This file contains only abstracts in HTML version. I intended ---as it is made by some of my colleagues--- to include PostScript versions of the complete papers, which contain mathematics and figures. However, PostScript versions are long, and anyway I am not sure at all whether a great number of readers will actually read them through the NET. I shall wait and see how many will really need the complete papers. And anyway I find it much simpler to send you a version on paper if you ask me by email.
If you wish to find one of these complete papers through the net, please send me an email.
PERTURBATIVE METHODS
IN THEORY OF PHASE GRATINGS.
by
J. Harthong
Abstract
Perturbative methods are generally invoked for problems in which there is a small parameter. In the theory of phase gratings, the small parameter is the modulation amplitude of the refractive index, and the classical perturbative method is then the Born approximation. But it is well-known that the Born approximation fails at the Bragg resonance, however small the modulation amplitude is. In this paper a perturbative method is presented, which is working at Bragg resonance as well. A sequence of numbers (called the eigenvalues of the problem) are introduced; they depend on the geometrical configuration (incidence angle, grating parameters). It is shown that the Bragg resonance occurs if (and only if) two eigenvalues become equal. These eigenvalues -- and the corresponding solutions of the equations -- can be expanded in powers of the modulation amplitude. The expansions are different according to whether the corresponding eigenvalue is simple or double.
Explicit formulae or algorithms are given. Computing programs have been written from them. These programs are efficient.
The complete paper has
been published in
Journal de Physique III, vol 4 (1994) pp 407 -- 421.
WAVE PROPAGATION IN MODULATED MEDIA
by
J. Harthong
Abstract
In this paper we propose mathematical methods for the study of the propagation of waves in a modulated medium. We call modulated medium a medium in which the refractive index varies in such a manner that it is approximately periodic in small regions (containing however a large number of periods). Periodic media are particular cases of modulated media: the surfaces along which the refractive index is constant (modulation surfaces) are then parallel planes. In non-periodic modulated media, the modulation surfaces are curved: they are the contour surfaces of a differentiable function.
Typical modulated media are holograms, because holograms record interference fringes, which are always contour surfaces.
The mathematical tools that we present in this paper are especially devoted to the analysis of the wave propagation in modulated media with a period of the same order of magnitude as the wavelength.
The complete paper has been published in
Proceedings of the First International Conference In
Mathematical and Numerical Aspects of Wave Propagation Phenomena.
Published by S.I.A.M. (1991)
THICKNESS MEASUREMENT FOR VOLUME HOLOGRAMS
BY ANALYSIS OF FIRST ORDER DIFFRACTION
by
J. Harthong and A. Medjahed
Abstract
We present a method for measuring the thickness of volume holograms by analyzing the variations of the diffraction efficiency as a function of the angle of incidence. This method can be justified theoretically within the Born approximation, for gratings of small modulation. But we prove experimentally that the method can work surprisingly well even for strongly modulated volume holograms. The principle of the method consists in the determination of the angles of incidence for which the first order diffraction efficiency takes its extreme (maxima and minima) values: these angles are related to the thickness of the grating.
The complete paper has
been published in
Applied Optics, vol 31, (1992) pp 1803 -- 1809.
THEORY OF MOIRÉ SENSING
BY MEANS OF CONTOUR FUNCTIONS
by
J. Harthong, H. Sahli
Abstract
We present a mathematical analysis of moiré sensing in which the basic theoretical concept -- and tool -- is the concept of contour function. We show that the mathematical analysis is greatly simplified by the systematic recourse to this tool. The analysis presented permits a simultaneous treatment of two different modes of implementing the moiré technique: the direct mode (widely used and well-known), and the converse mode (scarcely used). The converse mode consists in computing and designing a grating especially for one model of object, in such a manner that if (and only if) the object is in conformity with the prescribed model, the resulting moiré fringes are parallel straight lines. We give explicit formulas and algorithms for such computations.
For further work about converse moire see : converse moire
The complete paper has
been published in
Applied Optics, vol 31 (1992) pp 1436 -- 1443.
AN ALTERNATIVE THEORY
OF DIFFRACTION BY MODULATED MEDIA.
by
J. Harthong
Abstract
We present a mathematical tool for analyzing the wave propagation in modulated media. By modulated medium, we mean a medium in which the refraction index can be held to be periodic in small regions, but in such a manner that the period, or the direction of the modulation (i.e. the grating vector), can vary at a macroscopic scale. The most common realizations of such media are holograms.
Uniformly periodic media (in which the grating vector is constant) are particular cases of modulated media. In the first part of this paper we introduce the main concepts, and apply them sometimes to the case of uniformly periodic media, to show the relations with usual theories. The method presented in the paper uses modal expansions and is approximate; we show that in the case of uniformly periodic media, the theory becomes exact and reduces then to the well-known characteristic mode theory. The purpose of the paper is to give a method for treating the complete three-dimensional (and vectorial) problem, where an arbitrarily shaped wave is diffracted by a medium of arbitrarily shaped modulation. This is the matter of the second part. Only the mathematical method is described. Particular results, detailed formulas, or further developments, will be published in individual papers.
The complete paper has
been published in
Journal Opt. Soc. Amer. A vol 8 (1991) pp 3 -- 10.
PHASE GRATINGS PROFILE MODELISATION
AND ANALYSIS IN SILVER HALIDE.
by
S. Mechahougui and J. Harthong
Abstract
In the control of the parameters of phase holographic gratings, one of the most important to check is the modulation profile of the refractive index. In fact this parameter reflects the final outcome of various processing techniques.
The aim of this paper is the determination of the modulation profile in the silver halide gratings, a posteriori. A series of holograms of different exposures has been recorded, by interference of two plane waves. The grating parameters are determinated exerimentally and entered into a computing program, which computes a complete and exact solution of the Maxwell equations. We compare the numerical curves obtained for a set of standard profiles, which modelize some realistic profiles as they can be obtained by recording holograms with more or less saturation.
The complete paper has
been published in
Journal of Optics vol 25 (1994) pp 257 -- 261.