Page 87 - Fiber Optic Communications Fund

68 Fiber Optic Communications

2.6 Comparison between Multi-Mode and Single-Mode Fibers
MMFs have several advantages over SMFs. The core radius of a multi-mode fiber (25–35 μm) is much larger
than that of a single-mode fiber (4–9 μm). Therefore, it is easier to launch optical power into a MMF and
also to splice two MMFs. The large core of a MMF facilitates simple fiber-to-fiber or fiber-to-transceiver
alignment and, hence, is best suited to local area network (LAN) applications [14]. The relative index
difference Δ of a MMF is larger than that of a SMF. Therefore, the numerical aperture of a MMF is large,
which implies more light can be launched to the fiber from an inexpensive optical source that has a large
angular spread, such as a LED. To have a reasonable power coupling efficiency, SMFs are excited with laser
diodes. Inexpensive short-haul fiber-optic links can be designed using LEDs and multi-mode fibers. How-
ever, multi-mode fibers are not used for long-haul and/or high-bit-rate applications because of intermodal
dispersion. Although the dispersion can be reduced to some extent using graded-index multi-mode fibers,
the pulse broadening increases linearly with distance (Eq. (2.24)) and becomes unacceptably large for a
fiber-optic link that is hundreds of kilometers long. Typically, the transmission reach of a MMF fiber-optic
link at a bit rate of 1 Gb/s is limited to a few kilometers. Intermodal dispersion would be absent if there was
only one mode. Therefore, single-mode fibers are used for long-haul (1000 km–30,000 km) and high-bit-rate
(10 Gb/s–100 Gb/s) applications.
From the information theory point of view, the channel capacity of a multi-mode fiber is larger than that of a
single-mode fiber. This is because, in principle, each mode of a MMF can carry as much information as a SMF.
When different modes of a MMF carry independent sets of data it is known as mode-division multiplexing,
which has attracted significant attention recently [15–19]. In an ideal MMF with M guided modes, there is
no power coupling among modes and the channel capacity can be enhanced by the factor M. However, due to
refractive index fluctuations along the fiber, there is an exchange of power among modes, leading to cross-talk
between channels of a mode division multiplexed system. This cross-talk can be compensated for by using
digital signal processing techniques [15].

2.7 Single-Mode Fiber Design Considerations
The parameters that are important for the design of a single-mode fiber are (i) cutoff wavelength, (ii) fiber loss,
(iii) dispersion, (iv) dispersion slope, (v) polarization mode dispersion, and (vi) spot size. Using a step-index
optical fiber, it is not possible to optimize all these parameters. Therefore, the refractive index profile n(r)
is chosen so that the design parameters listed above are optimum for a specific application. For the given
refractive index profile n(r), the Helmholtz equation (2.28) is solved to obtain the propagation constant ()
and the mode distribution function Φ(x, y). From this data, design parameters can be calculated. As an inverse
problem, the refractive index profile n(r) can be constructed to meet the given specifications on the design
parameters. However, in some cases, a solution to the inverse problem does not exist. For example, it is
desirable to have a large spot size (to reduce nonlinear effects) as well as a low dispersion slope to improve
the performance of a wavelength-division multiplexing (WDM) system. But it turns out that as the spot size
increases, the dispersion slope also increases. In the following subsections, important design parameters of a
single-mode fiber and their interrelationships are discussed.

2.7.1 Cutoff Wavelength
For high-bit-rate and long-haul applications, it is essential that the fiber is single-moded. The single mode
condition for a step-index fiber is given by Eqs. (2.70) and (2.59),
2a 2 2 1∕2
V = (n − n ) ≤ 2.4048. (2.168)
1 2