Optics/Fibre optics

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An optical fibre is a transparent, thin (~120 micrometres) fibre of glass or plastic used for transmitting light.

How it is made
A fibre optic cable has a core and cladding. The core is the part that the light travels through. It is made out of plastic or glass. Glass is always used for long-distance applications due to its low optical absorption. It is surrounded by material that has a low refractive index. This is called cladding. Fibre optic cables will work without cladding, but this offers less protection; Ergo, cladding is always used in real-world situations. Cladding also ensures that outside light does not get into the cable and interfer with the light transmitted. In addition, the cladding keeps the value of the critical angle constant throughout the whole length of the fibre, regardless of what it travels through. This is important, since the cables often have to travel underground.

If the cables travel underground without cladding, then light would escape, since the optical density of the outside environment would be higher than that of the core, and total internal reflection only occurs when the optical density of the first medium is higher than that of the second.

Total internal reflection
Fibre optics takes advantage of total internal reflection by having the optical density of the core higher than that of the cladding:

$$n_1 = n_\text{plastic} = 1.6$$

$$n_2 = n_\text{air} = 1.0$$

$$\theta_1 = 60^\circ$$

$$\theta_2 = \text{angle of refraction}$$

$$\sin\theta_2 = \sin\theta_1 {n_1 \over n_2}$$

solve for $$\theta_2$$:

$$\sin\theta_2 = (\sin 60^\circ)(1.6) = (0.866)(1.6) = 1.39$$

$$\theta_2 = \arcsin 1.39 = \text{undefined}$$

(There are no angles whose sine is greater than one).

Therefore, there is no angle of refraction. This tells us that total internal reflection has occurred, since there is no refracted ray.

The fact that there is total internal reflection means that light doesn’t escape, since it does not refract outside, but rather keeps on reflecting inside the fibre. Total Internal Reflection (TIR) means 100% reflection. This is very useful in this case, since all light will remain inside the fibre.

The light which enters the fibre is a beam. It consists of many rays behaving in a similar way. They will keep on crossing each other - thereby filling up the core with light. A pulse of light traveling through a fibre optic cable is just a bunch of these rays.

There is a limit to how fast pulses of light can be sent through fibre optics. This is due to pulse spreading. Since light is dispersed over long distances, the pulses of light will change as they travel along the fibre. When pulses are sent, it is in a square wave shape. However, the pulses gradually get wider.

Pulse spreading
There are two types of dispersion which cause pulse spreading:

Chromatic dispersion
When different wavelengths of light are sent through the fibre, they will travel at different speeds. For example, since white light contains all the different wavelengths of light, if white light is shone through a fibre optic cable, chromatic dispersion will occur. This is due to the fact that the different colours in white light will travel at different speeds.

Modal dispersion
If rays are oblique they will take a longer route than others. The rays traveling parallel to the centre of the fibre reach the end the fastest, and the more oblique rays reach the end last.

Therefore, we can conclude that:

Total dispersion=Chromatic dispersion + Modal dispersion

Problems caused by pulse spreading
Pulse spreading causes a few major problems:
 * 1) Bandwidth limit: Pulse spreading limits the rate at which bursts of light can be sent, thereby limiting the bandwidth.
 * 2) Distance limit: Since light is dispersed more as the fibre optic cable becomes longer, the bandwidth is reduced as the distance is increased. After a certain distance, the bandwidth becomes unacceptably low.

Fibre optics in our world
Modern fibre optics can have up to a thousand fibres in one cable.

Fibre optics have advantages and disadvantages when compared to regular copper wires.
 * 1) lower loss
 * 2) large data-carrying capacity (thousands of times greater)
 * 3) immune to electromagnetic interference
 * 4) High electrical resistance (safe to use near high voltage equipment)
 * 5) Light weight
 * 6) Signals contain very little power
 * 7) Faster (speed of light)
 * 8) Very hard to tap fibre optic cables without being detected
 * 9) Existing wires must be replaced with fibre optics
 * 10) Much more difficult to splice. Requires special training and special tools

Fibre optics today are so advanced that no amplification is required for distances of up to hundreds of kilometers. However, longer-range systems still must use optical amplifiers.

Authors

 * Faraaz Damji (Frazzydee)