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This excerpt covers the following: Modes, Refractive Index Profile, Step Index Multimode Fiber, Graded Index Multimode Fiber, Single-Mode Fiber, and Dispersion-Shifted Fibers

Modes

Mode is a mathematical or physical concept describing the propagation of an electromagnetic wave through any media. In its mathematical form, mode theory derives from Maxwell’s equations. James Maxwell first developed mathematical expressions to the relationship between electric and magnetic energy. He proved that they were both a single form of electromagnetic energy, not two different forms as was then commonly believed. His equations also showed that the propagation of electromagnetic energy follows strict rules. Maxwell’s equations form the basis of electromagnetic theory.

A mode is a solution to Maxwell’s equations. For purposes of this chapter, a mode is simply a path that a ray of light travels down a fiber. The number of modes that a given fiber will support ranges from 1 to over 100,000 individual rays of light. This depends on the physical properties of the fiber and fiber diameter.

Refractive Index Profile

The refractive index profile describes the relationship between the indices of the core and cladding. Two main relationships exist: step index and graded index. The step index fiber has a core with a uniform index throughout. The profile shows a sharp step at the junc- tion of the core and cladding. In contrast, graded index has a nonuniform core. The index is highest at the center of the core and gradually decreases until it matches that of the cladding. Therefore, there is no sharp transition between the core and the cladding. By this classification, there are three types of fibers:

• Multimode step index fiber, commonly called step index fiber.

• Single-mode step index fiber, called single-mode fiber.

• Multimode degraded index fiber, called graded index fiber.

The characteristics of each type have an important bearing on its suitability for particular applications.

Step Index Multimode Fiber

The multimode step index fiber is the simplest type. It has a core diameter from 100–970 microns. This fiber type includes glass, PCS, and plastic fibers. The step index fiber is the most widely used fiber type. This is despite relatively low bandwidth and high losses.

Since light reflects at different angles for different paths, the different rays of light take a shorter or longer time to propagate down the fiber. The ray of light that travels straight down the center of the core arrives at the other end first. Other rays of light arrive later, since they refract back and forth in a zigzag path. Therefore, rays of light that enter the fiber at the same time exit the fiber at different times. The effect is that the light has spread out in time.

This spreading of an optical pulse is called modal dispersion. A pulse of light that began as a tight and precisely defined shape has dispersed or spread over time. Dispersion describes the spreading of light by various mechanisms. Modal dispersion is that type of dispersion that results from the varying path lengths of each mode of light as it propagates through the fiber.

The typical modal dispersion for a stepped index fiber ranges from 15–30 ns per kilometer. This means that when rays of light enter a 1 km long fiber at the same time, the ray of light that takes the longest path will arrive 15–30 ns after the ray of light that took the shortest path. The modal dispersion of 15–30 billionths of a second does not seem to be very much, but dispersion is a fiber’s main limiting factor to bandwidth. Pulse spreading results in the overlapping of adjacent pulses, as shown in Figure 6.10-7. Eventually the pulses will merge so that one pulse cannot be distinguished from another. This results in the loss of information. Reducing the modal dispersion in a fiber will increase a fiber’s bandwidth.

Graded Index Multimode Fiber

One way to reduce modal dispersion is to use graded index fiber. Here the core has numerous concentric layers of glass, somewhat like the annular rings of a tree. Each successive layer outward from the central axis of the core has a lower index of refraction.

Light travels faster in a lower index of refraction, so the further the light is from the center axis, the greater the speed. Each layer of the core refracts the light. Instead of being sharply refracted as it is in a step index fiber, the light is now bent or continually refracted in almost a sinusoidal pattern. Those rays that follow the longest path by traveling in the outside of the core have a faster average velocity. The light traveling near the center of the core has the slowest average velocity. As a result, all rays tend to reach the end of the fiber at the same time. The graded index reduces modal dispersion to 1 ns per kilometer or less.

Popular graded index fibers have a core diameter of 50 or 62.5 microns and a cladding diameter of 125 microns. The fiber is popular in applications requiring high bandwidth, especially telecommunications, local area networks, computers, and video applications.

Single-Mode Fiber

Another way to reduce modal dispersion is to reduce the core’s diameter until the fiber propagates only one mode efficiently. The single-mode fiber has a very small core diameter of only 5–12 microns. The stan- dard cladding diameter is 125 microns. The cladding diameter was chosen for three reasons:

• The cladding must be about 10 times thicker than the core in a single-mode fiber. For a fiber with an 8 or 9 μm core, the cladding should be at least 80 μm.

• It is the same size as a graded index fiber that promotes size standardization.

• It promotes easy handling because it makes the fiber less fragile and because the diameter is reasonably large so that it can be handled by technicians.

Since the single-mode fiber only carries one mode, modal dispersion does not exist. Single-mode fibers have a potential bandwidth of 50–100 GHz-kilome- ters. Present fiber has a bandwidth of several GHz and allows transmissions of tens of kilometers.

FIGURE 6.10-7 Pulse spreading due to modal dispersion.

Dispersion-Shifted Single-Mode Fibers

There are three types of single-mode optical fibers usually found in typical applications for telecommuni- cations and data networks. Beyond standard single- mode fibers, there are also dispersion-shifted (DS) fibers and nonzero-dispersion-shifted (NZ-DS) fibers. The purpose of these fibers is to reduce dispersion in the transmission window having the lowest attenua- tion. Normally, attenuation is lowest in the 1550 nm window and dispersion is lowest in the 1310 nm win- dow. Dispersion shifting creates a fiber that shifts the lowest dispersion to the 1550 nm region. This shifting of dispersion results in a fiber suited for highest data rates and longest transmission distances. In a standard single-mode fiber, the points of lowest loss and high- est bandwidth do not coincide. Dispersion shifting brings them closer together.

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