8 Signal transmission

 8.3.2 Transmission characteristics

Monomode cables have very simple transmission characteristics because the core has a very small diameter and light can only travel in a straight line down it. On the other hand, multimode cables have quite complicated transmission characteristics because of the relatively large diameter of the core.

Whilst the transmitter is designed to maximize the amount of light that enters the cable in a direction that is parallel to its length, some light will inevitably enter multimode cables at other angles. Light that enters a multimode cable at any angle other than normal to the end face will be refracted in the core. It will then travel in a straight line until it meets the boundary between the core and cladding materials. At this boundary, some of the light will be reflected back into the core and some will be refracted in the cladding.

For materials of refractive indices n₁ and n₂, as shown in Figure 8.8, light entering from the external medium with refractive index n₀ at an angle α0 will be refracted at an angle α1 in the core and, when it meets the core-cladding boundary, part will be reflected at an angle 1 back into the core and part will be refracted at an angle 2 in the cladding. α1 and α0 are related by Snell’s law according to:

                                            n₀ sin α₀ = n₁ sin α₁                       (8.1)

Similarly, ˇ1 and ˇ2 are related by:

                          n₁ sin ₁ = n₂ sin ₂                                       (8.2)

Light that enters the cladding is lost and contributes to the attenuation of the transmitted signal in the cable. However, observation of equation (8.1) shows how this loss can be prevented. If ₂ = 90°, then the refracted ray will travel along the boundary between the core and cladding and if ₂ > 90°, all of the beam will be reflected back into the core. The case where ₂ = 90°, corresponding to incident light at an angle α c, is therefore the critical angle for total internal reflection to occur at the core/cladding boundary. The condition for this is that sin ₂ = 1.

Setting sin ₂ = 1 in equation (8.1):

Therefore, provided that the angle of incidence of the light into the cable is greater than the critical angle given by θ = sin^-1 αc, all of the light will be internally reflected at the core/cladding boundary. Further reflections will occur as the light passes down the fibres and it will thus travel in a zigzag fashion to the end of the cable.

Whilst attenuation has been minimized, there is a remaining problem that the transmission time of the parts of the beam which travel in this zigzag manner will be greater than light which enters the fibre at 90° to the face and so travels in a straight line to the other end. In practice, the incident light rays to the cable will be spread over the range given by sin^-1 αc < θ < 90° and so the transmission times of these separate parts of the beam will be distributed over a corresponding range. These differential delay characteristics of the light beam are known as modal dispersion. The practical effect is that a step change in light intensity at the input end of the cable will be received over a finite period of time at the output.

It is possible to largely overcome this latter problem in multimode cables by using cables made solely from glass fibres in which the refractive index changes gradually over the cross-section of the core rather than abruptly at the core/cladding interface as in the step index cable discussed so far. This special type of cable is known as graded index cable and it progressively bends light incident at less than 90° to its end face rather than reflecting it off the core/cladding boundary. Although the parts of the beam away from the centre of the cable travel further, they also travel faster than the beam passing straight down the centre of the cable because the refractive index is lower away from the centre. Hence, all parts of the beam are subject to approximately the same propagation delay. In consequence, a step change in light intensity at the input produces an approximately step change of light intensity at the output. The alternative solution is to use a monomode cable. This propagates light in a single mode only, which means that time dispersion of the signal is almost eliminated.

 

8.3.3 Multiplexing schemes

Various types of branching network and multiplexing schemes have been proposed, some of which have been implemented as described in Grattan (1989). Wavelength division multiplexing is particularly well suited to fibre-optic applications, and the technique is now becoming well established. A single fibre is capable of propagating a large number of different wavelengths without cross-interference, and multiplexing thus allows a large number of distributed sensors to be addressed. A single optical light source is often sufficient for this, particularly if the modulated parameter is not light intensity.