# Gravitational Lensing of Gravitational Waves: Rotation of Polarization Plane

## TL;DR

This paper investigates how gravitational lensing affects gravitational waves, particularly focusing on the rotation of their polarization plane and its impact on detector signals, revealing subtle effects that are generally negligible.

## Contribution

It introduces the concept that gravitational lensing can rotate the polarization plane of gravitational waves and analyzes its effects on detector responses.

## Key findings

- Polarization rotation causes changes in detector response patterns.
- The effect of polarization rotation is negligible due to small deflection angles.
- Different gravitational wave rays produce varying strains due to lensing effects.

## Abstract

Similar to the light, gravitational waves traveling in multiple paths may arrive at the same location if there is a gravitational lens on their way. Apart from the magnification of the amplitudes and the time delay between the gravitational wave rays, gravitational lensing also rotates their polarization planes. This results in the changes in the antenna pattern function, which describes the response of the detector to its relative orientation to the gravitational wave. These effects are all reflected in the strain, the signal registered by the interferometers. The gravitational wave rays in various directions stimulate different strains. Their strains differ from each other due to different magnification factors, the phases and the rotation of the polarization plane. The phase difference mainly comes from the time delay. Moreover, the rotation of the polarization plane seemingly introduces the \textit{apparent} vector polarizations, when these strains are compared with each other. Because of the smallness of the deflection angles, the effect of the rotation is negligible.