Dear Dr. Rumpf Thank you very much for your lesson, doing CEM is often frustrating because everyone claims there is plenty of literature, yet few are the people that goes as in-depth as you. There is just one little but very important thing I am missing. I work on a 1D structure and have been able to calculate everything mentioned in the diagram (which is by the way a blessing, your lecture is the only one that have provided such a comprehensive thing), and I am now trying to plot the stationary electromagnetic field along the Z-axis. I don't understand what should be the procedure, or which equations I am supposed to use. Sincerely yours,
Thank you! I am actually writing a book right now that is intended for complete beginners to get started in computational EM. Not sure when it will be released as I am not even finished writing it, but close. Visualizing the field...what method are you using to simulate the 1D structure? TMM? If TMM, visualizing the field is a bit tricky. I have notes on it in the TMM Extras lecture you can get to on the course website. empossible.net/academics/emp5337/ I am a big fan of visualization. You may want to study the finite-difference frequency-domain method. It is much more versatile than TMM (although slower) and excellent for visualizing the field in a variety of structures.
Did you run the simulations? Unfortunately, I have lost all my homeworks and solutions in a Ryuk attack. My university lied to me and our "offsite and off network" backups were neither offsite or off network. If you get the simulations done, I will try to clear the time to redo the solution.
This is more complicated. The traditional TMM uses a 2x2 formulation. To handle full anisotropy, you must adopt the more general 4x4 formula. In this formation, when you solve the eigen-value problem you will have to sort the modes to separate the forward and backward waves so that you can assemble the scattering matrices and solve the problem in a stable way. I do not have much information on this, but what I do have you can find in Lectures 2b and 2c here: empossible.net/academics/emp5337/
Hi Prof Rumpf, Do you cover Plane Wave Expansion Transfer Matrix Methods such as that outlined by Zhi-Yuan Li and Lan-Lan Lin Phys. Rev. E 67, 046607 - Published 15 April 2003?
Yes. For some crazy reason the authors decided to rename rigorous coupled-wave analysis. The original developers of the method called it RCWA and later others keep trying to rename it to things like Fourier modal method, PWEM+TMM, among other things. I teach RCWA in Topic 7 here: empossible.net/emp5337/ To understand RCWA, you will first need to work through the transfer matrix method in Topic 2 and the plane wave expansion method in Topic 6 at the above link. RCWA = PWEM + TMM and there are topics in PWEM and TMM that I do not repeat in the RCWA lectures. Good luck and have fun!
Dear Dr. Rumpf, I would like to thank you first for the very interesting and educative videos. If i want to to also calculate the the phase ϕr of the amplitude reflection coefficient, could you help me to get for the 3 coordinates? x,y and z? Thank you! Best regards
I would try not to think of x, y, and z as having separate reflection coefficients. A wave travels as a single intact packet of electromagnetic energy. For linear, homogeneous, and isotropic (LHI) materials, these are the TE and TM polarizations in the framework of TMM. Therefore, there is a single reflection coefficient for TE and another for TM. There are two ways to get these coefficients. The easiest is simply pull it out of the global scattering matrix. These are 4x4 matrices. They are 4x4 because there are two polarizations and two ways to enter and exit the device, leading to a total of 4 combinations. For example, one of the numbers in the 4x4 global scattering matrix describes the amplitude of the reflected TE wave due to an incidence TM wave. This will be zero for LHI materials. Another will describe the amplitude of the reflected TE wave due to an incidence TE wave. This will be the TE reflection coefficient you are after. It will be a complex number where the polar form describes the amplitude and phase you are after. Hope this helps!!
@@empossible1577 Thank you s much for your answer. I implemented your scattering matrix TMM method using the diagram shown in your notes (slide 31 or page 16). after calculating the global S matrix we multiply the S11 with the e_scource, we get 2 reflection in x and y and then we calculate in the z direction... So i should directly from the first element of the S11 global extract the phase or from the combination of the reflection field x,y,z? My goal is to detect the reflection phase in a FP laser or a VCSEL where it is 0 at the FP Resonance frequency. Thank you so much again
@@bedouinsassya7510 I think you are missing an important concept. Refer to slides 17 and 18 in Lecture 7b from the course website: empossible.net/emp5337/ You first calculate esrc, which has the x and y information. However, you then calculate csrc which essentially determintes the amplitudes of your TE and TM polarizations. The S11 and S21 coefficients are applied to those and then projected back to x and y at the end. Fundamentally, the scattering matrix elements are relating the reflected and transmitted TE and TM modes. It is for this reason that you will extract your reflection or transmission coefficients from the scattering matrix elements. Keep in mind that S11(global) will be a 2x2 matrix because in general TE can scatter to TM and TM can scatter into TE. You will need to pick the correct scattering matrix element depending what information you are seeking.
No. This method can only handle homogeneous media. When the method is generalized to handle inhomogeneities, it becomes either method of lines or rigorous coupled-wave analysis. I have information on both of these methods in my Computational Electromagnetics course here: empossible.net/emp5337/ Hope this helps!!
Hi Professor, thank you for your great lectures. I am attempting to implement this, but I am having an issue with calculating the scattering matrix elements at normal incidence - at normal incidence, Omega_i is proportional to the identity matrix and Qi is proportional to [[0,1],[1,0]] so Vi = 0 and has no inverse. Am I missing something, or is it not possible to have _exactly_ normal incidence with this method?
Yes, normal incidence is possible and probably the most common thing. For this case, Vi = [ 0 1 ; 1 0 ]. Let me point you to the official course website where you can get links to download the notes, links to the latest version of the videos, and access to other learning resources. empossible.net/emp5337/ In the Homework "Help" section, you will see a "Benchmarking Aid for RCWA 1x1." RCWA using 1x1 spatial harmonics is the transfer matrix method. You can use this to benchmark you terms. In my notes I use the positive sign convention for TMM and the negative sign convention for RCWA so you may see some sign differences, but the document should still help you. Hope this helps!
You can choose anything for the gap medium and the code will work most of the time. However, it is best to choose something that prevents kz from being zero in the gaps so that your code always works. I cover this on slide 23 in Lecture 2g from the course website: empossible.net/emp5337/ While there are many proper choices, I use... urg = 1.0 erg = 1 + knx^2 + kny^2 where kn is the normalized wave vector.
Hi, professor! Thank you for your lecture :) I want to simulate coupling of incident wave to a dielectric waveguide where the evanescent field caused by total internal reflection interacts with dielectric waveguide mode so that it excites the waveguide. It's like surface plasmon resonance(SPR) using prism. Eventually, I want to do parameter sweep along the wavelength and incident angle based on which we can get dispersion relation of the waveguide mode sort of indirectly. What do you think is the best way to simulate this experimental situation? I'm thinking of TMM, 2D FDFD, and 3D RCWA. I can try all of them but I just want to know your opinion. Thank you for reading :)
I would use a 2D FDFD or a 2D FDTD to simulate your waveguide excitation. I think you are going to want to visualize the fields to help interpret the simulation results. TMM and RCWA can certainly visualize the fields, but it is a lot more work to do that with these methods. FDFD and FDTD will allow you to do other things as well much easier.
@@empossible1577 Oh, and I want to ask you whether all the methods I mentioned likeTMM and RCWA are at least also capable of doing that kind of simulation!
Dear Dr. Rumpf Thank you extremly for your wonderful lectures. At 11:25 of this lecture, mu_trans,r and mu_inc,r are used to calculate the transmittance.Why to do that? And is there a specific derivation process?
Thank you! I am glad the videos are helping you! First, let me point you to the official course website where all of the information is organized and you can get links to the latest versions of the notes, videos and other learning resources. empossible.net/emp5337/ These extra terms arise because the medium on the transmission side may be different than the medium on the reflection (or incident) side of the device. When in a different medium, the field quantities will be different if the same amount of power is flowing. Expect these equations to change in these lectures very soon. We are in the middle of figuring out how to modify them when the external mediums have loss.
@@empossible1577 Hi Dr.Rumpf Thanks for your reply. But according to dispersion relationship,k_Zs have already taken the difference of mediums into consideration.So i don't know the function of mu_inc,r and mu_trans,r.And where is my thinking mistake?
@@mihweighyung6312 For some reason, I cannot find where I have the detailed derivation. I found an almost complete derivation in Lecture 3g in the FDTD course: empossible.net/academics/emp5304/ Power flow is ExH. The equation is put in terms of the electric field. To do this, an impedance term arises in the equation. The reflected wave is the ratio of reflected power to incident power, but since they are same medium the impedance terms cancel. For the transmission region, the impedance terms do not cancel and the permeability terms are left after simplifying with other terms in the equation. The kz terms arise because it is only the z component of Poynting vector that should be considered in these calculations.
Hello, Dr. Rumpf! Thank you for your lectures! As I can see, you choose "plus sign convention" in that lecture. Does It leads to changing one terms in block-diagram only (X = exp(lambda*k*L)) by comparison with lectures at 2013 (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mOy5jyZe7_Y.html), where was (X = exp(-lambda*k*L)? Are there other differences between two block-diagram, inspired by sign convention?
I have derived and implemented both, but I sort of forget the differences. I do know it is very minimal. I would like to say it is only the X matrix, but I would hate to be wrong. I derive RCWA with the negative sign convention. Consider comparing TMM to RCWA in my block diagrams. Here is a link to the course website where you can download the notes and get links to the latest version of the videos: empossible.net/academics/emp5337/
