Optical Kerr Effect

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What is it?

The optical Kerr effect is a X(3) nonlinear
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).

1This need not always be the case. Some laser beams may have a minimum at the centre and two maxima towards the edges, before tailing off again.2A second type of lens, called graded index or GRIN, works on the differential refractive index principle, not differential thickness, but is designed so that the glass's refractive index changes deliberately through material effects, not optical ones.3Note that the natural tendency of light, even laser light, is to diffract (i.e. expand). If the Kerr lens can exactly counteract the diffraction, light can be trapped in what is known as a filament. This means that the light is self-guiding, like in a fibre, but without the fibre.4Intensity is power divided by area. The laser power remains the same, but the area shrinks so intensity gets higher.5And since many optical components are expensive, this is not a good thing to happen.6The variation in intensity with time comes from the fact that the wave oscillates. By definition, the field in an electromagnetic wave must be time varying, leading to a time varying intensity.7Usually 'modulate' refers to a periodic or quasi-periodic variation in a parameter8As mentioned elsewhere, when dealing with very short pulses the laser beam may span a large frequency bandwidth9This may not sound impressive, but consider that to obtain white light every colour in the spectrum must be present, from blue to red. Then realise that the system in question must span the same frequency difference in the other spectral direction.

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