Power introduced by FDTD soft sources in a waveguide problems

[peponas]

Hi all,

I have a simplified model to study, which is the excitation of a smooth cylindrical waveguide usint a TEmp mode. Up to now, I used hard sources and therefore the transverse components of the electric field on the boundary was forced to specific values, according to the mode eigenvector. The arbitrary amplitude of each of them was chosen appropiately, in order that the mean power of the field to be a specific value. Then, I measured the power (by integrating Poynting's vector on the transverse plane) and -except for a small discrepancy due to the discretazion- I get the same power as I forced the field to have.

Of course such a source reflects back the fields. For this reason I use a CPML to absorb ongoing waves.
Now I try to use a soft source in order to be transparent to ongoing and reflected waves. However, even I used the same strategy as in the hard source case regarding the power normalization, the power I measure by integrating the poynting vector is nowhere related to that I used before.
The soft source is implemented as En+1(r) = En+1_fdtd(r) + En+1_source(r), essentially a added source since the mode field is added to the FDTD calculated one at each timestep.
How can I normalize that power to the correct value without running the hard soft problem or mess up with impulse responces?

Thank you in advance!

 

[rrumpf]

I think the best way to control power of a soft source is to use the total-field/scattered-field technique. Essentially, you will define all the points on the grid forward of where you wish to launch a source as total-field (TF). All the points behind the source will be scattered-field (SF). Your finite-difference equations at the interface between the two will contain terms from both sides. These are not compatible. If the equation is on the TF side, make the SF terms look like TF by adding the source to them. If the equations is on the SF side, make the TF terms look like SF by substracting the source from them. By doing this, you launch a nice one-way source where you can easily control the amplitude.

I cover the TF/SF technique in my face-to-face class and have posted the notes here:

Electromagnetic Analysis Using Finite-Difference Time-Domain

Students will learn to implement the finite-difference time-domain (FDTD) method in MATLAB. Students will learn to analyze devices such as waveguide, thin film optical filters, gratings and frequency selective surfaces.

empossible.net

If you are willing to pay for an online course, there is an excellent online course for FDTD that teaches the TF/SF technique as well. It has MATLAB codes as well. Here is a link to that course:

All Products - EMPossible

empossible.thinkific.com

Here is a link to a video that shows what is taught in the online course:

BTW, it is possible to launch specific modes into your waveguide. To do this, simply replace your source with the mode you calculate from an analysis of the cross section of your waveguide. I cover the MATLAB implementation of calculating modes in waveguides in two places. First, I cover it in Topic 4 at the link below:

Computational Electromagnetics

Computational Electromagnetics (CEM) is how we model and simulate the behavior of electromagnetic fields in devices or around structures.

empossible.net

I also have devoted an entire chapter to waveguide mode calculation in the following book:

Electromagnetic and Photonic Simulation for the Beginner: Finite-Difference Frequency-Domain in MATLAB

Get an in-depth understanding of the Finite Difference Frequency Domain (FDFD) with Dr. Raymond C. Rumpf's book. Unravel the central concepts of computational electromagnetics and learn to simulate different devices.

empossible.net

The above code would use the exact grid of your FDTD code so the course is directly compatible.

Hope this helps!!

 

[peponas]

Hello,
thank you for the answer. I know the TF/SF technique but I try to avoid it since I have to also deal with a CFS-PML layer.

 

[rrumpf]

The TF/SF technique should not be a problem with your PML as long as the source is zero at the PML. If you are launching a guided mode source, the mode should be zero well before reaching the PML.

 

[peponas]

In other words, PML-SF-TF/SF source, correct?

 

[rrumpf]

I would not think of it as a PML-SF-TF/SF source. Just let your PML and your TF/SF source be two separate things in your code. Just make sure the source is zero at the PML regions and you will not have any problems.

 

[peponas]

Thank you for the detailed reply. I will have a look and in case of any problem I will come back.