Lecture 11 (CEM) -- Finite Difference Analysis of Waveguides

[@JordanEdmundsEECS]

1. Is there a reason we don’t add a PML around the edges instead of making our grid really large? It seems like that would be more efficient. Is it because these fields are not intended to be propagating out to infinity (they are confined) and we actually want their values everywhere, and a PML would wreck that? 2. A question on notation - are you now using gamma instead of kz because kx and ky no longer have (rigorous) meaning? Is this standard?

[@empossible1577]

The field outside of a waveguide is evanescent. PMLs do not handle evanescent fields very well at all. So, even if you used a PML you would need to keep it just as far away as the Dirichlet boundary conditions, but then also have the numerical complexity of having a PML. If you want to analyze leaky waveguides, then a PML is needed to absorb outgoing waves. In a non-leaky waveguide, there should be no outgoing waves.

[@JordanEdmundsEECS]

@@empossible1577 Got it, makes sense! Thanks.

[@NoahBenzing-ru5st]

I just read about the FDTD method as it applies to speech sensing using UltraWideBand networks and MBAN (Medical Body Area Networks). "Accurate and Efficient Electromagnetic Modeling of Antenna-Body Interactions: Application to Speech Sensing and BAN" By: Ahmed Mohamed Ali Moussa Eid

[@empossible1577]

+Noah Benzing You may be interested in our FDTD course in electromagnetics. Here is the website: emlab.utep.edu/ee5390fdtd.htm

[@TheSakr289]

Would you like to post a detailed video about adiabatic taper (slab expander) ?

[@empossible1577]

Perhaps. Seems easy enough to simulate if I understand what you are asking.

[@TheSakr289]

I mean, it would be great if you post a video about the design of the adiabatic taper. Adiabatic tapers are used in Photonic integrated circuits to couple the EM field from waveguide to grating emitters.

[@empossible1577]

@@TheSakr289 I am "slowly" developing a photonics course. I suspect it will be a while before that is finished enough to post, but the taper would be an excellent topic to include.

[@邱橙]

Thank you very much for your introduction. I have built a strip waveguide analysis simultion model. Everything seems fine at first glance,except when I begin to benchmark my simultion result with yours. I found that my effective refractive index is incorrect, and the field are more likely to stay in the high index area compares to that it supposed to be. As the result, the Neff is 1.89 in my simulation whereas in your poster is 1.76. Do you have any idea what happened?

[@empossible1577]

It is a very common mistake to enter refractive index directly as permittivity in your simulation, which can lead to results like this. Verify that you are squaring the refractive index to get permittivity.

[@Jeff-sf7jh]

where can I find the geometry and material property of the rib waveguide example?

[@sivaramaditya4610]

Thanks for the very elaborate lecture series. I'm trying to simulate a dielectric inside a WR 90 rectangular waveguide . I'm using soft source with the TE10 mode as incident wave and not the TFSF. a) How to subtract the reflected signal at the input port from the total field to get the S11. b) Does TFSF work as waveguide port for rectangular waveguides. Any reference material would also help. Thanks

[@skardykats]

@41:44 is it because of the numerical boundary conditions?

[@empossible1577]

We used Dirichlet boundary conditions (assume field is zero outside the grid). Due to the staggered nature of the Yee grid, this forced electric fields to be zero at two boundaries and magnetic fields to be zero at the other two. This is no longer a symmetric problem due to the asymmetric in the boundary conditions. It is the electric field being visualized and the sides that they appear to be drawn toward are the sides where the magnetic fields are assumed to be zero.

[@harshang8852]

I guess for photonic crystal type structures two dimensional mode calculation is needed. But my problem is in introducing the fundamental mode in the input of the wave guide.I have tried many ways but grid mismatch is occuring. Can you please explain how the input dielectric values,grid size for differential computation can be specified if 2D mode calculation is performing. I have used full vectorial analysis. Thanks for the great lecture.

[@empossible1577]

The algorithm in this lecture does not take the mode as the input. Instead, it is a mode solver and calculates the modes of a waveguide. At a high level, you will build a large array describing the permittivity in the cross section of the waveguide and also provide a guess for the effective refractive index of the guided mode. Grid resolution is found by testing for convergence. The size of the grid needs to be big enough to encompass the entire mode. These are all the inputs to the algorithm. If you keep following the lectures and learn the implementation of FDFD, many of those steps are the same for solving modes of the waveguide. I fear I have not answered your question adequately. Hope this helps!

[@harshang8852]

Thanks! I will go through the same. Is there any formula to pre-calculate how many guided modes exist in a rib waveguide ?

[@empossible1577]

Not that I know of. There are too many parameters to consider. With practice, you will be able to immediately recognize if a mode is guided or is something else.

[@sparkle4708]

Do you have a complete lecture on strip waveguide?

[@empossible1577]

I do not. I only have this one lecture on how to simulate waveguides. I have a small series of lectures on waveguides in general, but I don't think I mention strip waveguides at all in those lectures. You can find them under Topic 9 here: empossible.net/academics/emp3302/

[@julesbilluart9688]

The complex propagation constant is wavelength dependant since it appears from j*k0*n_eff. But does the effective refractive index itself is wavelength dependant? If so, how to implement the free space wavelength in the eigen value problem? Best,

[@empossible1577]

The free space wavelength is incorporated in the simulation through the normalized grid coordinates. Yes, the effective index is wavelength dependent. That is because as wavelength changes, the mode profile changes, causing the mode to overlap different proportions of dielectric, thus changing the effective index.

[@easonxiao3383]

When I use eigs to calculate the effective refractive index and the propagation constant of plasmonic waveguides, I found the following problems (when calculating the waveguide normal modes,such as TM01, it is ok): 1. the guess has a great influence on the results, so how can I get the biggest solution of the spp modes? or how can I use this function to get the spp relation? 2.when the grid resolution is changed, the result for spp modes would changed. So can I say this is because this function (eigs) is not so stable for spp modes? Do you have any good idea to avoid this problem? 3.the version of matlab have a great influence on the speed of the function. the speed on 2015a is much faster than the one on R2012a. Is this normal? Thanks!

[@empossible1577]

+Xiaofei Xiao Here goes... 1. Yes it does because there are many possible modes. Try to think of logical trends. Will the lowest order mode have the highest or lowest effective refractive index, etc.? Use these trends to make better educated guesses. 2. Yes, and this is completely a numerical artifact. Always look for convergence. That is, keep increasing grid resolution (more points) until the result you are getting does not change anymore. 3. I guess things are always getting better in MATLAB. I have noticed other weird things like changing the order of modes, etc.

[@sichen2330]

Thanks very much for you lecture. But I have a problem with the field distribution. I exactly follow your introduction and managed to get similar mode pattern for rib waveguide, as shown in your lecture notes. But my problem is that if you zoom in the plot of mode pattern, there are empty spots (means field is equal to 0) regularly located between any two adjacent colorful spots. Have you met similar case?

[@empossible1577]

Some modes will have nulls in the field pattern. Is this what you are seeing or are seeing random pixels zeroed out or something else? If you are seeing single pixels zeroed out, I would look carefully at your materials arrays. See if they contain any zeros or other crazy numbers.

[@sichen2330]

@@empossible1577 Sorry it is a bit hard to explain, so the point is that the whole pattern looks acceptable, they are the mode pattern. The problem is that between every two useful data points, there will be a zero value, no matter in x axis or yaxis

[@sichen2330]

@@empossible1577 Do you have a email address or some other contact details so that I can show you the figure? I have tried to send email to the address shown on your lecture. But seems not working

[@sichen2330]

@@empossible1577 something like 1 0 2 0 3 0 4 0 0 0 0 0 0 0 5 0 6 0 7 0 8 0 0 0 0 0 0 0 9 0 1 0 2 0 3

[@empossible1577]

@@sichen2330 Send me your code and a picture. rcrumpf(at)utep.edu

[@ruthtsega4268]

Thank so much!! pleas can you upload lecture 7 again (about PML) ,it is not Woking

[@empossible1577]

Lecture 8 is about the PML. I just tried it and it seems to work fine. Have you tried it again?

[@holgerschlueter5486]

Slide26: Could you provide the dimensions and ur,er of the device so we can benchmark our code against the results? Thanks.

[@empossible1577]

Absolutely. What an embarrassing oversight! I have revised the PDF notes at the following link with this information is now on Slide 30. emlab.utep.edu/ee5390cem.htm The width of the rib is 2.0 microns. The height of the rib is 0.6 microns and the thickness of the thin slab is 0.25 microns. The refractive index above the core is 1.0 (air). The refractive index of the substrate is 1.52. The refractive index of the core layer is 1.9. I think that is about all you need. Please let me know if there is anything else missing.

[@anujmodiphd34]

Dear Prof. Raymond C. Rumpf, Can you suggest any good book for FDTD method? Also, can you suggest any good book which includes all the known CEM like FDTD, FEM, MOM in one?

[@empossible1577]

Anuj Modi The best book on FDTD is the one by Taflove, but I am not sure it is the best to learn from. I learned a while ago using a book from Sullivan, I there are many others now. I have not been through them to recommend any. I would like at the description and see if they cater to the beginner. I do not know of any book that covers all known CEM methods. This course is the most comprehensive that I know of and it doesn't even cover all of them. For example, there is a lot of attention recently on discontinuous Galerkin. I suspect I will add at least something about that method next time I teach it at my university. Sadiku wrote a book that has several of the major methods and may be the most comprehensive book that I know of.

[@saurabhbedi195]

+Anuj Modi A book by Allen Taflove on Computational Electrodynamics is very good to understand FDTD Simulations.

[@okanerturk7837]

Sadiku's book also can attract your interest. It includes MATLAB codes but not well to intrerpret. But at least, you will have a practical code documentation.

[@winnis88]

TE and TM modes in waveguide, as I have read in Pozar, mean modes where the longitudanal magnetic and electric filed components are zero respectively. However you seem to use a different definition. Am I correct?

[@empossible1577]

TE and TM modes only exist in enclosed metallic waveguides that also have a homogeneous dielectric fill. Otherwise there are only ever hybrid modes. However there are still some approximations that can be used and I call those the "quasi" modes. At some point I intend to include the metallic waveguides and then you will see true TE, TM, and even TEM.

[@winnis88]

Actually I got the answer in Lecture 12 22:28. Thank you.

[@techtalk2382]

I was just reading through the comments. I have one doubt. 1. How to model photonic crystal waveguides making the fundamental mode to pass through? 2. If it was using 2D mode calculation method, the modes and effective n is determined, How we can calculate the modes at the point where source is introduced. From (nx_src1:nx_src2,ny_src) source is introduced. Here as we are only having one dimensional (line) surface for mode calculation, how 2D mode calculation can be done ? Or 1D will be enough? (if uniform one direction cant be assumed) 3.It is fine to use 2D mode calculation for mode pattern viewing and effective index calculation.But how that can be incooporated with input and output waveguides.?

[@empossible1577]

1. The technique described in this lecture does not take the mode as the input. Instead, it is a mode solver and calculates the modes. 2. The technique described here has no source. It does not make sense to talk about introducing a source. 3. I think you are wondering how to turn this code into something that simulates the mode actually propagating through a waveguide. Take a look at Lectures 20 and 22 here: emlab.utep.edu/ee5390fdtd.htm

[@techtalk2382]

CEM Lectures Thanks sir, It is true, I am confused at that point. I had heard all your lectures and simulated the ones upto lecture 23. In rib waveguide propagation modelling, a slab waveguide is extracted to introduce source. (Step-4, Lecture 22) How that step get modified if channel waveguide or photonic crystal waveguide is the case? Or is it enough to calculate 1D source mode (slab waveguide) for them ? The same doubt goes for extracting output waveguide also.

[@empossible1577]

In my lectures, I restrict most everything to 2D simulations in order to relax what is required of students' computers. For this reason, the waveguide circuits are sort of a top view of a waveguide circuit so the modes are calculated by analyzing slab waveguides. I do not cover simulating waveguide circuits in full 3D. The techniques for doing this are the same as in 2D. Maybe this clears up what I have done and why.