Faraday effect of light caused by plane gravitational wave

Abstract A gravitational field can cause a rotation of the polarisation vector of light. This phenomenon is known as the gravitational Faraday effect. We study the gravitational Faraday effect of linearly polarised light propagating in the gravitational field of a weak plane gravitational wave (GW) with “ $$+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>+</mml:mo></mml:math> ", “ $$\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> ", and elliptical polarisation modes. The corresponding gravitational Faraday rotation angle is proportional to the GW amplitude and to the squared distance traveled by the light and inversely proportional to the GW squared wavelength. The Faraday rotation is maximal if the light propagates along directions perpendicular to the GW propagation and tilted by $$\pi /4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>π</mml:mi><mml:mo>/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> to the directions of its polarisation. There is no a gravitational Faraday rotation when light and a GW propagate along the same directions, or when light propagates along directions of a GW polarisation. Helicity of an elliptically polarised GW gives cubic order contribution to the Faraday rotation.