Lecture 6 (CEM) -- Periodic Structures

[@mirkovukovic6517]

At 40 minutes, my head just exploded - from joy. I finally get what those band diagrams mean (I suspect I am still missing a lot), but I am enjoying the feeling very much. Thanks!

[@empossible1577]

This is great to hear! If you like this video, I have to tell you that this section of the course has been revised and improved considerably. I recommend using the course website as your main portal to the videos. The information is organized and you can download PDF of the notes, access other learning resources, and get links to the latest versions of the notes and videos. Here is a link the course website: empossible.net/academics/emp6303/ See Solid State Electromagnetics in Topic 4. Hope this helps!!

[@u571lxx]

I like your explanation with plots or illustrations, which clarifies many headache theory in plain words.

[@drrehabhelmy5508]

i saw the previous lectures and that helps me alot to understand the FDTD , thanks alot.

[@MatthiasLehnen]

Thank you so much for these lectures!

[@empossible1577]

You are welcome!

[@soukainaes-saidi7236]

Hello, thank you so much for all the serie of videos. Theses videos are helping me a lot understand the real meaning of physical phenomena. Have you a course / video about Plasmonic band gaps ? and Brillouin zones of SPP coupled with grating ?

[@empossible1577]

I some sparse notes on SPPs, but not band gap SPPs. Sorry!!!

[@thetonmoy2]

extremely helpful

[@yuanhexiong2751]

awesome video. thanks very much:)!

[@behroozsemnani289]

It was great !!, thanks

[@osmanmertyilmaz5494]

Thank you so much for these lectures! But i dont understand that how to find transmittance. Could you please explain this?

[@empossible1577]

Happy to help! First, this is a very old video and obsolete. I have considerably revised this material. This topic is in my “21st Century Electromagnetics” course. You find it in Topic 4 “Periodic Structures” under the section “Solid State Electromagnetics.” I recommend accessing the content through the course websites because you will always have links to the latest versions of the videos, notes, and other learning resources. Here is a link: empossible.net/academics/21cem/ Second, to answer your question about calculating transmittance. To do this, you will need to develop a numerical method to run the simulation, or obtain commercial software and learn how to use that. I recommend developing your own code because you will learn a lot doing that. Getting started in computational electromagnetics (CEM) is an area I have developed a lot of materials. I found it difficult and frustrating when I did it myself as I had no guidance. One of the first things you will need to do is pick a first method to learn. Pick something that is simple and versatile. I think finite-difference methods are the best first methods to learn because they can do anything and are usually the simplest to learn and implement. Any other method will only be able to do it faster and more efficiently, but at a cost. The cost can be the methods are highly specialized or much more difficult to learn and implement. I think finite-difference frequency-domain (FDFD) is the absolute best first method to learn. In fact, I wrote a book to help complete beginners learn the art of CEM and I do this through FDFD. Here is a link to the book website: empossible.net/fdfdbook/ A close second best method to learn is finite-difference time-domain (FDTD). It is the time-domain brother to FDFD and the two method work incredibly well together. FDTD is like Thor’s hammer for simulation methods. When the problem is not possible by any other technical, people use FDTD. For small simulations, FDTD is generally slower and less efficient than FDFD, but still obtains good solutions. FDTD is best for big bad ugly problems or problems involving nonlinearities. For FDTD, I developed online courses intended for the complete beginner. There is currently a 1D FDTD and a 2D FDTD course. The 3D FDTD course is just a couple weeks away from being available. The 1D course is prerequisite of the 2D course and the 2D course is a prerequisite for the 3D course. Here is a link to the FDTD courses: empossible.thinkific.com/collections/FDTD-in-MATLAB Here is a video showcasing the contents of the 1D and 2D FDTD course: kzbin.info/www/bejne/q3PMoaV_g52anLssi=-tsnC04RtAXKdw4B I do offer a considerable amount of free content as well, but these are my notes and videos that I use for my face-to-face classes. Compared to the materials above, you may find these harder to follow and they also do not contain any MATLAB codes as I do that in person. Here are two links to my Computational Electromagnetics course and my FDTD course: empossible.net/academics/emp5304/ empossible.net/academics/emp5337/ Hope this helps!!

[@osmanmertyilmaz5494]

​@@empossible1577 First of all, thank you very much for your answer. I watched all your videos about band structures, including your new videos. I also calculated the band diagrams by finding the eigenvalues using PWEM. However, when I looked at the transmittance formula, I did not understand how to make the necessary calculations. I have eigenvalues and eigenvectors. There are also complete band structures. However, I could not find how to find the transmittance from these values. Could you please give me a perspective on PWEM and how to do this analysis with the values I have?

[@empossible1577]

@@osmanmertyilmaz5494 Happy to help. The PWEM as I have formulated it cannot calculate transmission and reflection. This is because it was formulated as an eigen-value problem where there is no source. The closest numerical method to PWEM that can calculate transmission and reflection is rigorous coupled-wave analysis. You will need to use that, or a variety of other methods, to simulate transmission and reflection from a photonic crystal.

[@osmanmertyilmaz5494]

@@empossible1577 thank you teacher. With your permission, I would like to ask one more question. You visualized Bloch modes in your video "PWEM-2D Full Band Calculation and Visualization of Bloch Modes" (kzbin.info/www/bejne/d4bImnqhmr19oLM). I want to make this visualization. Do you have a chance to explain the mathematical formulation here?

[@empossible1577]

@@osmanmertyilmaz5494 What part of this are you asking about? The MATLAB graphics calls or the math behind calculating the fields associated with PWEM? I think you are asking about the later. I have some notes about doing this in Lecture 6e in my Computational Electromagnetics class. empossible.net/academics/emp5337/

[@winnis88]

@CEM Lectures In the document posted on your website for this lecture (#7), slide 31 gives the impression that the the field remains perturbed after encountering periodic structure, while slide 33 gives the impression that the field go back to normal (single plane wave) after the periodic structure has ended. Could you please clarify?

[@empossible1577]

+_jp88 Nice catch. I cheated a little bit on those simulations on Slide 33. I adjusted the refractive indices outside of the lattice to match the external wave almost perfectly to the internal Bloch wave. The interference pattern caused by the ordinarily mismatched lattice I felt would be too confusing for what I was trying to convey. However, if the lattice is subwavelength, there can only be a single plane wave exciting the lattice. If the lattice is greater than a wavelength, then the external wave will diffract into multiple plane waves. There is a lecture somewhere on gratings and the plane wave spectrum that goes into a little more detail about this.

[@winnis88]

+CEM Lectures Thank you.

[@winnis88]

Do periodic structures made of isotropic materials give rise to only diagonally anisotropic structures? Or is there an example when a fully anisotropic structure be realized using just normal isotropic materials arranged in periodic fashion?

[@empossible1577]

+_jp88 Think of this way. All structures give rise to diagonally anisotropic tensors. This is because we live in a three dimensional world. Numbers only arise in the off diagonal terms when the structure is rotated so that it is being analyzed in a coordinate system that doesn't match the principal axes.

[@empossible1577]

+_jp88 Take a look at Lecture 3 here: emlab.utep.edu/ee5390em21.htm

[@winnis88]

+CEM Lectures Ah yes. I had forgotten! Thank you.