Sources free-space’ radiation

In this first set of examples, we determine radiation from sources in free space , using the free-space radiation modes, and compare the results with the antenna methods of Chapter 21. 

Having set up the formalism for the calculation of free-space radiation from current sources, we now account for the effect of the fiber on the radiation fields. We could proceed by solving Eq. (34-16) for a given profile, which leads to the fields through Eqs. (34-15) and (34-13). However, rather than superpose the far fields of point sources, we prefer to determine the Green s function for the tubular source introduced in Section 21-6 and illustrated in Fig. 21-3 [7]. The advantage of the tubular source is that it has the same geometrical symmetry as the circular fiber. Furthermore, an arbitrary current source can be described either by a distribution of dipoles or by a complete set of tubular sources. Here we examine the latter approach. 

Figure 29.9 shows a comparison between the components of a rudimentary EPR spectrometer and the corresponding elements of a more familiar apparatus for visible spectrometry. In EPR, the source of excitation radiation is a microwave device called a klystron. The microwaves would disperse in free space and must therefore be conducted to the sample by waveguide or coaxial cable. The sample, contained in the sample tube, is held in a microwave cavity between the poles of a magnet. The detector is usually a diode that produces a dc output propor-... 

THz spectroscopy was born from research efforts to produce and detect ultra-short electrical currents as they traveled down a transmission line.26 In 1988-1989, it was discovered that electromagnetic radiation pulses produced by time-varying current could be propagated through free space and picked up by a detector.27 By placing a sample between a THz source and detector, one could measure the differences in radiation pulses due to scattering or absorption by the sample to understand its chemical properties. 

Quasioptics relies on free-space propagation of radiation, which is inherently low loss. Given that sources of FIR radiation are, generally speaking, less powerful than their microwave frequency counterparts. 

The form (29) is derived from integrating the conservation law (25 a) over all of space and using Gauss law. It includes the self-energy terms (m = n) as well as the free-held (radiation) terms that are independent of any sources. The latter terms are automatically absent from the expression (28), which is finite from the outset and entails no free radiation. ... 

In a free space, the sound source can be considered as a point source (see Figure 13.1). In practical industrial applications, however, sound is either radiated from the source of definite size (e.g., loudspeaker membrane) or, more frequently, reflected from the point source by surfaces of different shapes such as horn, paraboloid, ellipsoid, etc. In both cases such sound radiation can be regarded as coming from a plane source. This results in a specific pattern of sound intensity in the zone near the sound source, the sound intensity is constant (Fresnel zone), whereas outside this zone (the Fraunhofer zone) the sound intensity decreases inversely with the square of the distance from the plane source, i.e., in the same way as for a point source (Figure 13.4). 

Strict compliance with AN SI-92 or NCRP-86 requires not only determination, by calculation or by measurement, of the total far-field equivalent power density from all nearby sources, but also measurement of body current from contact with potentially radiating objects and, for ANSI-92, measurement of body current induced by immersion in fields near such objects. Power density measurements are straightforward to take, using specialized broadband equipment calibrated in power density (or even in percent of some standard) such measurements can also be made using broadband or narrow-band equipment calibrated more traditionally in field strength. The conversion from field strength to equivalent far-field power density S, in milliwatt per square centimeter (mW/cm ), uses the impedance of free space, 377 as follows ... 

Andrews [9] and others [10] have listed the emission lines of the most commonly available discrete-wavelength lasers (such as ruby, Nd YAG, Er YAG, excimer lasers) over the range 100 nm-10 /u.m. Molecular lasers (HF, CO, CO2, NO) can be tuned to a large number of closely spaced but discrete wavelengths. Continuously tuneable lasers comprise some metal ion vibronic lasers (e.g. alexandrite and Ti sapphire [11]), some diode and excimer lasers, dye and free-electron lasers. Tuneable sources of coherent radiation span the electromagnetic spectrum from 300 nm to 1 mm, with limited tune-ability down to about 200 nm. Wavelength coverages of tuneable lasers have been reported [8]. In operation lasers can be either pulsed (e.g. various metal ion tuneable vibronic lasers, excimer and dye lasers, metal vapour) or continuous wave (major types atomic and ionic gas lasers, dye and solid-state lasers). Most lasers with spectral output in the UV are bulky and expensive devices (especially sub 200 nm) and operate in the pulsed mode. On the contrary, many visible lasers are available which are compact, require low maintenance expenses and operate in continuous-wave (CW) mode. 

When a current source is located within a clad fiber of arbitrary profile, the determination of the radiation field is extremely complicated. However, if the fiber is weakly guiding the determination is greatly simplified [2]. It is intuitive that when the variation in the refractive-index profile is small, the source radiates as if it were located in a virtually uniform, infinite medium of refractive index equal to the cladding index n j. The problem is then analogous to the radiation from an antenna in free space. Consequently, we can borrow from standard antenna theory, and couch the solution to radiation from the weakly guiding fiber in terms of the electromagnetic vector potential A [3-5]. 

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). 

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... 

A tubular source of radius ro is located symmetrically within the core of a weakly guiding, step-profile fiber, i.e. 0 < ro < p, where p is the core radius. To account for the fiber profile, we repeat the analysis of Section 25-13 using the weakly guiding radiation modes of Table 25-4 instead of the free-space modes of Table 25-2. The modal amplitudes of Eq. (25-34a) are replaced by... 

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 radiation fields of the tubular source depend on the solution of Eq. (34-22) for the cartesian components of A,. Nevertheless, we can make a general deduction about these fields regardless of the fiber profile [7]. First consider the free-space solution when n = Mji everywhere. The spatial dependence of A at radius r outside of the tube is proportional to... 

---