The solutions to Maxwell's equations in vacuum are linear and so can be added to each other without affecting each other.

There are lots of non-linear materials (e.g. lots of magnetic materials) where this isn't true, and light can be bent or its polarization rotated or its phase changed, or it can be attenuated using static (slowly varying) electric or magnetic fields).

Non-linear materials are used in lots of devices to exploit this.

In general relativity the energy density of EM waves curves space in the same way that mass does, so EM waves do affect each other even in space, but only minutely, because the equivalent mass density is usually very small.

Respected Malcolm,

To some extent , I know some nonlinear behaviour of em waves inside different materials.

Also the bending in high gravitation field is well established and basically this is a mass effect.

BUT I DON'T KNOW WHAT HAPPENS TO EM WAVES IN VACUUM . IS THERE ANY EFFECT OF ELECTRIC OR MAGNETIC FIELD ON EM WAVES IN VACUUM? ( NOT GRAVITATIONAL BENDING ?

Regards

Nityananda Das

No there are no non-linear effects in vacuum, except gravity, which is not in Maxwell's equations, I think. The equations are linear. This means there is no effect. Any addition of electromagnetic waves or fields still obeys Maxwell's equations, so the individual parts don't affect each other.

I think you missed the point about gravity. Beams of light have gravitational attraction for each other. This is a non-linear effect, I think. I think that given a long enough path two parallel beams would spiral round each other or repeatedly cross over

Preston Guynn

Thank you for your links, they are very intersting.

I am not certain, but it seems to me that Delbrück scattering requires the presence of a third body, not just two photons, so may not be a non linear effect in vacuum.

However, the second effect seems to be real photon-photon scattering and is described here https://www.clf.stfc.ac.uk/Pages/44.pdf

Please see the link below:

https://www.quora.com/Can-electromagnetic-waves-be-deflected-by-an-electric-or-a-magnetic-field.

Best regards

Doufnoune RACHIDA Rachida

The forum at the link you provide does not deal with the subject in enough depth,, and does not know of the effects described by Preston Guynn , which I think are only noticeable in very high energy physics.