Fibra Optica

Propagation of Signals in Optical Fiber

communication medium compared to other media such as copper or free space. An optical fiber provides low-loss transmission over an enormous frequency range of at least 25 THz~even higher with special fibers~which is orders of magnitude more than the bandwidth available in copper cables or any other transmission medium. For example, this bandwidth issufficient to transmit hundreds of millions of phone calls simultaneously, or tens of millions of Web pages per second. The low-loss property allows signals to be transmitted over long distances at high speeds before they need to be amplified or regenerated. It is due to these two properties of low loss and high bandwidth that optical fiber communication systems are so widely used today. Astransmission systems evolved to longer distances and higher bit rates, dispersion became an important limiting factor. Dispersion refers to the phenomenon where different components of the signal travel at different velocities in the fiber. In particular, chromatic dispersion refers to the phenomenon where different frequency (or wavelength) components of the signal travel with different velocities in thefiber. In most situations, dispersion leads to broadening of pulses, and hence pulses corresponding to adjacent bits interfere with each other. In a communication system, this leads to the overlap of pulses representing adjacent bits. This phenomenon is called Inter-Symbol Interference (ISI). As systems evolved to larger numbers of wavelengths, and even higher bit rates and distances, nonlineareffects in the fiber began to present serious limitations. As we will see, there is a complex interplay of nonlinear effects with chromatic dispersion. We start this chapter by discussing the basics of light propagation in optical fiber, starting from a simple geometrical optics model to the more general wave

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PROPAGATION OFSIGNALS IN OPTICAL FIBER

Figure 2.1 Cross section and longitudinal section of an optical fiber showing the core and cladding regions, a denotes the radius of the fiber core.

theory model based on solving Maxwell's equations. We then devote the rest of the chapter to understanding the basics of chromatic dispersion and fiber nonlinearities. Designing advanced systems optimized with respect to theseparameters is treated in Chapter 5.

2.1

Light Propagation in Optical Fiber
An optical fiber consists of a cylindrical core surrounded by a cladding. The cross section of an optical fiber is shown in Figure 2.1. Both the core and the cladding are made primarily of silica (SiO2), which has a refractive index of approximately 1.45. The refractive index of a material is the ratio of the speedof light in a vacuum to the speed of light in that material. During the manufacturing of the fiber, certain impurities (or dopants) are introduced in the core and/or the cladding so that the refractive index is slightly higher in the core than in the cladding. Materials such as germanium and phosphorous increase the refractive index of silica and are used as dopants for the core, whereas materialssuch as boron and fluorine that decrease the refractive index of silica are used as dopants for the cladding. As we will see, the resulting higher refractive index of the core enables light to be guided by the core, and thus propagate through the fiber.

2.1.1

Geometrical Optics Approach
We can obtain a simplified understanding of light propagation in optical fiber using the so-called raytheory or geometrical optics approach. This approach is valid when the fiber that is used has a core radius a that is much larger than the operating wavelength k. Such fibers are termed multimode, and first-generation optical communication links were built using such fibers with a in the range of 25-100/~m and )~ around 0.85 ~m.

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Light Propagation in Optical Fiber

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