band diagram
is anyone concerned about this method?
Who is Qiu? Are you writing your own code or using an FDTD software package?
FDTD can "miss" certain bands if the source and probe points are placed incorrectly. Photonic crystal modes do not look like plane waves. The modes have intense points and null points. If the photonic crystal is sourced at a null, the mode will not get excited and will be completely missed. It is usually good practice to place a number of source and probe points at different places and polarizations throughout the unit cell.
I devote Chapter 4 in my dissertation to FDTD. Section 4.2.11 (pp. 100-102) describes how to modify the code and place source/probe points to calculate photonic band diagrams. This is very different than calculation transmission and reflection spectra. You can download my dissertation in a discussion about 3D UPML:
https://www.edaboard.com/download.php?id=124081
-Tip
I have enough points to see your dissertation.
thank you for Dr. R.C.Rumf's good advice.
actually, I'm writing my own code, I just downloaded your dissertation from central florida univ.
I'll check the code according to the chapter 4 of your paper.
anyway, I still can't sure to get the exactly right result.
thanks again.
Added after 2 minutes:
btw, I use about 100 random probe points according to one of Dr. Min Qiu's papers.
but is it really neccesary to get 100 poits, as it is also time consuming compared with Plane Wave Expansion Method.
For 3D structures, I have found FDTD and PWEM take roughly the same amount of simulation time. See Fig. 5-4 (page 124) in my dissertation. This is a comparison of a photonic band diagram computed by PWEM and FDTD. They took nearly the same amount of time to compute.
While plenty of people will debate this, I find PWEM is great for dielectric photonic crystals with low to moderate index contrast. FDTD works better for very large unit cells and structures that contain metals or have high index contrast. PWEM solves Maxwell's equations as an eigen-value problem so you are assured to compute all the modes and compute them distinctly. In FDTD, there is always a chance you will "miss" modes and it is more difficult to distinguish modes since you are looking for peaks in a Fourier transform to identify modes.
As for number of source and probe points, I have played with this a bit and seem to get pretty good results with just around 10. I think I used less than 20 for Fig. 5-4. I suggest reproducing band diagrams from literature and vary the number of source/probe points and see what happens. I also redistribute my source/probe point for every Bloch wave vector I simulate. This way, if I miss a mode at one bloch vector, I will probably catch it on the next simulation. Given small enough steps between wave vectors, bands are more apparent.
Good luck!!
-Tip
Doc Rumpf,
it seemed you hadn't given obvious tips when probing a excited source in your dissertation.
Sorry. Perhaps I was a bit too brief or cryptic. The specific text from my dissertation reads:
"To ensure energy is present in all possible modes, multiple dipole sources with multiple polarizations must be implemented. Position of the sources must be away from any point of symmetry or Bragg plane to ensure the sources are not placed at the nulls of a Bloch mode. Similarly, time response should be recorded at several locations within the unit cell that are also away from any points of symmetry."
I will take this opportunity to fill in some details for each of these sentences.
"To ensure energy is present in all possible modes, multiple dipole sources with multiple polarizations must be implemented."
A "dipole" source describes applying a source to just one field component at one point in the grid. "Multiple polarizations" means that you should apply sources to Ex, Ey, and Ez fields, not just one of those. "Multiple dipole sources" refers to the fact that you should apply a number of sources throughout the unit cell to better ensure that all modes are excited.
"Position of the sources must be away from any point of symmetry or Bragg plane to ensure the sources are not placed at the nulls or a Bloch mode."
Bloch modes are not plane waves and they have regions of high intensity (nodes) and regions of low intensity (anti-nodes). If you apply a dipole source at a point where a Bloch mode has a null for that polarization, it will not couple any energy into that mode and your FDTD algorithm will not be able to detect the mode exists. The symmetry of the Bloch modes take on the same symmetry as the lattice so the nodes and anti-nodes tend to occur at the lattice points. It would be a bad idea, for example, in a simple cubic lattice to place source and probe points at the corners or center. It is better to place them at "strange" intermediate points and scatter them througout the unit cell. The same rules for source points apply to probe points.
I feel like I am doing a very poor job at explaining this. Fortunately, if you just randomly choose where to place source and probe points, and you use at least 10 points, you are very likely to catch all of the modes. I redistribute my source and probe points for every Bloch wave vector I simulate. This way if I miss a mode during one simulation, I will probably catch it on the others.
Does this help?
-Tip
Can you send me your codes for the band diagrames, so that i can help you??
Ashu