What is Kerr Effect?

Explain the Working of a Kerr Cell?

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- GoPhotonics

Mar 28, 2023

The Kerr effect is a phenomenon that occurs when a material's refractive index changes in response to an electric field. The Kerr effect was discovered by a Scottish physicist named John Kerr in 1875 and it was named after him. This effect is a type of electro-optic effect, which refers to the interaction between light and an electric field. 

When a strong electric field is applied to a transparent substance in a direction transverse to the beam of light, double refraction is induced in it. So, the refractive index of the material is varied with the electric field and it behaves like a crystal with its optic axis parallel to the electric field. 

Figure 1: Working of Kerr Cell

In general, the Kerr effect can be observed in all materials. But some liquids tend to exhibit a stronger Kerr effect compared to others. The material that exhibits the Kerr effect is called the Kerr cell, also known as the Kerr electro-optical shutter. It employs the Kerr effect to interrupt a light beam up to 1010 times per second. The working of the Kerr cell is shown in Figure 1.

Working of Kerr Cell

A linearly polarized light is passed through a cell with transparent walls containing a liquid, such as nitrobenzene. The light beam that comes out of the cell is blocked by an analyzer set at 90° to the direction of light’s polarization.

When an electric field or voltage is applied across two plates on both sides of the cell, the light beam is straddled at 45° with respect to the plane of polarization. The polarized light beam is separated into two components: one parallel and one perpendicular to the electric field. The light beam that comes out of the cell is circularly polarized because its two components move at different speeds and create a phase difference. Hence, the beam will be partially transmitted by the analyzer. The Kerr cell is a useful tool in studying laser and communication technologies, as well as measuring the speed of light in transient phenomena through photography.

The Kerr effect can be classified into two types: Kerr electro-optic effect, or DC Kerr effect, and the Optical Kerr effect, or AC Kerr effect.

Kerr electro-optic effect

In the Kerr electro-optic effect, when a slowly varying electric field (such as a voltage supplied to electrodes) is applied across the sample material, it becomes birefringent. This means that the passage of a light beam through the material causes a change in the optical phase, which depends on the light's polarization. The amount of change in phase is proportional to the square of the voltage applied to the electrodes. This effect induces birefringence even in optical materials that are not naturally birefringent. This material can then be used as a waveplate that can be controlled by electricity. 

Consider the electric field strength over some path length L to be constant, then the phase change induced by the electric field is given by,

where Δn represents the difference in refractive index between two polarization, K is the Kerr constant of the material and E represents the electric field strength applied.

Some liquids, such as nitrotoluene and nitrobenzene, have a high Kerr constant, meaning that they can be strongly affected by an applied electric field. When these liquids are placed inside glass cells, they are known as Kerr cells.

Optical Kerr effect

The Optical Kerr effect happens when light generates an electric field that can change the refractive index based on the intensity of the light. It occurs without an externally applied electric field. The Kerr effect is a nonlinear response that occurs instantaneously and is characterized by the modification of the refractive index. The modification of the refractive index for the high-intensity light beam itself occurs according to

Where n2 is the nonlinear refractive index and I represent the optical density which is proportional to the modulus squared of the electric field strength. 

At very high optical intensities, the Kerr effect reaches a point of saturation, meaning that the refractive index does not increase further in proportion to the intensity of light. Also, there may even be a decrease in refractive index.

Applications of Kerr Effect

The Kerr effect is used in the design of optical switches and modulators, which can rapidly control the transmission of light in optical communication systems. Kerr cells are also used in laser technology for pulse shaping and Q-switching.

It is used to measure ultrafast phenomena such as the speed of light in a medium or the response time of electronic circuits. It is also an essential tool in nonlinear optics, where it is used to study nonlinear optical phenomena such as four-wave mixing, self-phase modulation, and optical solitons.