Decomposition of the radiation field

The last five chapters have shown how the radiation fields of an optical waveguide can be represented in different ways. In Chapter 24, we introduced the notion of leaky modes to describe the bulk of the radiation field close to the waveguide axis at distances sufficiently far from the source of exdtatioa The remaining portion of the radiation field corresponds to a space wave, as defined in Eq. (24-1). The same radiation field can also be represented either by an expansion over radiation modes, as we showed in Chapter 25, or by a superposition of the fields of point dipole sources, using the Green s function techniques for waveguides described in Chapters 21 and 34. In this chapter, we show how to find the space-wave component of the radiation field by formally decomposing either representation into leaky modes and a space wave. 

In the following discussion, we use the modal expressions of Eq. (25-3) to represent the radiation field. Since the analysis applies equally to the magnetic or electric fields, we need only consider the latter. Further, we use the weak-guidance approximation for simplicity and when we require an example, we refer to the step-profile fiber for any functional dependence. Thus 

When the source of excitation is specified, either as a current distribution J within the fiber, or as illuminating fields E, and H, over the endface, the aj Q) are given explicitly by Eqs. (25-12) and (25-11), respectively. In either case, we substitute the expression for aj Q) into Eq. (26-1), and take advantage of the symmetry properties of the integrand to extend the range of integration to Q= — 00. For the step-profile fiber, each cartesian, or scalar component, of the field is proportional to an integral / of the form 

We have intentionally omitted the details in progressing from Eq. (26-1) to Eq. (26-2) because of their algebraic complexity. Since we only want to show, the formal procedure for decomposing the radiation field, such details are counter-productive from a pedagogical point of view, and are to be found elsewhere [1-3]. Similarly, the approach from the Green s function representation to integrals of the form of Eq. (26-2) is available in Refs. [3,4]. 

We now examine the singularities of the integrand of Eq. (26-2) in the complex Q-plane, with a view to deforming the path of integration away from the real 

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Figure 1 Structure of [2Fe-2S] cluster and Mossbauer spectra of the [2Fe-2S] " " cluster of the reductase of methane monooxygenase from Methylosinus trichosporium OB3b (a) The 200 K spectrum consists of two quadrupole doublets representing a ferric (inner doublet) and a ferrous site. The triangles mark the isomer shift of each site, obtained by taking the centroid of the spectrum, (b) 4.2 K spectrum, recorded in a field of 6.0 T applied parallel to the observed Mossbauer radiation. The solid lines above the experimental data show a decomposition of the high-field spectrum into contributions from the ferric and ferrous site. Details are...

The Ea for the dissolution of hematite by mercapto carboxylic acids in acid media in the presence of UV radiation was lower (64 5 kj mol ) than that for dissolution in the absence of radiation (94 8 kJ mol ) (Waite et al. 1986). The reaction in both cases was considered to involve formation of an intermediate organic-Fe surface complex which decomposed as a result of intramolecular electron transfer to release Fe". UV irradiation enhanced the decomposition of the surface complex either through excitation of the ligand field states associated with the free electrons on the S atoms, or through high energy charge transfer states. 

An attempt to prepare Np(BTif)if using the above method resulted in the decomposition of the borohydride due to the extremely high radiation field of the T2 gas (66 Ci) and no volatile Np compound was recovered. 

The reprocessing of used reactor fuel elements involves solvent extraction processes with organic solvents. In these processes the solvents are subjected to high radiation fields with subsequent decomposition of the organic solvent. The design of chemical reprocessing systems must take into account any interference by the radiolytic products (Ch. 20). 

Nitric acid can be formed by the radiolysis of moist air. This nitric acid will rapidly dissolve in water and cause a decrease in the pH. On the other hand, intermediate products in the air radiolysis process interact rapidly with surfaces and other chemical species in the atmosphere. Furthermore, nitric acid is susceptible to decomposition in a radiation field. It has been difficult, then, to assess the overall effect nitric acid formation by radiolysis will have on solution pH. 

Microfabrication by means of laser radiation covers a wide range of different methods (24,25). On the one hand, these are processes where material is removed in an intense electromagnetic field by melting, evaporation, decomposition, photoablation, or a combination of these phenomena. On the other hand, generating processes exist where structures are built up from liquid resins, laminated layers, or powders using, e.g., photochemically induced crosslinking of organic compounds... 

Three-dimensional CFD-coupled with radiation field modeling and photocatalytic reaction dynamics was employed by Salvado-Estivill et al. (2007b) to model the decomposition of TCE in a flat-plate, single-pass photocatalytic reactor containing immobilized P25. The outcome was pollutant-specific kinetic rate parameters, which were independent of the reactor geometry, radiation field, and fluid dynamics. This was followed by... 

The problem of the action of radiation on azides, particularly lead and barium azide has been review cd [116]. Irradiation prior to thermal decom-Jposition often effects a reduction or elimination of the induction period, a de-ICrcasc in activation energy and an increase in the rate of decomposition. Zak-rov and co-workers [117] have found that the application of a moderate electric field can affect the rate of thermal decomposition of azides. 

The organic-cooled CANDU concept was proposed by McNelly of CGE in 1958 (71), This began an extensive investigation of coolant properties, decomposition, control of deposition, and many other aspects of coolant chemistry. An organic-cooled, heavy-water-moderated research reactor, WR-1, began operation at WNRE in 1965. It has demonstrated reliable operation with coolant outlet temperatures of up to 675 K. Low corrosion and a low potential for activity transport result in very low radiation fields around the piping. 

Such a reaction of Fe(CO)5 (at 293-363 K, PVP) without ultrasonic radiation proceeds very slowly and only after few days there, a material is formed with very low Fe content (2%, the isolated particles 2-5 nm in size). It is of interest that the sonochemical decomposition of Fe(CO)5 does not proceed in the presence of PVP if THF is used as the solvent, but the reaction is very effective when anisole is used as the solvent and PFO is used as the polymer matrix [93]. A black product formed contains up to 10% (in mass) of the spheric particles of nonoxidized Fe (mainly y-Fe, with little content of a-Fe) with 1-12 nm in size (the mean diameter is 3nm, as shown in Figure 3.7). It is likely that the big particles present the flocks of little ones ( 2-2.5nm). The sonochemical synthesis allows us to produce the functionalized amorphous nanoparticles of ferric oxide with 5-16 nm in diameter [94]. The ultrasonic irradiation in the PFO presence allows us to also produce the stabilized nanoparticles of copper, gold, and so on. In the literature the findings are not about the bimetallic particle formation in the ultrasonic fields by carbonyl metal reduction in the polymer matrices presence (as, for example, in the case of the carbon-supported Pt-Ru from PtRu5C(CO)i6 reduced clusters [95]). 

Oxidizers such as ammonium perchlorate, chlorates, and periodates have been exposed to UV radiation, and in many cases chemical activity and decomposition rates could be increased. The pre-irradiation of ammonium perchlorate has been studied by Freeman and Anderson, the decomposition of potassium periodate by Phillips and Taylor,and NavOrd 7147 quotes several authors in connection with work on chlorates. A growing literature in this special field is to be expected and present interest is indicated in several articles in the book Reactivity of SoIidsJ ... 

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