Material dispersion optimum profile

It is well known that the dispersion in the optical fibers is divided into three parts, modal dispersion, material dispersion, and waveguide dispersion. In the case of the SI POF, the modal dispersion is so large that the other two dispersions can be approximated to be almost zero. However, the quadratic refractive-index distribution in the GI POF can dramatically decrease the modal dispersion. We have succeeded in controlling the refractive-index profile of the GI POF to be almost a quadratic distribution by the interfacial-gel polymerization technique (2). Therefore, in order to analyze the ultimate bandwidth characteristics of the GI POF in this paper the optimum refractive index profile is investigated by taking into account not only the modal dispersion but also the material dispersion. 

The crucial factor defining the refractive index profile in GI POFs is the coefficient g, and the optimum value for maximizing the bandwidth can be determined from the modal and material dispersions [79-81]. From analyses using the Wentzel-Kramers-Brillouin (WKB) method, the modal dispersion niate-rial dispersion total dispersion fftotai can be expressed as follows ... 

Fig. 3-3 The solid curve is the normalized pulse width ctj/2 co of E<1-(3-7) for clad power-law profiles as a function of q, and the horizontal line is the corresponding value of Eq. (3-2) for the step profile. When the fiber materials are dispersive, the dashed curve plots the normalized pulse width cti/zn, which shifts the optimum profile exponent from g p, s 1.98 to gopt -I- gopt = 2.26, assuming weak guidance [4]. For all three plots A = 0.01, or 6c = 0.14.

Although the correction to ray transit time due to fiber nonuniformities is small, we recall from Chapter 3 that the pulse width on a weakly guiding fiber is also small. For example, the minimum pulse width of Eq. (3-9) for the optimum clad power-law profile is proportional to A, or 6. We investigated the effect of material dispersion on pulse spreading in Section 3-8 here we account for the effect of slight nonuniformities on the pulse minimum. 

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