Further comments on the theory of the frustrated total reflection filter.
In view of the comments made by Iogansen it would be worthwhile to compare first the two methods of analysis. The method developed by Iogansen is based on an approximate solution of the wave equation by means of orthogonal waves. When the direction of propagation of the incident wave is such that the angle between the wave normal and the normal to the boundary surfaces of the layers is sufficiently large, the orthogonal waves approximate closely the solution to the wave equation. However, in order to relate the transmitted field in each of the layers to the incident field, further approximations are necessaiy. In particular, in the approach used by Iogansen the orthogonal waves are expanded in a Taylor series and only the first linear term of the series is retained. Clearly, such an expansion yields a reasonable approximation to the actual solution if, and only if, the thickness of each of the layers is of the order of a wavelength of the incident light or smaller. When the thickness of the layers is large compared with the wavelength, the approximation becomes poor and the method of analysis breaks down completely. The approximation is therefore limited to the analysis of frustrated total equation filters or similar resonant systems involving a limited number of layers of limited thickness. In contrast, the method of plane wave expansion as proposed in our paper does not basically involve any approximations (assuming of course that the model of blackbody boundaries is accepted). It can, therefore, be used independently of the thickness and the number of layers involved. All results of interest
The frustrated total reflection filter. 1. Spectral analysis.
The method of modal expansion is used to develop a theory for the analysis of frustrated total reflection (FTR) filters or similar layered systems of finite lateral extent. The theory is applied to determine the (spectral) transmission properties of the FTR filter of finite lateral extent (for an incident plane wave propagating in direction of maximum transmission). It is found that the finiteness of the lateral dimensions of the filter has a great effect on the transmission properties of the filter. The results are in agreement with available experimental data and clearly show that the unbounded wave theory (i.e., an analysis which assumes that both the incident electromagnetic radiation and the filter are of infinite lateral extent) cannot be applied to FTR filters even when the lateral filter dimensions are several orders of magnitude larger than the wavelength of the incident radiation.
Igneous Rock Associations 23. The Bushveld Complex, South Africa: New Insights and Paradigms
SUMMARYThe Bushveld Complex has continued to serve as the basis for study into the fundamental nature of petrological processes for layered intrusion formation and for oxide and sulphide hosted Platinum Group Element (PGE)–Cu–Ni ore deposits. These studies have included discoveries in terms of the physical extent of Bushveld magmatism, both laterally and internally. Lateral variations in the mafic to ultramafic Rustenburg Layered Suite of the Northern Lobe of the complex have also revealed petrologically distinctive Upper Critical Zone equivalent rocks (the so-called Flatreef) with enhanced contamination and mineralization traits that reflect a transition between Eastern and Western Lobe equivalent stratigraphy and Platreef-style complexity. Traditional magma mixing models have been re-examined in light of radiogenic isotopic evidence for crustal involvement early in the chromite precipitation or formation process, combined with evidence for associated heterogeneous fluid contents, cryptic layering profiles, and textural evidence. A wide variety of alternative ore-genesis models have been proposed as a consequence. The fundamental mechanics of magma chamber processes and the existence of the magma chamber as an entity have been called into question through various lines of evidence which have promoted the concept of progressive emplacement of the complex as a stack of not-necessarily-quite-sequentially intruded sills (with or without significant quantities of transported phenocrysts), emplaced into variably crystallized and compacted crystal-liquid mush mixtures, modified by compaction-driven late magmatic fluid (silicate and aqueous) activity. Alternatively, petrological and geochemical observations have been used to discount these interpretations in favour of more conventional cooling and gravity-driven accumulation of silicate and ore minerals in a large, liquid-dominated system.RÉSUMÉLe complexe de Bushveld a demeuré à la base d’études sur la nature fondamentale des processus pétrologiques de formation d’intrusions litées et des gîtes des éléments du groupe platine (ÉGP)-Cu-Ni hébergés dans les oxydes et les sulfures. Ces études ont comporté des découvertes sur l’étendue physique, à la fois latérale et interne, du magmatisme de Bushveld. Les variations latérales de la suite stratifiée et mafique à ultramafique Rustenburg du lobe nord du complexe ont également révélé des roches équivalentes pétrologiquement distinctes de la zone critique supérieure (le communément désigné Flatreef) avec des traits de contamination et de minéralisation accrus qui reflètent une transition entre la stratigraphie équivalente des lobes est et ouest et la complexité de type Platreef. Les modèles traditionnels de mélanges magmatiques ont été réexaminés à la lumière de preuves isotopiques radiogéniques indiquant une implication de la croûte au début du processus de précipitation ou de formation de la chromite, combinées à des preuves de contenu fluide hétérogène associé, de profils de litage cryptique et de preuves texturales. Ainsi, une grande variété de modèles alternatifs de genèse de minerai a été proposée. La mécanique fondamentale des processus de la chambre magmatique et l'existence de la chambre magmatique en tant qu'entité ont été remises en question au moyen de divers éléments de preuve qui ont mis en avant le concept de mise en place progressive du complexe sous forme d'un empilement non-nécessairement séquentiel de sills injectés (avec ou sans quantités significatives de phénocristaux transportés) mis en place dans des mélanges de bouillie cristaux/liquide à cristallisation et compaction variable, modifiés par une activité tardive de fluide magmatique (silicaté et aqueux) induite par la compaction. Alternativement, des observations pétrologiques et géochimiques ont été utilisées pour écarter ces interprétations en faveur d'un processus plus conventionnel de refroidissement et d’accumulation de minérais silicatés et minéralisés induite par la gravité dans un vaste système à dominance liquide.