Grating theory

J. Guild, The Interference Systems of Crossed Diffraction Gratings theory of Moire Fringes (Clarendon, Oxford, 1956)... 

The relative importance of the two mechanisms - the non-local electromagnetic (EM) theory and the local charge transfer (CT) theory - remains a source of considerable discussion. It is generally considered that large-scale rough surfaces, e.g. gratings, islands, metallic spheres etc., favour the EM theory. In contrast, the CT mechanism requires chemisorption of the adsorbate at special atomic scale (e.g. adatom) sites on the metal surface, resulting in a metal/adsorbate CT complex. In addition, considerably enhanced Raman spectra have been obtained from surfaces prepared in such a way as to deliberately exclude one or the other mechanism. 

I am grateful in some of the following to the analysis by Seddon [now Curtis], "The Development of Electronic Theory in Organic Chemistry." Cited in Seddon, 17. 

Seddon, "The Development of Electronic Theory," 46.1 am grateful to Mrs. Jennifer Seddon Curtis for making this thesis available to me. 

The DFB grating concept was extended to higher dimensions. Two-dimensional (2D) gratings can be made in a variety of forms, from the simple overlapping of two orthogonal gratings up to concentric rings, or more complicated structures. In modern theory, they can be treated as 2D photonic crystals. 

DR. HUSH For myself, if I gave the impression of any feeling of self-satisfaction, it was certainly in the sense that I think we can say that there is a glimmer of light in the darkness. And in chemistry we must be grateful for the smallest spark. I have stressed also that our present theoretical approaches to rate calculations have been almost entirely confined to outer-sphere processes, and that the task of formulating reliable theories for inner-sphere transfers will be a formidable one. 

This work has been supported in part by an IBM SUR grant to the Quantum Theory Project. This support is gratefully acknowledged. 

Koistinen et al [7] present a number of graphs on the grate fluxes (W/m, s). However, no theory of the method to calculate the grate effect was described. It must be based on the measured mass loss rate. Furthermore, no plots on the combustion rate (kg/m, s) are shown. Magnitudes of the air factor is presented, but no theory of how it is determined. No uncertainty analysis is carried out and no verification method is... 

Conversion system (updraft) in theory Hypothetically analogue conversion system in theory (updraft) Analogue grate system in theory and in practice (updraft) Analogue combustion systems in practice (updraft)... 

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

Above roughening (see Figure 6), the decay of the gratings is well described by the classical continuum theory for sufficiently small ratios amplitude/wavelenght, with g = 2 for evaporation, and 4 for surface diffusion. Deviations, observed otherwise, can be explained mostly by the anisotropy of the surface tension. ... 

Kogelnik, H. 1969. Coupled wave theory for thick hologram gratings. Bell Syst. Tech. J. 48 2909 7. 

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