction. Therefore, the introduction of K+, K-, S+ and S- should be considered. Results for IC' and K- have been obtained. The diffusion pattern has also been used to derive coefficients for reflection of the diffuse radiation at boundaries where the index of refraction changes, assuming that the diffusion pattern of the emerging radiation is the same as in the unbounded medium. Results with this method are compared with results using the diffusion approximation and with Monte Carlo simulations in order to determine the accuracy of calculated values of K and S.

The goal of the present paper is to better understand the mechanisms of light scattering from randomly rough surfaces,both dielectric and metal surfaces. We compare two vector scattering theories that are commonly used and that are simple to imoolement. The two theories are a first-order perturbation theory by J.M. Elson and an asymptotic theory by D. Maystre et al. We work in one dimension and compare the two theories with each other for surfaces having different values of the root-mean-square (rms) roughness and of the lateral correlation length σ. The surface profiles used are those of various real surfaces measured with a Talystep profilometer. In order to relate the numerical results to experimental data we compare them with measurements of the total integrated scattering (TIS) and with calculations of TIS.

Experimental investigations ofilgser scintillation through atmospheric turbulence require measurements of irradiance at points in the space. Theories are usually in terms of the irradiance at points; therefore point-aperture results are easier to interpret. Also, the statistics of irradiance at points give more complete information than does aperture-averaged irradiance. Practical reasons however require use of apertures of non-negligible dimensions. Extremely small apertures imply extremely low signal levels and low signal to-noise ratio giving rise to poor measurements. One is therefore faced with the problem of choosing aperture sizes that represent a reasonable compromise between the two opposite requirements. It is therefore important to know whether or not use of a given aperture size simulates a point measurement.

First, we examine the different kinds of problems encountered in the field of scattering from random rough surfaces. After a review of the electromagnetic theories, the specific difficulties are emphasized, by comparison with the problem of scattering by deterministic rough surfaces. Some numerical results are shown, in order to investigate the differences and similarities with periodic rough surfaces, for the perfectly conducting 2D model and the influence of the finite conductivity of the metal.

A non paraxial formulation of non linear optical mixing is presented. The method is based on the angular spectrum representation of the interacting waves and it considers depletion effects for copropagating beams. Applications for far infrared generation by three wave mixing are made. Photon conversion efficiency, its angular distribution, and the influence of walkoff and frequency of the pumping beams are studied. We have compared the results with those of the parametric and paraxial approximations.

In linear optics, the visualization of phase object and the contrast improvement of the image of amplitude object are obtained using a small absorbing and dephasing screen at the Fourier spectrum plane of the objet (Zernike method). In this communication it is shown that the screen can be replaced by a non linear medium displaying either non linear absorption or depletion of the exciting beam by non linear scatterings, and non linear change in the refractive index at convenient levels. The conditions leading to the visualization of phase object or to contrast inversion in amplitude objects are studied for a tenth of liquids. The advantage of the proposed method is that it needs neither the construction of a screen nor precise alignments.

A numerical study of the propagation in Kerr nonlinear prism and grating couplers is presented based on singularity expansions for the field coefficients. The numerical results show that the change of location of pole and zeros in the complex plane explain the bistable behaviour of the prism-coupler and that an analytic description of the hysteresis loops can be obtained. It is also found that the grating coupler is a more complex case but that the relative position of pole and zeros does not change when the guide index is changed, allowing to define a scalar dynamic detuning parameter.

The result of a recently established random-phase-approximation description of the electric-dipole contribution to the nonlinear current density, stemming from the breaking of inversion symmetry in the selvedge region and in the bulk, is summarized. The symmetry scheme for the electric-dipole response tensor is discussed, and relevant surface-response parameters are introduced. On the basis of a simple two-band bulk model, the so-called parallel-band contribution to the nonlinear electric-dipole response in Al is calculated. It is emphasized that the role of the electric-dipole response from the bulk of metal crystals, which are referred to as centrosymmetric in macroscopic terms, should be further investigated. The rotational anisotropy effect in Al is discussed within the framework of the two-band model. Finally, preliminary experimental results, demonstrating the rotational effect in Al, are presented.

This paper presents the last developments of Surface Enhanced Second Harmonic Generation by gratings, linked with electromagnetic resonances like Delocalized Surface Plasmons or Guided Waves which occur at the pump frequency. Two rigorous electromagnetic theories have been developed to deal with metallic or dielectric nonlinear materials, and implemented numerically. They allow calculating and optimizing the enhancement of the Second Harmonic Signal, compared to the flat interface. It is shown that not only the groove depth plays a key role in the enhancement process, but also the groove spacing and groove shape. Moreover, the nature of the electromagnetic resonance (Surface Plasmon or Guided Waves) may influence the enhancement by an order of magnitude. The study of the enhancement of the linear local field may give interesting predictions for other nonlinear effects like Surface Enhanced Raman Scattering or Kerr effect and Optical Bistability, but does not seem to give very useful predictions for second harmonic generation.

When both the integral and differential methods are applicable in the study of anisotropic gratings, we show that they lead to numerical results which are in good agreement. We think that it is a convincing proof of the reliability of our computer programs.

We report on our work about the electromagnetic theory of gratings made with anisotropic materials. We describe briefly and give the fields of application of both differential and integral methods. At the present time, a computer program based on the integral method works for an arbitrary uncoated dielectric anisotropic grating, the surface of which is given by y=f(x), provided that the principal axes of the permittivity matrix be the ones used to describe the geometry of the structure. The differential method, which is very flexible and easy to implement, allows us to deal with a great variety of problems. A computer program has been written which treats the problem of an anisotropic substrate covered with an anisotropic layer, and does not require any restrictive condition on the permittivity matrices. Unfortunately, the numerical difficulties which appear especially for deep and lossy gratings are not yet completely removed.

When a mirror is produced by numerically controlled diamond turning, its surface may be optically smooth except for a sinusoidal height modulation in the radial direction. If the amplitude of the modulation is small compared with its wavelength and the mirror has no aberrations, the reflected light will be a converging spherical wavefront with a radial, sinusoidal modulation superimposed on it. To determine how such a modulation affects the image produced by the mirror we study the reflected light in the focal region.

Gabor's theorem concerning the number of degrees of freedom of an image, (space-band-width product), is proven in two different ways. It is indicated in which way this theorem can be generalized for the case of aberrated images, leading to an increase of the number of degrees of freedom in the presence of certain aberrations. A paradox, generated by the calculation of this number in two different ways, leading to different results, is formulated, and its solution indicated.

In optical imaging by laser through sea-water, the polarization difference between the optical signals backscattered by the medium and reflected from the targets can improve visibility ; it is also possible to use polarization and speckle informations in order to discriminate different targets. In this experiment speckle patterns were used in different states of polarized labelling in partially polarized and coherent light. The time average Stokes parameters were measured to identify the polarization state of each pixel of the numerical images : different parameters using these observables are pre-sented in global images and histograms. A range gating technique underwater imaging system was used : a double Nd:YAG laser (spectral width : 0.01 nm ; pulse duration : 5 ns) and a pulsed digital camera (gate width : 10 ns). In conclusion a multiparameter imaging model for identification of immerged targets is possible using this underwater lidar system which takes into account the vector nature of the optical signal (intensity, frequency, Solarization, phase).

This paper demonstrates a novel technique for locating speckle in ultrasound pulse-echo images, based on the phase information contained in the acquired signals. This information, which is normally considered to be of little interest, is also proposed as the basis for a real-time speckle reduction process.