Optical Fibres are thin transparent strands of glass or plastic that can carry light pulses over long distances with very little loss of intensity. They are used in telecommunications to link distant telephone exchanges, in industry to link machines, and in medicine in endoscopy to name but a few common uses.
An optical fibre system is composed of the following:
- An optical fibre cable to carry signals in the form of light pulses
- A source of visible or invisible radiation. These are usually LEDs or solid-state lasers
- A photodetector at the end to convert the light back into electricity
The optical fibre is the signal carrying part. It is like the metal conductor in an electrical circuit. The fibre is placed in a protective jacket and the whole is called a cable. Optical fibres have the following advantages over standard metallic conductors.
- Have a much wider bandwidth
- Have lower propagation losses
- Immunity to EM Radiation
- Smaller Size
- Safe – cannot be easily hacked
- More flexible
Optical fibres rely on total internal reflection unlike metal wires and can be bent around obstacles without affecting electrical properties.
Optical fibres work on the principle of reflection and refraction of light through optical media and the angle of incidence at which the light enters the media.
The figure below shows a ray of light entering the interface between two media such as air and glass.
The amount that the light is refracted depends on the refractive indices of the two media.
Refractive index is defined as the ratio of the speed of light in free space to the speed of light in the medium.
The refractive index is given the symbol n. It is 1 for air and 1.5 for glass. i and r are the angle of incidence and refraction made with the normal respectively.
In the figure here, light is passing from a material with a higher refractive index to one with a lower index.
Consequently, the light is bent away from the normal in the second medium. Note that the normal is an imaginary line perpendicular to the two media.
Snell’s Law
States that the refractive indices are connected by the angles of incidence and refraction viz.
Sin i.( n1) = Sin r.(n2)
In the second figure, the angle of incidence i has been increased until the angle of refraction is 90 degrees, and the refracted ray grazes the interface between the two media.
Using Snell’s law:
Sin i.( n1) = Sin 90. (n2) Sin 90 =1
Sin i = n2/n1
This value of i is called the critical angle and given the symbol c. If the angle of incidence is increased beyond the critical value c the incident ray will be reflected as shown by the dotted lines. These principles are used in optical fibres.
Two Media with different refractive indices
The figure below shows two media with refractive indices
n1 = 1.48 and n2 = 1.46, values used in optical fibres.
Using the equation that we had earlier, the critical angle is given by:
c = arcsine (1.46/1.48) = 80.6 degrees.
Light striking the boundary between the two layers at an angle greater than the critical angle of 80.6 degrees, will be reflected into the first media at an angle equal to the angle of incidence.
The figure also shows a third layer with refractive index equal to 1.46 placed under the first layer. Successive reflections now take place at the two boundaries and the ray is trapped between the layers.
In each case the angle of incidence is equal to the angle of reflection. This is the basic principle of the optical fibre except that the optical fibre has a circular configuration.
Numerical Aperture
The figure here shows a ray of light entering a medium with refractive index n1 between two media with refractive indices n2. The core refractive index n1 is greater than n2.
The maximum entry angle is given by
Sin i (max) = (Sqrt (n1**2 - n2**2))/n0
i (max) is the largest angle that allows total internal reflection. Light entering at angles greater than i (max) will be refracted through the core – cladding and will be lost.
Sin i (max) is called the Numerical Aperture. NA. It gives the half angle of the cone of acceptance for propagation in the fibre. The figure below shows the cone of acceptance.
The numerical aperture indicates how much light can be off axis and still be propagated.
Fibre Classification
Fibres can be classified according to the materials they are made of or the path in which light propagates through them. Optical fibres, as we stated earlier are made of glass or plastic. The more common is glass, which has a better performance than plastic. Glass fibres are made of silica or components having good purity and transparency. Plastic fibres are more flexible than glass, are cheaper to manufacture but less durable. They are made of polymers such as polystyrene or polycarbonate.
A mode is also a path by which light can travel through a fibre.
We have three modes. Multimode step index, Single-mode step index and Multimode graded index.
Multimode step index fibre
The multimode step index fibre is shown below.
The lowest order mode travels in the axis, the middle order is reflected twice, and the higher order is reflected several times. As a result of the different paths, the light entering the fibre takes different times to reach the detector.
The output pulse is consequently distorted or stretched as shown. This is called pulse distortion and limits the rate of propagation of data along the fibre. The effect increases with fibre length.
Fibres are rated in bandwidth/length. For example, a 200MHz/Km cable can transmit a pulse rate of 200MHz for 1 Km successfully. Long transmissions require repeaters at appropriate locations.
Mono-mode Step Index Fibre
Only one mode is propagated as shown in the figure below. The output is very little distorted compared to the input. They are used with laser sources and the input must be carefully aligned with the source to ensure a suitable amount of energy into the fibre
The refractive index profiles for both types are shown
below.
Graded index fibre
The graded index fibre is shown above with its refractive index profile. It was developed to overcome the distortion problem described above.
The refractive index follows a parabolic profile.
The low order mode travels in the constant density material at the centre. High order modes travel through lower density material away from the core and the velocity of propagation increases from the core. This gives nearly the same time length of travel for all modes, and all reach the end at nearly the same time. The distortion in the received pulse is now significantly reduced.
Light Sources
The sources used in fibre optics are required to convert electrical signals into light pulses. They are required as far as possible to be single frequency emitters or monochromatic sources.
Two devices are used. The Light Emitting Diode (LED) and the Laser Diode (LD).
The most efficient is the laser diode which we shall discuss here.
Laser Diode
The word laser is an acronym for Light Amplification by the Stimulated Emission of Radiation. The laser diode works just like a normal LED, except that here radiation is confined to the junction area of the diode.
The basic structure is shown here.
A very thin layer of gallium arsenide (pGaAs) is sandwiched between two layers of aluminium gallium arsenide (AlGaAs). The ends are cleaved from the same crystal and are perfectly parallel and polished. One end is more polished than the other. The other end is slightly transparent.
When a current is applied, carriers are injected across the junction where holes and electrons combine producing photons. This is called spontaneous emission. Some of these photons excite electrons into a higher level where they have a very short lifetime and fall into a level intermediate between the ground and upper levels. They are now in an unstable or meta state. The photons produced stimulate the carriers and each one produces two photons. That is, carrier stimulation has taken place. They all have the same phase, amplitude and direction. The photons produced travel to the polished ends where they bounce several times and stimulate the production of other photons until an avalanche of photons is produced. Finally, they exit the partially transparent end as a beam of laser light.
The system is analogous to an oscillator. The power source is the current, the amplifier is the stimulated carriers and the polished ends the feedback circuit.
The p-n junction is like a resonant cavity and the laser beam travels parallel to the junction.
The refractive indices of the two materials confines the radiation to the cavity like in an optical fibre.
The Receiver
The device used to convert the light from the fibre into electricity is called a photodiode. There are several types of these but the most popular is the avalanche photodiode.
Avalanche photodiode
A cross section of the avalanche photodiode with its associated electric field is shown here.
The avalanche photodiode can withstand high reverse voltages and is generally biased to breakdown or avalanche point. Note the connections to the power source. The p+ and n+ regions are heavily doped and have a low resistance giving a small voltage drop. Light, that is, photons enter through the p+ layer. Most of the photons are absorbed in the π region, which is an intrinsic layer of semiconductor and electron hole pairs are generated in it. The π region is in a weak electric field as shown by the graph and the electron hole pairs generated are further separated and drift into the high field formed by the p -n+ layers
The electrons now have high kinetic energy and can release further electron hole pairs. These carriers can generate still more secondary carriers in a process called photomultiplication. The device has a number called a multiplication factor which is an average of how many secondary carriers a photon can create.
The whole effect is like a snowball gathering snow as it rolls down a hill.