Optics, electromagnetic theory Definition

Faraday effect

Builds on Polarization of light Magnetic field Optical activity Refractive index

Definition

Let a transparent medium be placed in a static uniform magnetic field $\mathbf{B}$ . Let linearly polarized light travel through it in a direction $\hat{\mathbf{k}}$ over a path of length $d$ , and let $B_\parallel = \mathbf{B} \cdot \hat{\mathbf{k}}$ . The Faraday effect is the rotation of the direction of linear polarization caused by the field. Its angle is $\beta = V B_\parallel d$ , where $V$ , the Verdet constant, depends on the medium and the wavelength.

Remarks

The field makes the two circular polarizations propagate with different refractive indices, as in optical activity. The sense of rotation is fixed by $\mathbf{B}$ , not by $\hat{\mathbf{k}}$ .

Example: light that passes through the medium and is reflected back sees the rotation $\beta$ twice in the same sense, a total of $2\beta$ . With $\beta = 45^\circ$ , the returning light is orthogonal to the incoming light, and a polarizer then blocks it; this is the principle of the optical isolator.

Non-example: the rotation in a sugar solution is optical activity, not the Faraday effect. It needs no magnetic field and cancels on a round trip.

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Tag	`S3GTPZ9WBZ`
URI	`m2://S3GTPZ9WBZ`
Kind	definition
Writing	W0 stub
MSC	78A10, 78A25
Defines	Faraday effect
Uses	Polarization of light, Magnetic field, Optical activity, Refractive index
Changed	3 November 2026

Faraday effect

Definition

Remarks

Reading path

Further reading

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