56 Radio Engineering for Wireless Communication and Sensor Applications

3.6 Optical Fiber

TE and TM wave modes may propagate, not only in hollow metal waveguides, but also in dielectric waveguides. An optical fiber is actually a dielectric waveguide with a circular cross section, in which total internal reflection confines light in the fiber. Optical fibers are used in many kinds of communication networks, usually at wavelengths of 0.8 to 1.6 mm at infrared. The optical carrier is modulated with data rates up to several gigabits per second.

Optical fibers are made of quartz, glass, or plastic. An optical fiber consists of a core and a cladding. The index of refraction n = √er of the core is larger than that of the cladding. The refractive index of the cladding is adjusted to a proper value by doping quartz with metal oxides as TiO2 , Al2O3 , GeO2 , or P2O3 . Optical fibers can be divided into three types, as shown in Figure 3.11:

1. Single-mode fiber: core radius 1–16 m m, cladding radius 50–100

mm.

2.Multimode fiber with a step in the index of refraction: core radius 25–60 m m, cladding radius 50–150 m m.

3.Multimode fiber with a continuous change in the index of refraction: core radius 10–35 mm, cladding radius 50–80 mm.

Figure 3.11 Structures of optical fibers: (a) a single-mode fiber; (b) a multimode fiber with a step in the refractive index; (c) a multimode fiber with a continuous change in the refractive index.

An optical cable is usually made of several optical fibers. Steel wires and textile fibers as nylon give strength to the cable and support the fibers. Copper wires carry current for the repeater amplifiers if needed.

The solutions of the longitudinal field components in the core are

In these equations, Jn (kr ) is the Bessel function of the first kind of order n ; Hn ( x r ) is the Hankel function of the first kind of order n ; k is the transverse propagation constant in the core; and x is the transverse propagation constant in the cladding. Other field components are solved from these longitudinal fields, as in the case of metal waveguides, except now the boundary conditions are different, that is, the tangential components of E and H are continuous at the boundary of two dielectric materials.

From the expressions of longitudinal fields we can see that only cylindrically symmetric (n = 0) wave modes are either TE or TM wave modes. Other wave modes are hybrid modes, denoted as EH or HE wave modes, for which both electric and magnetic fields have nonzero longitudinal components.

In a multimode fiber the number of propagating wave modes may be very large. The number of modes is approximately [7]

where l 0 is the wavelength in free vacuum, n 1 and n 2 are the refractive indices of core and cladding, respectively, and a is the radius of the core.

Example 3.3

Find the number of wave modes at a wavelength of 1.55 m m in a quartz fiber having a core radius of 40 mm. The refractive index of the cladding is 1% lower than that of the core.

58 Radio Engineering for Wireless Communication and Sensor Applications

Solution

The loss mechanisms of an optical fiber are:

•Dielectric absorption loss;

•Scattering loss due to the imperfections of the fiber;

•Radiation loss due to the bending of the fiber.

Properties making the optical fiber an excellent transmission medium for many applications are

•Small size and weight;

•Low attenuation—only 0.2 dB/km at 1.55 mm—allowing cables hundreds of kilometers long without any repeater amplifiers;

•Immunity to interference and difficulty of interception;

•Reliability;

•Broad bandwidth;

•Low price compared to copper cable.

3.7Coaxial Line

A coaxial line consists of two concentric conductors with circular cross sections and insulating material between them, as shown in Figure 3.12.

Figure 3.12 Cross section of a coaxial line.