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A multimode graded-index fiber has a core of radius (a). Unlike step-index fibers, the value of the refractive index of the core (n1) varies according to the radial distance (r). The value of n1 decreases as the distance (r) from the center of the fiber increases.

The value of n1 decreases until it approaches the value of the refractive index of the cladding (n2). The value of n1 must be higher than the value of n2 to allow for proper mode propagation. Like the step-index fiber, the value of n2 is constant and has a slightly lower value than the maximum value of n1. The relative refractive index difference (Δ) is determined using the maximum value of n1 and the value of n2.

Figure 3-3 shows a possible refractive index profile n(r) for a multimode graded-index fiber. Notice the parabolic refractive index profile of the core. The profile parameter

(α) determines the shape of the core's profile. As the value of &agr; increases, the shape of the core's profile changes from a triangular shape to step as shown in figure 3-4. Most multimode graded-index fibers have a parabolic refractive index profile. Multimode fibers with near parabolic graded-index profiles provide the best performance. Unless otherwise specified, when discussing multimode graded-index fibers, assume that the core's refractive index profile is parabolic (α=2).

Figure 3-3. - The refractive index profile for multimode graded-index fibers.

Figure 3-4. - The refractive index profiles for different values of &agr;.

Light propagates in multimode graded-index fibers according to refraction and total internal reflection. The gradual decrease in the core's refractive index from the center of the fiber causes the light rays to be refracted many times. The light rays become refracted or curved, which increases the angle of incidence at the next point of refraction. Total internal reflection occurs when the angle of incidence becomes larger than the critical angle of incidence. Figure 3-5 shows the process of refraction and total internal reflection of light in multimode graded-index fibers. Figure 3-5 also illustrates the boundaries of different values of core refractive index by dotted lines. Light rays may be reflected to the axis of the fiber before reaching the core-cladding interface.

Figure 3-5. - Refractive index grading and light propagation in multimode graded-index fibers.

The NA of a multimode graded-index fiber is at its maximum value at the fiber axis. This NA is the axial numerical aperture [NA(0)]. NA(0) is approximately equal to

However, the NA for graded-index fibers varies as a function of the radial distance (r). NA varies because of the refractive index grading in the fiber's core. The NA decreases from the maximum, NA(0), to zero at distances greater than the core-cladding boundary distance (r>a). The NA, relative refractive index difference (Δ), profile parameter (α), and normalized frequency (V) determine the number of propagating modes in multimode graded-index fibers. A multimode graded-index fiber with the same normalized frequency as a multimode step-index fiber will have approximately one-half as many propagating modes. However, multimode graded-index fibers typically have over one-hundred propagating modes.

Multimode graded-index fibers accept less light than multimode step-index fibers with the same core Δ. However, graded-index fibers usually outperform the step-index fibers. The core's parabolic refractive index profile causes multimode graded-index fibers to have less modal dispersion.

Figure 3-5 shows possible paths that light may take when propagating in multimode graded-index fibers. Light rays that travel farther from the fiber's axis travel a longer distance. Light rays that travel farther from the center travel in core material with an average lower refractive index.

In chapter 2, you learned that light travels faster in a material with a lower refractive index. Therefore, those light rays that travel the longer distance in the lower refractive index parts of the core travel at a greater average velocity. This means that the rays that travel farther from the fiber's axis will arrive at each point along the fiber at nearly the same time as the rays that travel close to the fiber's axis. The decrease in time difference between light rays reduces modal dispersion and increases multimode graded-index fiber bandwidth. The increased bandwidth allows the use of multimode graded-index fibers in most applications.

Most present day applications that use multimode fiber use graded-index fibers. The basic design parameters are the fiber's core and cladding size and Δ. Standard multimode graded-index fiber core and cladding sizes are 50/125 μm, 62.5/125 μm, 85/125 μm, and 100/140 μm. Each fiber design has a specific Δ that improves fiber performance. Typical values of Δ are around 0.01 to 0.02. Although no single multimode graded-index fiber design is appropriate for all applications, the 62.5/125 μm fiber with a Δ of 0.02 offers the best overall performance.

A multimode graded-index fiber's source-to-fiber coupling efficiency and insensitivity to microbending and macrobending losses are its most distinguishing characteristics. The fiber core size and Δ affect the amount of power coupled into the core and loss caused by microbending and macrobending. Coupled power increases with both core diameter and Δ, while bending losses increase directly with core diameter and inversely with Δ. However, while these values favor high Δs, a smaller Δ improves fiber bandwidth.

In most applications, a multimode graded-index fiber with a core and cladding size of 62.5/125 μm offers the best combination of the following properties:

  • Relatively high source-to-fiber coupling efficiency
  • Low loss
  • Low sensitivity to microbending and macrobending
  • High bandwidth
  • Expansion capability

For example, local area network (LAN) and shipboard applications use multimode graded-index fibers with a core and cladding size of 62.5/125 μm. In LAN-type environments, macrobend and microbend losses are hard to predict. Cable tension, bends, and local tie-downs increase macrobend and microbend losses. In shipboard applications, a ship's cable-way may place physical restrictions, such as tight bends, on the fiber during cable plant installation. The good microbend and macrobend performance of 62.5/125 μm fiber permits installation of a rugged and robust cable plant. 62.5/125 μm multimode graded-index fibers allow for uncomplicated growth because of high fiber bandwidth capabilities for the expected short cable runs on board ships.

Q.8 The profile parameter (α) determines the shape of the multimode graded-index core's refractive index profile. As the value of the α increases, how does the core's profile change?
Q.9 Light propagates in multimode graded-index fibers according to refraction and total internal reflection. When does total internal reflection occur?
Q.10 What four fiber properties determine the number of modes propagating in a multimode graded-index fiber?
Q.11 Light travels faster in a material with a lower refractive index. Therefore, light rays that travel a longer distance in a lower refractive index travel at a greater average velocity. What effect does this have on multimode graded-index fiber modal dispersion and bandwidth?
Q.12 What multimode graded-index fiber offers the best overall performance for most applications?
Q.13 What are the most distinguishing characteristics of a multimode graded-index fiber?
Q.14 How are source-to-fiber coupling and microbending and macrobending losses affected by changes in core diameter and Δ?
Q.15 While coupled power and bending loss favor a high Δ, which Δ value, smaller or larger, improves fiber bandwidth?

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