# Electromagnetic waves interacting within space

1. May 8, 2014

### Fedders

Hello everyone. I have a question about waves and how they interact in certain settings.

1.) What happens when two EM waves (of different frequencies and amplitudes) arrive at the same space at the same time, and are traveling 45 degrees to one another? Do their trajectories, amplitudes, and frequencies change at all? I've heard of cancelling, but I thought this cancelling wasn't really cancelling at all.

2.) Is there any scenario in which an EM wave traveling through air, goes into a medium and then comes out of the medium with different characteristics other than velocity and direction? (wavelength, frequency)

Thank you for taking the time to read this. I have to come up with a senior project this summer. I will have access to a 3D printer which can print materials with certain properties which can effect an EM wave. (permittivity, permeability, reflectivity). I will first model the concept in Comsol, then have the concept printed and tested.

I'm actually a Physics major but was assigned to work in the EE department for this project. I'm trying to come up with ideas for what I can do for this project.

2. May 8, 2014

### phyzguy

Classically EM is completely linear, so two EM waves in free space simply pass through each other and continue on their way.

In a medium is a different story. Since there are non-linear interactions, lots of interesting things can happen. For example, you can take light of a given frequency, put it into a non-linear medium, and get out light of twice the frequency. You might want to Google "nonlinear optics".

3. May 8, 2014

### sophiecentaur

If EM waves always interfered with each other, it would not be possible to see across the room because the light from every other point on in the room, going to every other point, would get in the way of the light that's going directly to your eye. If you sit in a darkened cinema and look into the beam from the projector you can see the path of the light because it is scattered by small particles of dust. If you look in the sky, you see a blue sky because some of the light from the Sun, which is heading over your head to the horizon is scattered by air molecules. But both of those phenomena are because there is a medium.
Empty space is a Linear Medium and the total E vector is the vector sum of all the E fields of all the EM waves passing that point. (Same for the H Fields) so the waves have no effect on each other.
In some circumstances, when the EM waves are passing through a non-linear medium, the waves will interact. This can happen in some crystals and it also happens in the Ionosphere, where high power radio transmissions can cross-modulate weaker signals that are passing through the same region but join along an entirely different path.