What is it?

The optical Kerr effect is a X⁽³⁾ nonlinear
optical effect. The third order nonlinear polarisation of a material depends on the electric field strength cubed. In optics there is a direct relationship between electric field and the intensity of the light, which is that the intensity varies as the square of the field. This in turn leads to an intensity dependent refractive index, which is the optical Kerr effect. The higher the intensity of the light, the greater the refractive index. This can be thought of as having two components, a spatial variation in refractive index and a temporal variation of refractive index. Each leads to different effects.

What does it do?

The Kerr effect has a number of consequences, especially in the field of fibre optic communications, but also in straightforward laser physics. The effect is very dependent on intensity, so it is far more noticeable when using pulsed laser systems.

1. Self-focusing

The spatial variation in refractive index means the Kerr effect can cause a high intensity laser beam to self-focus. That is, in any medium, laser light may tend to focus itself, without the use of a focusing lens. This can be understood directly in terms of refractive index change.



A laser beam does not have a constant intensity across the full beam width. Instead, intensity tails off towards the edges, and is maximised in the centre¹. When this is the case, the central maximum experiences a higher refractive index than the outer areas, slowing that part of the beam down. This is a similar effect to a focusing lens, where the difference in thickness at the lens centre and edges contributes to the slowing down in the centre². The light in the laser beam is then said to self-focus, and this is often called a Kerr lens.³


Self-focusing can lead to all sorts of problems. It is like a positive feedback loop, since as the light self-focuses it reaches higher intensities⁴ which causes stronger self-focusing, and so on. If there is any absorption in the most intense regions of the beam, sudden and catastrophic damage can occur⁵. Even beams propagating in air can be self-focused, and this can sometimes be heard, as the air molecules are ripped apart by the high intensity laser pulses.

2. Self-phase modulation

Self-phase modulation is the temporal part of the Kerr effect. A wave has a property called phase; the rate of change of phase gives the frequency of that wave. The refractive index varies in time, as the intensity varies in time⁶, and this cause the phase of the wave to vary in time, as there is a direct relationship between phase and refractive index. If the phase is modulated⁷in time, the frequency of the wave may shift or broaden⁸. In high intensity or high nonlinearity situations, this can result in huge frequency shifts. Examples of this are infrared light being injected into high nonlinearity fibres, resulting in green light being output, and the effect of continuum generation, where very high intensity infrared pulses are fired into a material and white light is generated⁹

Can it be useful?

The simple answer to this is 'Yes'. The effect of self-phase modulation can actually be useful in fibre optic communication, as it can be used to counteract the effects of group velocity dispersion at certain frequencies, allowing optical solitons to form.

Self-focusing can be used too, especially in the filaments previously mentioned. As well as being used to generate high intensity short pulses, it can be used in optical switches (i.e. switches in fibre optics that don't actually require electronics - making them faster).