Measurements Paul Hernday
All forms of dispersion degrade the modulation-phase relationships of lightwave signals, reducing information-carrying capacity through pulse-broadening in digital networks and distortion in analog systems. Designers of optical fiber transmission systems must cope with three basic forms of fiber dispersion, illustrated schematically in Figure 12.1. Inter-modal dispersion, which limits data rates in systems using multimode fiber, results from the splitting of the signal into multiple modes that travel slightly different distances. Chro-matic dispersion, which occurs in both singlemode and multimode fiber, results from a variation in propagation delay with wavelength that is shaped, in turn, by the interplay of fiber materials and dimensions. Polarization-mode dispersion, caused by the splitting of a polarized signal into orthogonal polarization modes with different speeds of propagation, becomes a limiting factor in singlemode fiber when chromatic dispersion is sufficiently reduced. This chapter deals with the dispersion characteristics of the physical layer of a telecommunications system-the fiber, components, and installed transmission paths-providing a brief introduction to the causes of dispersion and a sampling of measurement methods. Measurement approaches to these critical attributes take many forms; some of the methods described here are widely used commercial methods, and others are pre-sented simply because they provide good insight into the dispersive phenomena. The de-tail with which the methods are discussed reflects, to some extent, the author's experience with the methods. Measurement methods for many fiber, component, and system attrib-utes are developed by standards groups such as Telecommunications Industry Association and its international counterparts. Guidance in the measurement of dispersive effects is provided by formal fiber optic test procedures (FOTPs), referenced herein.
476 Dispersion Measurements
Multimode fiber (step Index)
SMF Optical \1 1 ~ frequencies \1
2 _________ ~~
Polarization \)(/ modes D
Sec.12.2 Measurement of Intermoclal Dispersion
Electrical pulse source
Sampling oscilloscope (optical)
Figure 12.2 Measurement of multi mode fiber bandwidth by the pulse distortion method.
12.2.2 The Pulse Distortion Method
The most common method for measuring multimode fiber bandwidth, illustrated in Fig-ure 12.2, is based on measurement of the impulse response. I A pulsed laser source is cou-pled through a mode scrambler to the input of the test fiber. The source spectrum must be narrow enough that the results are not significantly influenced by chromatic dispersion. The output of the fiber is measured by a sampling oscilloscope with built-in optical re-ceiver. A horizontal trigger is supplied through a variable delay to offset the difference in delay between a short reference fiber and the fiber to be tested. The reference fiber is typi-cally a few meters in length. In operation, a fast pulse is launched into the test fiber and the output pulse is digitized, including leading and trailing edges down to 1 % of the peak amplitude. Next, the input pulse is measured in the same way, using a short reference path in place of the test fiber. The reference fiber can be a short length cut from the input of the test fiber, or a short length of fiber having similar optical characteristics. The transfer function of the test fiber is given by
H(f) = B(f) A(f) (12.1)
where 8(j) and A(f) are the Fourier transforms of the output and input pulses, respectively. Fiber bandwidth is defined as the lowest frequency for which IH(f)1 = 0.5.
Multimode fiber bandwidth measurements are sensitive to optical launch conditions and the deployment of the test sample. For stable, repeatable measurements, a mode-scrambling device should be inserted ahead of the test device to assure excitation of a large number of modes. In addition, cladding light should be removed. In some cases, the fiber coating dissipates cladding modes. Altematively, cladding mode strippers can be used at both ends of the test fiber.
Fiber c::==~ under
Figure 12.3 Measurement of multimode fiber bandwidth by the fre-quency domain method.
12.2.3 The Frequency Domain Method
An alternative method for the measurement of multimode fiber bandwidth is the baseband AM response method2 shown in Figure 12.3. A narrowband cw optical carrier is sinu-soidally intensity modulated by a swept-frequency RF or microwave signal Source and coupled through a mode scrambler to the test fiber. Cladding mode strippers may also be needed. The modulation is detected by a photodiode receiver. The instrumentation records the received optical power as a function of modulation frequency. In operation, the test fiber is generally measured first, resulting in the measurement Poulf.) The input signal is then determined by measuring again ,with a short reference fiber. As in the pulse method, the reference fiber can be a short length cut from the input of the test fiber, or a short length of fiber having similar optical characteristics. The reference measurement yields the function Pin(j). The frequency response in optical power is given by
H(fJ = log [Pout(fJ] 10 Pin(f) . (12.2)
Fiber bandwidth is defined as the lowest frequency at which H(j) has decreased by 3 dB from its zero-frequency value.
For convenience, source and receiver functions may be performed using a lightwave component analyzer or a network analyzer with appropriate transducers. In either case, sweeping of the modulation frequency, subtraction of the calibration values and display of the resulting transmission response are performed automatically. When an electrical net-work analyzer is used with external laser source and photodiode receiver, care must be taken to properly interpret the frequency response. Because an electrical network analyzer mea-sures RF power and the photodetector produces a current that is proportional to optical power, the network analyzer will indicate a 6 dB change for a 3 dB change in optical level.
Sec. 12.3 Measurement of Chromatic Dispersion 479
12.3 MEASUREMENT OF CHROMATIC DISPERSION
Chromatic dispersion is simply a variation in the speed of propagation of a lightwave sig-nal with wavelength. The optical source in a high-speed communication system is typi-cally a single-line diode laser with nonzero spectral width. Pulse modulation increases the spectral width. Each wavelength component of the signal travels at a slightly different speed, resulting in the pulse broadening illustrated in Figure 12.1d. This section provides an introduction to chromatic dispersion, the primary dispersive mechanism in singlemode fiber, and describes several chromatic dispersion measurement methods appropriate to singlemode fiber. Chromatic dispersion is also an important parameter of multimode fiber.34
12.3.2 Causes of Chromatic Dispersion In singlemode fiber, chromatic dispersion results from the interplay of two underlying effects-material dispersion and waveguide dispersion.s Material dispersion results from the nonlinear dependence upon wavelength of the refractive index, and the corresponding group velocity, of doped silica. Waveguide dispersion is rooted in the wavelength-dependent relationships of the group velocity to the core diameter and the difference in index between the core and the cladding. A third component, called second-order PMD or differential group delay dispersion, arises from the details of fiber PMD and produces an effect which is identical to chromatic dispersion.s-7 Second-order PMD sets the ultimate limit to which a transmission path can be compensated for chromatic dispersion.
The information-carrying capacity of a fiber optic system is highest when the group delay is flat with wavelength. In dispersion-unshifted singlemode fiber. the zero-dispersion wavelength ~o is near 1300 nm, where the two main underlying mechanisms, material dispersion and waveguide dispersion, naturally cancel one another. Control of the refractive index profile can place ~o anywhere in the 130011550 run wavelength range. In dispersion shifted fiber, Ao is set to approximately 1550 nm.
12.3.3 Definitions and Relationships The discussion will make use of several specialized terms, defined in Table 12.1
An example of the chromatic dispersion of a dis person-shifted singlemode fiber in the region of 1550 nm is shown in Figure 12.4. The upper curve shows the typical wave-length dependence of the relative group delay. The chromatic dispersion coefficient D. shown in the lower curve, is the attribute used to estimate pulse broadening. Its value at a particular wavelength is determined by differentiating the relative group delay curve with respect to wavelength and dividing by the length of the transmission path
_l~ D" - L dA (12.3)
where 'T g is the group delay in ps, L is the path length in lan, and A is the wavelength in run. To a first approximation, the broadening T of a pulse is given by
480 Dispersion Measurements Chap. 12
Table 12.1 Definitions for Chromatic Dispersion.
T I or T-Group delay ps
~hr . d' . omatlc lsperslOn d)" pslnm
D-Dispersion coefficient pslnm-km
Ao- Lambda-zero nm
So-Slope at ~ . ps/nm2km