Fly by Light

If we use a copper wire to transmit data from several sensors, we have to be very careful to screen it from unwanted signals.  Ordinary wires are very prone to this, especially in long runs.  Screening is easy enough; we simply surround the wire with an insulating layer and then copper braiding to shield the wire.  We have a coaxial cable.

The problem with coaxial cable is that:

• It is heavy;
• It is bulky.  Lots of coaxial cables take up a lot of space.

More recently there have been projects that use fly-by-light technology.  This uses optical fibres, which are much less heavy and take up a lot less space; several optical fibres can take the space of one coaxial cable.  An optical fibre looks like this:

The fibres are 50 mm across (including the sheath).  The core has a diameter of 5 mm (5 × 10^-6 m).

Optical Fibres

Optical fibres work by total internal reflection.  The light ray makes a certain angle of incidence when it hits the boundary of an optically dense material (like glass) and an optically less dense material (like air).  If this angle is greater than the critical angle, the ray is totally internally reflected.  The critical angle, qc, is determined by the formula:

m =    1

           sin qc

Where m is the physics code for the refractive index.

The rays of light should travel like this:

But instead light rays can travel several paths:

This means that the light rays can arrive at different times, resulting in dispersion or smearing.  The signal that was sharp when it left the transmitter is smeared.

The picture shows us how the signal can be unacceptably distorted and even produce spurious signals that were not there.

The problem can be resolved by cladding the core with a material of slightly lower refractive index.  For example the core might have a refractive index of 1.6, while the cladding has a refractive index of 1.4.

Dispersion can be reduced further by use of a graded index or multimode fibre.  Some light is passes down the middle, which has a higher refractive index, therefore slower rate of travel.  With clever manipulation of the refractive indices, the ray travelling down the middle can be made to arrive at the same time as the ray that goes from side to side.  They can meet with a time difference of about 1 ns km^-1.  In aircraft where the distances are less than 50 metres, this is not too bad.

Monomode fibres are designed such that the rays pass only down the middle.  If the light were perfectly monochromatic, i.e. of one wavelength only, the rays would all arrive at the same time.  However even the best lasers produce a slight spread, and since refractive index varies with wavelength, there can be slight differences in arrival times, leading to smearing.

Attenuation

As light travels down an optical fibre, it loses intensity.  This attenuation is caused by very slight impurities that you get even in the purest of glass.  Also there will be defects and anomalies in the crystal structure caused by the manufacturing process.  Light may even "leak out" of the fibre.  Whatever the cause the light at the receiver will be dimmer than the light at the transmitter.

If the light intensity travels through 1 km of optical fibre, and its intensity is reduced to 50 % of its original, we can expect that after 2 km, then intensity is 25 % of the original, and after 3 km, it's 12.5 % (1/8) of the original.  The change is exponential.

So the relationship between the intensity and the distance is going to be governed by an exponential function:

I = I0 e^-mx

Where:

• I is the intensity (W m^-2)

• I0 is the intensity of the source (W m^-2)

• m is the attenuation coefficient (m^-1)

• x is the length of the optical fibre (m)

• e is the exponential number 2.718...

  The physics code for the attenuation coefficient, m, is the same as the physics code used for refractive index.  In other syllabi the code n is used for refractive index.

Of we have 1000 metres of optical fibre with an attenuation coefficient of 0.002 m^-1, the graph is like this:

We can see that the intensity has dropped to 50 % of its value after 350 m.

If we plot the natural logarithm of the intensity against the distance, we get a straight line:

We would get a similar shape if we used logs to the base 10.

Typically attenuation coefficients are in the order of 10^-5 m^-1.  For the distances in an aeroplane, this is negligible.  For long distance communication, it can be significant.   Also the attenuation coefficient is different for different wavelengths in the same optical fibre.