Optics, electromagnetic theory Definition

Kerr effect

Builds on Nonlinear susceptibility Refractive index Birefringence

Definition

Let a transparent medium be isotropic in the absence of fields, with refractive index $n_0$ at vacuum wavelength $\lambda$ .

The electro-optic Kerr effect is the birefringence induced by an applied static electric field of strength $E$ . Light polarized parallel and perpendicular to the field sees indices that differ by $\Delta n = \lambda K E^2$ . Here $K$ is the Kerr constant of the medium.
The optical Kerr effect is the dependence of the index on the intensity $I$ of the light itself, $n = n_0 + n_2 I$ . Here $n_2$ is the nonlinear index of the medium.

Remarks

Both effects come from the third-order nonlinear susceptibility $\chi^{(3)}$ . For a linearly polarized monochromatic wave in an isotropic medium, with $I = \tfrac12 n_0 \varepsilon_0 c \abs{E}^2$ , SI units give $n_2 = 3\chi^{(3)} / (4 n_0^2 \varepsilon_0 c)$ , where $\chi^{(3)}$ is the relevant component.

Example: in silica glass $n_2$ is positive and small, of order $10^{-20}\ \mathrm{m^2/W}$ . Over many kilometres of optical fibre, this small index change still gives a large phase shift.

Non-example: the Pockels effect is a change of index linear in the applied field. It is not a Kerr effect, and it needs a medium without a centre of inversion.

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Tag	`TKG280TFPM`
URI	`m2://TKG280TFPM`
Kind	definition
Writing	W0 stub
MSC	78A60, 78A10
Defines	Kerr effect
Uses	Nonlinear susceptibility, Refractive index, Birefringence
Changed	3 November 2026

Kerr effect

Definition

Remarks

Reading path

Further reading

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