Visualizing EM Waves: 3D Model & Resonant Cavity Simulation in Java Applet

[protonic_mass]

I am trying to code a java applet to give a physical representation of an EM wave, and how it will react in a resonant cavity. However, I am having a very hard time finding a good physical representation of what an EM wave actually looks like.

For example, If I take a 2 meter wave, place it in a 2 meter long resonant cavity, shouldn't I be able to present a 3D representation of that EM wave as a standing wave in that cavity somehow?

 

[Born2bwire]

It's not an easy thing to do. The first thing we usually do is separate the system into the eigenmodes and TM/TE modes. That is, for many problems, we can separate the electromagnetic solutions into two sets. One set is TE_z, characterized by the H_z field, and the other is TM_z, characterized by the E_z field. This way, we only need to solve for the E_z and H_z fields to fully describe the system. The rest of the fields are taken as the cross products of these fields and of course you can orient the fields as needed by your problem.

The next problem is that the solutions to a resonant cavity, among other problem geometries, can be described as the superposition of eigenmodes. So if you were to just put in a random excitation into the cavity, it could be described, once the transients died out, as a liner superposition of various eigenmodes.

So how would we visualize these solutions? Usually we map out the magnitude and phase of the field components. These two values will encompass the full amount of information. You could also do the real and imaginary parts too. Either way, you could do field plots over 2D cross-sections of the eigenmodes for the H_z and E_z fields. That would be one way to visualize a large amount of information for the cavity solution. You will typically see these kinds of visualizations for waveguides, especially because a waveguide is typically solved assuming that the guided direction is invariant (infinite). Thus, for a waveguide a 2D cross-section can fully show the fields but with a 3D cavity that is not true.

As to a 3D representation, no, you cannot do a true 3D representation very well. The problem is that the field is spatially dependent but it's values are a fourth and fifth dimension. We are interested in the field vector at all points so there is more information than can be shown in 3D. The best you could do is a flow plot in 3D space, this would have arrows that represent the direction and magnitude of the field vectors but since the fields are complex you would still lose the phase information in some way or another. But typically, signed magnitude would provide a good picture so you could do it that way, Matlab has ways of doing this but I have always found them to be cumbersome.

 

[astrokreng]

As a fellow scientist, I am intrigued by your project and the use of a java applet to visualize EM waves in a resonant cavity. EM waves are an integral part of our understanding of the natural world and being able to see a physical representation of their behavior in a resonant cavity can enhance our understanding of their properties.

I can understand the challenge you are facing in finding a good physical representation of an EM wave. EM waves are not tangible objects that we can see with our eyes, and their behavior can be complex and difficult to visualize. However, there are various mathematical models and simulations that can help us understand their behavior.

One approach you could take is to use vector fields to represent the electric and magnetic fields of the EM wave. This can give a visual representation of the direction and strength of the fields at different points in space. Additionally, you could use color mapping to represent the amplitude of the wave at different points, creating a 3D representation that changes over time as the wave propagates in the cavity.

Another approach could be to use a ray tracing method, where you track the path of individual rays of the EM wave as they reflect and interfere within the cavity. This could give a more intuitive understanding of how the wave behaves in the resonant cavity.

I would also suggest looking into existing simulations and visualizations of EM waves in resonant cavities to get some inspiration and guidance for your applet. There are many resources available online, such as simulations from universities or educational websites.

Overall, I commend your efforts to create a visual representation of EM waves in a resonant cavity and I am sure your applet will be a valuable tool for understanding these complex phenomena. Keep exploring and experimenting, and I am sure you will find a compelling way to present the behavior of EM waves in a resonant cavity.