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Optical and Quantum Electronics

Simultaneous diffraction of two finite waves at non-uniform dynamic volume reflection gratings

Gunther Notni, Richard M. Kowarschik

Published Sep 1, 1990• 2 citations
Publisher
DOI
10.1007/bf02113967

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Abstract 1. As soon as it was appreciated that the phenomenon of the "spinning electron" was to be attributed to the existance of simultaneous wave functions, the question naturally arose as to how far there would be an analogy with the polarisation of light, and in particular whether in diffraction by a slit or grating or in reflexion from a mirror, electrons would be selected having a preferential direction of magnetisation. Dynamical conceptions suggest that it would require a magnetic force to produce a change in the polarisation, so that the general indication was rather strongly negative, and it seemed hardly worth while to verify the fact by direct soultion. I believe, however, that recently experiments have been undertaken to search for such an effect (by means of successive diffractions from two crystals), and in view of this I have examined the question more closely. The result, broadly speaking, bears out the first conjecture that no effect could be observed in practice, but in certain cases (of a rather hypothetical kind) an effect might be found and the whole problem is interesting as an example of the wave theory. The essence of the matter is sufficiently represented by taking a line grating instead of a crystal, and, furthermore, by limiting the electric and magnetic forces of the grating in such a way that there shall only be first order spectra on each side, two reflected and two transmitted. The grating is supposed made out of periodic distribution of electric or magnetic material. Actual crystals will consist of almost purely electric material, but the magnetic case is as easy to treat and, though unpractical, gives rise to interesting results. It will appear that when a polarised electron wave falls on such a grating, the direction of magnetisation may be changed in the diffracted rays. It is a true polarisation effect in that the change in direction is independent of the strength of the field in the grating, which only determines the total intensity.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Oct 1, 1928•13 citations
Abstract The orientation-dependence of the diffraction patterns of the transmission grating experiments have been systematically studied by rotating the 1D- and 2D-gratings around three axes. There are two kinds of gratings, transmission and reflective gratings. In this article, we show the novel phenomena: (1) the transmission grating creates simultaneously both the transmission diffraction pattern and the reflective diffraction pattern respectively, namely the transmission grating functions as both a transmission grating and a reflective grating in one experiment; (2) the reflective pattern is non-uniform, expanded, curved and inclined when the grating rotates, namely the reflective pattern has the same characteristics as that of the transmission patten in the same transmission grating experiment. We refer both as the “twin patterns” in the same experiment. We suggest to do the grating experiment with the experimental setups in this article by emitting photons one at a time.
A medium described by an imaginary potential (or imaginary (refractive index) ), that varies sinusoidally in one direction, acts as a volume grating for plane waves incident on it obliquely or normally. Two peculiar features are identified. First, if the potential is weak, so that there are only two significant diffracted beams near the Bragg angle, and three for normal incidence, diffraction is strongly affected by degeneracies of the non-Hermitian matrix generating the `Bloch waves' in the grating; the effect of these degeneracies is very different from that of the Hermitian degeneracies for transparent gratings. Second, if the potential is strong and the grating thick, the asymptotic distribution of intensities among the diffracted beams (momentum distribution) is a rather narrow Gaussian, and dominated by a single set of complex rays; this is very different from the semiclassical limit for transparent gratings, where the rays form families of caustics proliferating with thickness, and with a wider momentum distribution.
Abstract 1. As soon as it was appreciated that the phenomenon of the "spinning electron" was to be attributed to the existance of simultaneous wave functions, the question naturally arose as to how far there would be an analogy with the polarisation of light, and in particular whether in diffraction by a slit or grating or in reflexion from a mirror, electrons would be selected having a preferential direction of magnetisation. Dynamical conceptions suggest that it would require a magnetic force to produce a change in the polarisation, so that the general indication was rather strongly negative, and it seemed hardly worth while to verify the fact by direct soultion. I believe, however, that recently experiments have been undertaken to search for such an effect (by means of successive diffractions from two crystals), and in view of this I have examined the question more closely. The result, broadly speaking, bears out the first conjecture that no effect could be observed in practice, but in certain cases (of a rather hypothetical kind) an effect might be found and the whole problem is interesting as an example of the wave theory. The essence of the matter is sufficiently represented by taking a line grating instead of a crystal, and, furthermore, by limiting the electric and magnetic forces of the grating in such a way that there shall only be first order spectra on each side, two reflected and two transmitted. The grating is supposed made out of periodic distribution of electric or magnetic material. Actual crystals will consist of almost purely electric material, but the magnetic case is as easy to treat and, though unpractical, gives rise to interesting results. It will appear that when a polarised electron wave falls on such a grating, the direction of magnetisation may be changed in the diffracted rays. It is a true polarisation effect in that the change in direction is independent of the strength of the field in the grating, which only determines the total intensity.