Sources within fibers

21-3 Example Current dipole within an arbitrary fiber 445 

21-4 Example Transverse dipole within a weakly guiding fiber 445 

In the previous chapter we examined the excitation of modes of a fiber by illumination of the endface with beams and diffuse sources, i.e. by sources external to the fiber. Here we investigate the power of bound modes and the power radiated due to current sources distributed within the fiber, as shown in Fig. 21-1. Our interest in such problems is mainly motivated by the following chapter, where we show that fiber nonuniformities can be modelled by current sources radiating within the uniform fiber. Thus, isolated nonuniformities radiate like current dipoles and surface roughness, which occurs at the core-cladding interface, can be modelled by a tubular current source. 

The fiber or waveguide in Fig. 21-1 has arbitrary refractive-index profile and cross-sectional geometry, and supports modes with the properties described in Chapter 11. Outside of the region occupied by currents, the total fields E and H 

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Considerable investigation has been reported on the effects of increasing dietary fiber on utilization of various minerals. Fiber supplementation may dilute the concentration of minerals by increasing fecal bulk, may lessen the absorption by decreasing fecal transit time, may encourage absorption of minerals upon fiber residues or trap minerals within residues, and/or may complex with phytate and other Inhibitors of mineral utilization. However, results of studies investigating utilization of different minerals under conditions of additions of different levels and sources of fiber have in no way been conclusive (26-29). 

We can now calculate the source power carried by bound rays when the fiber is illuminated by the diffuse source. In this part of the chapter we determine the total source power, the total bound-ray power and the radial distribution of bound-ray power over the core cross-section. Later in the chapter we show how to derive the distribution of power among the various bound-ray directions. We assume that the source of Fig. 4-3(a) is placed against the fiber endface in Fig. 4—4, and its surface covers at least the core cross-section. Only the portion of the source within the core cross-section can excite bound rays, so we ignore any effects due to the source outside of this region. The excitation of leaky rays by sources is examined in Chapter 8. 

In the two examples above, we determined the power radiated from current sources within a fiber by ignoring the variation in profile and assuming an unbounded medium of uniform refractive index n i. Now we determine the correction to the free-space result due to the variation in profile [2], As the fiber is assumed to be weakly guiding, it is intuitive that the correction is small except when the radiation is directed predominantly close to the axis, i.e. 00 = 0. Thus we anticipate that the free-space results are, in general, highly accurate. 

To determine radiation from sources within weakly-guiding fibers, we must solve Eq. (21-17) for the vector potential. However, if the free-space solution for the particular problem is known, we need only determine the modification due to the fiber profile. The free-space solution is the solution of Eq. (21-17) when n(x, y) = everywhere. The solution to Eq. (21—17)as (x, y) varies, can... 

Fig. 21-6 (a) Plots of the factor C,(0) of Eq. (21-38) as a function of the radiation angle 0q for an axisymmetric source within a step-profile fiber, (b) Normalized power P as a function of the radiation angle 0q for an axisymmetric tubular source coinciding with the interface of a step-profile fiber. The solid curve is calculated from Eq. (21-41b) and the free-space dashed curve from Eq. (21-32). 

When light propagates along a fiber and impinges on nonuniformities due to imperfections in the fiber, some of its power is scattered, as shown schematically in Fig. 22-1 (a). Part of the scattered power is distributed into forward-and backward-propagating modes, while the remainder is radiated. For multimode fibers, the distribution of scattered power is best treated by the ray methods of Chapter 5. Here we are primarily interested in fibers that propagate only one or a few modes. We treat the nonuniformities of the perturbed fiber as induced current sources within the unperturbed fiber. The results of the previous chapter can then be used to describe excitation of bound modes and the radiation field [1-3]. 

We showed in Sections 21-8 and 21-11 that when the fiber profile is included the far-field radiation pattern due to sources within a weakly guiding fiber can be described by a correction factor to the free-space pattern. The correction factor is, in turn, expressible as a product of two factors, Cj (0) and (6), as we showed for the step-profile fiber in Section 21-13. By examining the definitions in Eqs. (21-38) and (21-36b), we find that (0) is inversely proportional to G([/) of Eq. (24-31), provided... 

Example Dipole within a step-profile fiber 25-15 Example Tubular source within a step-profile fiber 25-16 Effect of a finite cladding... 

Consequently Eq. (25-37) is identical with the angular integral of the product of the far-field of Eq. (21-24b) in free space and the correction factor Cq (6) of Eq. (21-36a) for an on-axis source within the fiber, as discussed in Section 21-13. 

Example Tubular source within a step-profile fiber... 

Tubular sources within weakly guiding fibers... 

We are principally interested in determining only the radiation, or far field. As explained in Section 21-8, radiation from sources within weakly guiding fibers is nearly identical to radiation in free space , i.e. in an unbounded medium of uniform refractive... 

The term solid-state laser refers to lasers that use solids as their active medium. However, two kinds of materials are required a host crystal and an impurity dopant. The dopant is selected for its ability to form a population inversion. The Nd YAG laser, for example, uses a small number of neodymium ions as a dopant in the solid YAG (yttrium-aluminum-gar-net) crystal. Solid-state lasers are pumped with an outside source such as a flash lamp, arc lamp, or another laser. This energy is then absorbed by the dopant, raising the atoms to an excited state. Solid-state lasers are sought after because the active medium is relatively easy to handle and store. Also, because the wavelength they produce is within the transmission range of glass, they can be used with fiber optics. 

The paper and allied products industry comprises three types of facilities pulp mills that process raw wood fiber or processed fiber to make pulp paper and board mills that manufacture paper or board and converting facilities that use these primary materials to manufacture more specialized products such as writing paper, napkins, and other tissue products. The process of converting paper is not a source of water or air pollution, as is the case for the first two facilities. This chapter focuses primarily on the greatest areas of environmental concern within the pulp and paper industry those from pulping processes. 

Simply put, paper is manufactured by applying a watery suspension of cellulose fibers to a screen that allows the water to drain and leaves the fibrous particles behind in a web. Most modem paper products contain nonfibrous additives, but otherwise they fall within this general definition. Only a few paper products for specialized uses are created without the use of water, using dry forming techniques. The production of pulp is the major source of environmental impacts from the pulp and paper industry. 

All types of muscle require calcium for contraction. In skeletal muscle, Ca++ ions are stored within an extensive membranous network referred to as the sarcoplasmic reticulum. This network is found throughout the muscle fiber and surrounds each myofibril. Furthermore, segments of the sarcoplasmic reticulum lie adjacent to each T tubule that, with a segment of sarcoplasmic reticulum on either side of it, is referred to as a triad. As the action potential is transmitted along the T tubule, it stimulates the release of Ca++ ions from the sarcoplasmic reticulum. The only source of calcium for skeletal muscle contraction is the sarcoplasmic reticulum. 

Air samples collected in one acrylonitrile-fiber plant ranged from 3 to 20 mg/m3 (EPA 1980a). Mean 24-hour acrylonitrile concentrations in atmospheric samples collected within 5 km of 11 factories producing or using acrylonitrile ranged from less than 0.1 to 325 pg/m (Suta 1979). The occurrence of acrylonitrile was correlated to wind patterns the highest concentrations were downwind of and in close proximity to the plant. The median concentration of acrylonitrile for 43 measurements in "source-dominated areas" (i.e., near chemical plants) was 2.1 pg/m (Brodzinsky and Sing 1983). There were no data available on the concentration of acrylonitrile in air near chemical waste sites, but because acrylonitrile is easily volatilized, this is an exposure pathway of concern. 

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