Advanced Communication: Optical Fiber

INTRODUCTION TO OPTICAL COMMUNICATION

Communication may be broadly defined as the transfer of information from one point to another. When the information is to be conveyed over any distance a communication system is usually required. Within a communication system the information transfer is frequently achieved by superimposing or modulating the information onto an electromagnetic wave which acts as a carrier for the information signal. This modulated carrier is then transmitted to the required destination where it is received and the original information signal is obtained by demodulation. Sophisticated techniques have been developed for this process using electromagnetic carrier waves operating at radio frequencies as well as microwave and milli meter wave frequencies. However, ‘communication' may also be achieved using an electromagnetic carrier which is selected from the optical range of frequencies.

Transmission of Light in Optical Fibre:

The transmission of light via a dielectric waveguide structure was first proposed and investigated at the beginning of the twentieth century. In 1910 Hondros and Debye conducted a theoretical study, and experimental work was reported by Schriever in 1920. However, a transparent dielectric rod, typically of silica glass with a refractive index of around 1.5, surrounded by air, proved to be an impractical waveguide due to its unsupported structure (especially when very thin waveguides were considered in order to limit the number of optical modes propagated) and the excessive losses at any discontinuities of the glass-air interface. Nevertheless, interest in the application of dielectric optical waveguides in such areas as optical imaging and medical diagnosis (e.g. endoscopes) led to proposals for a clad dielectric rod in the mid-1950s in order to overcome these problems. This structure is illustrated in Figure , which shows a transparent core with a refractive index n₁ surrounded by a transparent cladding of slightly lower refractive index n₂ The cladding supports the waveguide structure while also, when

 Fig:    Optical fiber waveguide showing the core of refractive index n₁ surrounded by the cladding of slightly lower refractive      index n₂

sufficiently thick, substantially reducing the radiation loss into the surrounding air. In essence, the light energy travels in both the core and the cladding allowing the associated fields to decay to a negligible value at the cladding-air interface.

Total internal reflection

To consider the propagation of light within an optical fiber utilizing the ray theory model it is necessary to take account of the refractive index of the dielectric medium. The refractive index of a medium is defined as the ratio of the velocity of light in a vacuum to the velocity of light in the medium. A ray of light travels more slowly in an optically dense medium than in one that is less dense, and the refractive index gives a measure of this effect. When a ray is incident on the interface between two dielectrics of differing refractive indices (e.g. glass-air), refraction occurs, as illustrated in Figure 4(a). It may be observed that the ray approaching the interface is propagating in a dielectric of refractive index n₁, and is at an angle ϕ₁ to the normal at the surface of the interface. If the dielectric on the other side of the interface has a refractive index n₂ which is less than n₁, then the refraction is such that the ray path in this lower index medium is at an angle ϕ₂ to the normal, where ϕ₂ is greater than ϕ₁. The angles of incidence ϕ₁ and refraction ϕ₂ are related to each other and to the refractive indices of the dielectrics by Snell’s law of refraction which states that:

n₁ sin ϕ₁ = n₂ sin ϕ₂

_{Fig:  Light rays incident on a high to low refractive index interface (e.g. glass-air): (a) retraction; (b) the limiting case of retraction showing the critical ray at an angle ϕci (c) total internal reflection where ϕ > ϕc}

When the angle of refraction is 90° and the refracted ray emerges parallel to the interface between the dielectrics, the angle of incidence must be less than 90°. This is the limiting case of refraction and the angle of incidence is now known as the critical angle ϕ_c, as shown in Figure (b). From above equation, the value of the critical angle is given by:

The transmission of a light ray in a perfect optical fibre

Numerical aperture

The acceptance angle for an optical fiber was defined in the preceding section. However, it is possible to continue the ray theory analysis to obtain a relationship between the acceptance angle and the refractive indices of the three media involved, namely the core, cladding and air. This leads to the definition of a more generally used term, the numerical aperture of the fiber. It must be noted that within this analysis, as with the preceding discussion      of acceptance angle, we are concerned with meridional rays within the fiber.

Figure  shows a light ray incident on the fiber core at an angle θ₁ to the fiber axis which is less than the acceptance angle for the fiber θ_a. The ray enters the fiber from a

The ray path for a meridional ray launched into an optical fiber in air at an input angle less than the acceptance angle for the fiber .

Medium (air) of refractive index n₀, and the fiber core has a refractive index n₁, which is slightly greater than the cladding refractive index n₂. Assuming the entrance face at the fiber core to be normal to the axis, then considering the refraction at the air-core interface and using Snell’s law given by:

n₀ sin θ₁ = n₁ sin θ₂

The numerical aperture (NA) is defined as;

Step index fibres

The optical fiber considered in the preceding sections with a core of constant refractive index n₁ and a cladding of a slightly lower refractive index n₂ is known as step index fiber. This is because the refractive index profile for this type of fiber makes a step change at the

The core-cladding interface, as indicated in Figure 10, which illustrates the two major types of step index fiber. The refractive index profile may be defined as:

Multimode step index fibers allow the propagation of a finite number of guided modes along the channel. The number of guided modes is dependent upon the physical parameters (i.e. relative refractive index difference, core radius) of the fiber and the wavelengths of the transmitted light which are included in the normalized frequency V for the fiber. It was indicated that there is a cut off value of normalized frequency V_c for guided modes below which they cannot exist. However, mode propagation does not entirely cease below cut off. Modes may propagate as unguided or leaky modes which can travel considerable distances along the fiber. Nevertheless, it is the guided modes which are of paramount importance in optical fiber communications as these are confined to the fiber over its full length. It can be shown that the total number of guided modes or mode volume Ms for a step index fiber is related to the V value for the fiber by the approximate expression:

which allows an estimate of the number of guided modes propagating in a particular multimode step index fiber.

Single-mode fibers

The advantage of the propagation of a single mode within an optical fiber is that the signal dispersion caused by the delay differences between different modes in a multimode fiber may be avoided. Multimode step index fibers do not lend themselves to the propagation of a single mode due to the difficulties of maintaining single-mode operation within the fiber when mode conversion (i.e. coupling) to other guided modes takes place at both input mismatches and fiber imperfections. Hence, for the transmission of a single mode the fiber must be designed to allow propagation of only one mode, while all other modes are attenuated by leakage or absorption.

Following the preceding discussion of multimode fibers, this may be achieved through choice of a suitable normalized frequency for the fiber. For single-mode operation, only the fundamental LP₀₁ mode can exist. Hence the limit of single-mode operation depends on the lower limit of guided propagation for the LP₁₁ mode. The cut off normalized frequency for the LP₁₁ mode in step index fibers occurs at V_c = 2.405. Thus single-mode propagation of the LP₀₁ mode in step index fibers is possible over the range:

as there is no cut off for the fundamental mode. It must be noted that there are in fact two modes with orthogonal polarization over this range, and the term single-mode applies to propagation of light of a particular polarization. Also, it is apparent that the normalized frequency for the fiber may be adjusted to within the range given in above equation by reduction of the core radius, and possibly the relative refractive index difference) which, for single-mode fibers, is usually less than 1%.

Cut off wavelength

It may be noted by rearrangement of above equation that single-mode operation only occurs above a theoretical cut off wavelength λc given by:

where V_c is the cut off normalized frequency. Hence λ_c is the wavelength above which a particular fiber becomes single-moded.

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