8 Dispersion compensators for fibre optic paths
8.1 Dispersion in optical fibres

Dispersion causes pulse extension or pulse compression (if dispersion is negative) in time domain. It can lead to Inter Symbol Interference. If neighbour pulses stand for logical 1, the space between pulses stands for logical 0, if the two pulses cover each other partially, the decoder will not be able to recognize the “0” symbol.

The unit of dispersion is [ps/nm] (picoseconds/nanometre), but in fibre optics, where the length of optical structures is a key parameter, dispersion is referred to the unit length and is expressed as [ps/nm/km]. The dispersion of 1 ps/nm/km means that the delay between the slowest and the fastest frequency component of an optical pulse, its bandwidth is 1 nm, will be 1 ps after the distance of 1 km.

## Chromatic dispersion

Chromatic dispersion consists of two components: material dispersion and waveguide dispersion.

Material dispersion (DMat) is due to the bandwidth of a laser source, which is not endlessly narrow. In practice, there is no ideal monochromatic light (with endlessly narrow bandwidth). Emitted light, transmitted pulse contains couple of frequency components (they correspond to many similar colours). Each frequency component is characterized by specific phase constant of propagation – there is different index of refraction for specific colours. Each frequency component (each colour) is then propagated at different phase velocity and reaches the end of a fibre at different time instant.

- Material dispersion is present in both: single mode and multimode fibres.
- Material dispersion can be negative or positive.

Waveguide dispersion (WD) is caused by the change of mode shape at certain distance and is strictly associated with the waveguide geometry, which causes the change of group velocity (the shape of the whole pulse “envelope”) as a function of wavelength. It is a suitable tool to adjust the dispersion property of a fibre, because by the suitable design of geometrical parameters describing your waveguide, one can specify the value of waveguide dispersion, which is then responsible for the total dispersion.

- Waveguide dispersion is always negative, thus, it can be used for the compensation of material dispersion.

Solution: the use of Dispersion Compensating Fibres (DCF) or special fibre gratings.

## Modal dispersion

In modal dispersion (MD) each of beams passes through the fibre to its output along different trajectory. The shortest trajectory is for the beam propagating along the fibre axis of symmetry, the longest path refers to the beam, which exhibits the maximum number of reflections at the core/cladding interface. With increasing the input angle of NA, there is greater number of reflections during propagation and the overall path of a beam is getting longer. Particular beams (modes) reach the fibre end at different time instants. They are detected as superposition; the result is an extended current pulse at the output of a photo detector.

- Modal dispersion is present only in multimode fibres (there is only one mode in single mode fibres, so we cannot consider the difference between two modes), it is usually few ns/nm/km.

It is NOT caused by different speed of particular components (beams, modes) – they are all guided at the same phase and group velocity = modal dispersion is not the function of a wavelength.

### Multimode graded-index fibres

Solution: to decrease the speed for short trajectories, to increase the speed for long trajectories.

In Multi-mode Graded Index (MM-GI) fibres, the index of refraction of a core is not constant; it decreases gradually as a function of distance from the core centre. The densest material is in the centre of a core, layer around it is less dense. The greater the distance from the core is, the lower refractive index of a material is used. There is refraction on couple of layers and finally the beam is reflected at specific layer or at the boundary between the last core layer and the cladding. The beam propagating along axis of symmetry has the shortest trajectory, but its speed is slow, because the centre of a core is a high-index material. On the other hand, beams propagating along longer trajectories are gradually getting to the low-index, “fast” material.

Modal dispersion in multimode graded-index fibre.