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modulation of a broadband optical source such as a light-emitting diode, and a lowfrequency dithering of a wavelength-selecting device such as a monochromator As in the modulation phase shift method, the phase difference of the amplitude modulation is measured between a test fiber and a reference fiber Again, the reference fiber and reference receiver can be replaced by an electrical cable when both ends of the fiber under test are close together After an electrical signal proportional to the phase difference is generated by a phase meter, variations in this signal caused by wavelength dithering are detected by a low-frequency lock-in amplifier A low-frequency oscillator generates a signal that provides the reference for the lock-in and causes the wavelength-selecting device to dither over a range of /2 at a center wavelength of The CD is then given by D( ) = where D( ) is the CD as a function of wavelength is the radian peak-to-peak modulation phase shift f is the amplitude modulation frequency is the mean wavelength selected is the peak-to-peak dither of the wavelength selection L is length of the fiber under test In practice, Equation 288 must include a multiplicative correction factor to account for the temporal characteristics of the dither waveform and other factors The constant correction factor can be determined by measurement of a fiber of known CD This method determines CD directly, without the need for fitting of an analytical function to measured data
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2873 Polarization-mode dispersion (PMD)
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In single-mode fibers where chromatic dispersion has been carefully compensated, or when operating at a wavelength near the chromatic dispersion minimum of a fiber, the effects of chromatic dispersion may be small enough that polarization-mode dispersion (PMD) becomes a dominant limitation of the maximum bit rate The effect of PMD is simplest in certain components that incorporate birefringent crystals (Examples include optical isolators and electro-optic modulators) The group delay through such a component depends on the polarization of the optical signal A detailed analysis of the situation (Poole and Giles, 1988) shows that only two polarizations called the principal states of polarization (PSPs) will experience pure group delays, and that the PSPs are orthogonal in the absence of polarizationdependent loss The difference between these delays is called the differential group delay (DGD) A pulse coinciding with a PSP propagates through the device without suffering first-order broadening The energy of a more general input pulse, however, is distributed between the PSPs At the output, the two PSPs arrive at different times and add together at the photodetector (Figure 2819) to form an electrical output pulse
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Figure 2819 Pulse splitting caused by polarization-mode dispersion The two
output pulses are polarized along the principal states of polarization, and separated in time by the differential group delay A polarization-independent receiver responds to the sum of the two pulses, effectively resulting in pulse broadening
that is broadened or even split into two The PMD of a simple component is simply the DGD, usually expressed in picoseconds In a long fiber or in a concatenation of many fiber components, the pulse-broadening phenomenon is more complicated In this case, both the DGD and PSPs depend on the optical wavelength Moreover, the slow drift in birefringences of different sections of the fiber cause both the DGD and PSPs to vary over time, even when measured at a constant center wavelength For this reason, the PMD of a long fiber, or of a network incorporating long lengths of fiber, is specified as a statistical quantity Both the mean DGD and the RMS DGD, ie, the square root of the mean squared DGD, are used to characterize the statistical distribution of DGD; in this context, both quantities currently are used to define PMD Using either definition, fiber PMD is found to increase proportionally to the square root of the fiber s length, so PMD is specified in ps/ km The PSPs are assumed to vary uniformly over all states of polarization Pulse distortion and broadening are different for a long fiber versus for a simple birefringent component After transmission through a long fiber, pulses much shorter than the mean or RMS DGD are broken up into a distribution of pulses with an envelope that is roughly Gaussian As shown in Figure 2820, broader input pulses result in coarser variation of the output amplitude When the input pulse width is greater
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