## Material dispersion in fibers

Material dispersion is another mechanism limiting the capacity of optical fibers. Material dispersion is due to the dependence of the refractive index on the wavelength. Figure 22.5 shows, as a function of wavelength, the phase refractive index and the group refractive index of silica. The indices are defined as

 c

 (22.4)

 n=

 (phase refractive index)

vph

and

 c

 (22.5)

 n

 gr

 (group refractive index)

gr

where vph and vgr are the phase and group velocity in silica, respectively. The phase refractive index and the group refractive index are related by

 dn ~dX

 dn dXo

 ngr = n _ X

 = n _ X0

 (22.6)

where AX is the spectral width of the optical signal.

The time delay between the leading edge and the trailing edge of an optical signal after traveling in the fiber for a length L, called the material dispersion, is given by

 L л v2 Avgr vgr

 At =

 (22.8)

 c dX,

 0

 L ax = L 3!L AX0

 c dX

The material dispersion is measured in ps/(nm km) and it is illustrated for silica fibers in Fig. 22.5. LEDs have a broad emission linewidth. Therefore material dispersion is, along with modal dispersion, the bandwidth-limiting factor in optical fiber communication systems operated with LEDs.

Exercise: Material dispersion in waveguides. Derive Eqs. (22.6) and (22.7). Why does material dispersion have a much smaller significance for semiconductor lasers than for LEDs?

Substantial material dispersion exists in plastic fibers at all wavelengths of interest. These wavelengths are the local loss minimum at 650 nm and the low-loss region of 500-600 nm. The material dispersion is given in Table 22.1. The data indicates that 650 nm is the wavelength of least dispersion, making 650 nm the preferred communication wavelength in plastic optical fibers.

Table 22.1. Material dispersion in PMMA plastic optical fibers (courtesy of R. Marcks von Wurtemberg, Mitel Corporation, 2000).

 Wavelength 525 nm 560 nm 650 nm Material dispersion 700 ps/(nm km) 500 ps/(nm km) 320 ps/(nm km)

Exercise: Comparison of material and modal dispersion. Consider a 62.5 pm core diameter multimode step-index fiber of 3 km length with a core index of n1 = 1.45 and a cladding index of n2 = 1.4. Assume that the fiber inputs come from either an LED or a laser emitting at 850 nm. Assume that the LED and the laser have a linewidth of 50 and 5 nm, respectively. Calculate the material and the modal dispersion for each case and explain the result.

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