We see from the capture fraction results in table 2 that slightly over one half the experimental F values do not have limits of error that bracket the values predicted from simple theory. The experimental values are consistantly low. We feel that the experimental determinations of capture fractions described here represent a realistic approach to the measurement of these physical quantities and that the low values are real. This conclusion implies that there are deficiencies in the theoretical model we have used, at least as it applies to certain fiber configurations. Neumann [4] has discussed some of the approximations and physical effects which have been neglected in the derivation of eqs (4-2) and (4-3). The presence of leaky modes, mode selective attenuation, variations in the fiber material as a function of length, variations in scattering as a function of fiber radius and changes in modal energy distributions could all effect the simple theoretical predictions. Pending independent F measurements by other investigators, we tentatively conclude that the magnitude of the capture fraction as given by eqs (4-2) and (4-3) may yield excessively large values in some fibers. The discrepancies are largest for the step-index fibers which we tested. 4.4 Length Determination and Fault Location The OTDR also yields a quick estimate of the length of the fiber L from time-of-flight measurements. This distance is determined from observations of the time interval between Fresnel reflections at the front and far ends of the fiber according to the relation where T is the time interval, c the velocity of light, and N the group index of the fiber. In order to measure time intervals with precision, it is necessary to have a source capable of emitting a fast-risetime pulse. Measurement accuracy requires a knowledge of the group index N. This information may be available from manufacturers. Experimentally, group velocities, c/N, can be fixed for a short sample of a given fiber, by means of a shuttle-pulse technique with a precision of about 0.1 percent and accuracies of approximately 0.2 percent [48]. A more convenient, though less accurate, method of estimating L from backscatter scans is by assuming a representative value of N for use in eq (17). We will now examine a possible way of accomplishing this. The value of N can be calculated from the equation if the wavelength dependence of the index of refraction is known. The required dispersion data for silica and a number of doped silica glasses used in optical fibers has been tabulated by Malitson [49], and Fleming [50,51]. The dispersion information may be expressed as a three-term Sellmeier relationship of the form 2112 a212 a312 + where the coefficients a are related to the material oscillator strength, and b the corresponding oscillator wavelengths. We have calculated N and n1 as a function of wavelength for three typical fiber materials using the data of Fleming and eqs (4-10) and (4-11); these appear in figures 4-17, 4-18 and 4-19. For our purposes we will assume that the 13.5 Ge02:86.5 Si02 sample represents a fairly typical on-axis material for a high-bandwidth telecommunicaions fiber. Some experimental values of N at 824 nm have been reported by Franzen [48] for a number of high-bandwidth graded-index fibers. These are reproduced in figure 4-20. It can be seen that they are consistent with the above approximation scheme. We have been concerned above with fiber length measurements. also apply to fault location. The same considerations In this section we will consider the effect that various local perturbations have on the backscatter response of an otherwise uniform and reciprocal fiber. These perturbations may be either extrinsic, for example bends, or intrinsic, for example an impurity region of high loss in the fiber. We will refer to the characteristic backscatter features as "fault signatures" which generate a change in the background Rayleigh response. It will be convenient to divide the signal returns into two categories which will be referred to as absorption-like and scatter-like fault signatures. The distinction is made clear from an examination of the computer-generated plots shown in figures 5-1 and 5-2. Scatter-like signatures. are defined as those which have an increase in backscatter signal larger than the associated decrease (fig. 5-1). Likewise figure 5-2 illustrates an absorption-like signature, from which defect loss may be inferred as shown. The most general form of fault signature is a combination of both (fig. 5-3). It should be noted that there is always some absorption associated with scatter-like signatures, even though this can be rather small. Also the decrease in backscatter power on a decibel scale is twice the actual fault loss. 5.1 Absorption-like Signatures Absorption-like fault signatures are produced by perturbations which convert the radiation in the probe pulse into heat energy, or by perturbations which scatter the radiation exclusively in the forward direction. Figure 5-4 shows the absorption-like fault signature for a fusion splice which exists at the center of the fiber. The one-way loss is approximately 0.18 dB at the splice. The cause of the other irregularities which can be seen, has not been identified. Fusion splices are known to weaken the fiber, and the backscatter technique is the only practical means of detecting the presence of these flaws once the fiber is cabled. INDEX INDEX 1.490 Figure 4-17. Index of refraction and group index for silica. Figure 4-18. Index of refraction and group index for 13.5 Ge02:86.5 Si02 glass. |