EM Pulse Effects & Calculation: Fourier vs Laplace

[lttung]

Hi Physics Forum,

I am a student, doing something about electromagnetic pulses.
I want to ask a question:
If we find the effects of EM pulses on some systems, is it convenient to use Fourier transformation to make these pulses look like sinusoidal? Or we can use other kinds of transformations like Laplace one.
Can you recommend me the simplest books telling ways to calculate with EM pulses.

Ah, they tell about the sinusoidal pulse, the Gaussian pulse and the rectangular pulse with the same energy. What does "the same energy" of pulses mean?

Thank you very much.

 

[jtbell]

Ah, they tell about the sinusoidal pulse, the Gaussian pulse and the rectangular pulse with the same energy. What does "the same energy" of pulses mean?

It means that if they hit something and are absorbed, they deliver the same number of joules of energy to the absorbing object.

 

[Born2bwire]

You could do a Fourier transform, but then you need to solve over a range of frequencies and then do an inverse transform to get the time domain solution. Depending on the type of pulse and the number of points you need to do the inverse transform, this could be more time consuming than a time-domain analysis. It all depends. I reallly simple way to model pulses is to use FDTD, finite-difference time-domain. Allen Taflove is a great authority on FDTD.

 

[dexturelab]

Thank two members very much.

It is appealing to learn new method such as FDTD. However, in my problem, the previous author had analytical result of a sinusoidal wave, and there are several surfaces with surface currents (a cell with an organelle inside). I wonder that is this method effective with surface regions, and with the small regions when the quantum effects are important?

I am a student in biophysics, not in engineering fields. So, is this method convenient for soft-condensed matters. I intend to skim such book like "A First Course in Finite Elements". It looks basic and simple for an amateur like me.

Thank you very much.

 

[Born2bwire]

Quantum effects... I guess that all depends on whether or not you can incorporate them into the differential equations. I have seen FDTD used in quantum problems, the most recent in Casimir force. But that all depends on how you formulate the problem. FDTD is mainly a method to solve partial differential equation, in this case one that is dependent upon time and space. However, FDTD is very useful in inhomogeneous problems. The only problem is that you will have to divide up your inhomogeneities in accordance with a grid. I don't know of a way to use a non-rectangular grid. So if you have a surface with very small feature sizes then you will need to make a small grid which will increase memory and computation time. Using a triangular mesh, like in finite element or method of moments, can result in a more accurate mesh for a given mesh size.

I'm not sure if finite element can model a pulse very well but, I guess it depends on how you do the excitation. I know, though, that I have done a point source current and the results were mediocre. The reason for this is that you assign a current that is "smeared" across a single mesh element. If you have a signal that is supposed to be very small spatially, you will need to make a very dense mesh otherwise the interpolation of the signal across a mesh element may distort it from what is desired. Of course, with a point source current this is impossible to do so there was a bit of deviation.