Fiber parameter

Physical testing appHcations and methods for fibrous materials are reviewed in the Hterature (101—103) and are generally appHcable to polyester fibers. Microscopic analyses by optical or scanning electron microscopy are useful for evaluating fiber parameters including size, shape, uniformity, and surface characteristics. Computerized image analysis is often used to quantify and evaluate these parameters for quaUty control. 

Bleaching causes the fiber parameters to become more uniform [5]. Due to removal of some extra-cellular materials, the degree of chrystallinity increases [28], fibers acquire a whiter color and the inherent yellowness is decreased. Fibers lose some weight and become finer [12]. Increase in water absorption was reported to occur with bleaching of okra bast fibers. This might be due to the removal of hydrophobic substances which exposes hydrophilic cites [5]. Contrarily, the water absorption of banana fibers was reported to decrease from 61% to 45% for 70 hour water immersion upon sodium hypochlorite bleaching [28]. 

Fiber/parameter Wavelength (pm) Attenuation index, core temperature (°C)... 

Another important fiber parameter is the refractive index difference between the core and cladding, i.e., - Wj. Generally it is represented in normalized fashion and is referred to... 

The dimensionless parameter Vof Eq. (1-1) also applies to fibers, and will be referred to as the fiber parameter. Thus... 

Fig. 6-3 The normalized impulse response for a fiber with an absorbing cladding and (a) a step profile or (b) a clad parabolic profile. Fiber parameters in both cases are K = 70, A = 0.01 and co = 1 -5. Curves are for differing values of the product iiz/p [6],...

The duration Zq of the spatial transient depends on wavelength, or, equivalently, on the fiber parameter V, since the attenuation of tunneling rays is a wavelength-dependent phenomenon. Taking zq to be the position where tunneling ray power has decreased by 90 %, we shall show in Section 8-8 that [6,7] ... 

The attenuation of tunneling-ray power in Eq. (7-3) depends on the product y(P, l)z, where the attenuation coefficient is the ratio of the transmission coefficient r to the ray half-period Zp. For the step profile, the latter is given in Table 2-1, page 40, and we use the linear approximation of Eq. (7-21) for T, which is an excellent approximation for all but the most weakly tunneling rays. If we express k in terms of the fiber parameter using the definition inside the front cover, then... 

A measure of this balance is given by the fiber parameter. If we set a = p in the definition of V, and substitute from Eq. (10-2a), we deduce that... 

The physical parameters o the fiber and the free-space wavelength 2 of the source of excitation are contained in the fiber parameter V and the profile height parameter A defined inside the back cover. 

Table 12-12 Step-profile uniaxial fiber. Parameters not defined in the table are given inside the back cover. Prime denotes differentiation with respect to argument. 

Table 14-3 Fundamental and HEi modes of the weakly guiding step profile fiber. Parameters are defined inside the back cover. Modal power is given by where a is the modal amplitude.

Fig. 14-10 (a) The distortion parameter for the fundamental modes of clad power-law profiles and (b) the values of the fiber parameter at which waveguide dispersion vanishes, the q= oo line corresponding to the value for the step profile. 

On a weakly guiding clad fiber of otherwise arbitrary profile, the fraction of fundamental-mode power residing in the core becomes negligible as F-+ 0. For the step profile, this is clear from the plot of in Fig. 14-3(a). Simultaneously, the fields become nearly uniform over the core, as is evident from the intensity distributions in Fig. 14-3(c), and hence are comparatively insensitive to profile shape. Accordingly, we postulate that the fields depend primarily on the profile volume Q of Eq. (14-42). It then follows from the discussion of the previous section that we can relate the fields of an arbitrary profile, with fiber parameter F, to the known fields of the step profile with fiber parameter Fthrough Eq. (14-46). Thus we replace Fby Fin the small-Fforms for the step-profile fiber listed in Table 14-5. The same conclusion can be derived more formally from the scalar wave equation, as we now show. 

If the fiber parameter F for an arbitrary profile fiber decreases and A is fixed, then the wavelength X increases, as is clear from the definition inside the back cover. When Fis sufficiently small that A > p, where p is the radius of the core, then the core electric field is given by the quasi-static approximation, as expressed in Eq. (11-52). Since the fiber is weakly-guiding we ignore the term in V, Inn and obtain Laplace s equation for the potential describing the transverse electric field... 

Table 15-1 Gaussian approximation for circular fibers. Gaussian approximation for the fundamental-mode fields of weakly guiding, circular fibers. Parameters are defined inside the back cover and coordinates are illustrated in Fig. 14-1...

One piece of information not provided by the Gaussian approximation is the upper value of the fiber parameter for single-mode operation. In Section... 

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