Lecture -- Electromagnetic Waves in Periodic Structures

[@andIam_IronMan]

I can't count how many times I said "Wow!". The animations were so amazing. I got so many concepts clarified. Kudos to you for making such complicated concepts so easy and understandable. Liked and Subscribed

[@empossible1577]

Thank you very much!!! I work on these videos almost every day, constantly improving! I appreciate you noticing!

[@ARodenas]

Dear Prof. Rumpf, I've been studying and working on PhCs for many years and this is, by far, the best ever basic explanation of PBG principles I've ever seen. Congratulations! and THANKS!!!

[@empossible1577]

Thank you!! This is great to hear!

[@zozozoli]

Not only you did just make me (who is a practical engineer guy and who get lost at the first pages of metamaterial books) understand the topic, but I enjoy your lecture so much, I can't thank you enough!

[@empossible1577]

That is awesome to hear!! Thank you!!!

[@RV_version2]

You are the Best!! Your videos and the animations are so helpful at explaining the idea. 1 animation is worth 10 textbooks! Thank you!!!

[@empossible1577]

I agree about the worth of animations and I am slowing making more and more. Thanks for the compliments!

[@yuhe7283]

Wonderful illustrations of profound concepts!

[@abdulrahmanmohamed8800]

I can't really express my true graditude and thankfulness to this amazing explanation

[@empossible1577]

Thank you!

[@shikharchandra1411]

Very neat animations and crystal clear explanations. Currently in my final semester of undergraduate studies and about to graduate, your videos have rekindled my interest in electromagnetic physics which I had during my classroom studies. Thanks for putting in the effort in making these videos Sir!

[@empossible1577]

Thank you!! You made my day!

[@rajatsharma6256]

This is awsome. Extremely helpful. Thank you very much.

[@mimArmand]

Very cool, especially with all the awesome diagrams and animation, well done.

[@empossible1577]

Thank you!!

[@shiqinghuang2981]

Best tutorials I've ever watched. Could you please explain the reasons why periodical structures form bandgaps, cause I learned what bloch-wave is, I also learned what band diagram shows, but, why, why can why periodical structures form bandgaps? Please.

[@empossible1577]

Thank you! Happy to answer your question. I address the reason for the band gap in Lecture 5c. Here is the link to the course website where you can get links to the latest version of the notes and videos and get access to other learning resources. empossible.net/academics/emp6303/ Here is the short answer. The modes in a photonic crystal are required to be orthogonal. This means they have to look very different from each other. The first mode places its energy primarily in the dielectric. The second mode has to be orthogonal so it places the majority of its energy outside of the dielectric. If you pick a wave vector where there is a band gap, both the first and second mode will have the same wavelength, but one has its power inside the dielectric so it will experience a higher effective index. The other has its power outside of the dielectric so it experiences a lower effective index. How can do waves have the same wavelength but experience different effective refractive index? They must be at different frequencies! This is the band gap.

[@shiqinghuang2981]

@@empossible1577 Thank you for the response, it's pretty intuitive but I am gonna need a while to digest, and I will definitely keep up with your tutorials.

[@baigao6062]

This video is so useful!

[@thonghchau]

Awesome, I will watch the lecture again. Now, I need to try some dizziness spinning to experience the analogy of wave vector and Poynting vector ^^.

[@jeffreygatlin2039]

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[@kingcamdyn7976]

@Jeffrey Gatlin Instablaster ;)

[@jeffreygatlin2039]

@King Camdyn thanks for your reply. I found the site on google and I'm trying it out now. Looks like it's gonna take a while so I will reply here later with my results.

[@jeffreygatlin2039]

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[@kingcamdyn7976]

@Jeffrey Gatlin glad I could help =)

[@denisbaranov1367]

Awesome. Are you going to make a video about scattering matrix and complex eigenmodes?

[@empossible1577]

Sorry I missed your message! That is weird because I respond to everything right away. I have made some comments about this in my waveguide videos and certainly my computational electromagnetic videos. Complex eigen-values simply means that the modes decay as they propagate. Here is the link to get to all of the course websites: empossible.net/academics/

[@sollinw]

BRILLIAAAAANT!!!! THAAAANKS! ILOVE U

[@empossible1577]

Ha ha. I love you too! 🙂

[@nguyenngo188]

Hi Prof, how can I find the reference from your video? I want to learn more about this calculation because it is too abstract for beginner like me.

[@empossible1577]

I don't really use any textbook for this class because there would be too many. I pull from many sources. Incase you are not aware, here is a link to the official course website that has the notes, links to the videos, and other learning resources: empossible.net/academics/emp6303/ Some years ago, I wrote a book chapter on this subject. That may be a good place to start. Here is a link to that chapter: www.sciencedirect.com/science/article/abs/pii/S008119471500003X If you want more advanced solid state theory, I recommend the Ashcroft/Mermin book on Solid State Physics. www.amazon.com/Solid-State-Physics-Neil-Ashcroft/dp/0030839939/ref=sr_1_3?crid=1DTY9KD1XIP8T&keywords=solid+state+physics&qid=1650288803&s=books&sprefix=solid+state+%2Cstripbooks%2C98&sr=1-3 Hope this helps!

[@nguyenngo188]

@@empossible1577 Thank you a lot for your materials.

[@empossible1577]

@@nguyenngo188 You are welcome!

[@anjalibhatia8843]

Prof, why does the power go normal to the isofrequency contour?

[@empossible1577]

I cover this subject in Lecture 1f here: empossible.net/academics/emp6303/ The short answer is that waves travelling in slightly different directions experience slightly different phase velocities. This happens in a way that the interference pushes power in a direction normal to the contours.

[@ignatiolu863]

I was wondering how can I implement a sinusoidal interface between to dielectric media into my grid using matlab.

[@empossible1577]

I think you are asking how to build a device on a grid that has a sinusoidal grating as the interface between the two? There are always many ways to do things, but I think the most straight forward is to first setup a loop that progresses from the left side of your grid to the right. Maybe it is something like... for nx = 1 : Nx2 end Inside that loop, calculate the sin() function and scale the value so you now how high it is on your grid. From this, calculate the array index ny for where the interface is vertically in your grid. Then, fill in your ER2 array something like ER2(nx,1:ny-1) = er1; ER2(nx,ny:Ny2) = er2; All of these calculations would occur inside of your loop. I have a set of notes devoted to different techniques for building device geometries into a grids. See Lecture 2b here: empossible.net/academics/emp4301_5301/ Notice I have used the variables ER2, Nx2 and Ny2 implying this should be done a 2x grid. Hope this helps!

[@anjalibhatia8843]

And, having chosen a direction, is it never possible to have a transmission band, rather than discrete transmission frequencies?

[@empossible1577]

Yes, you can have continuous spans of frequency that transmit through a lattice. The horizontal axis of a band diagram varies over direction and wavelength. If you pick a direction, while the bands are discrete there is a span of Bloch wave vectors that have different wavelength, but all have the same direction. This leads to the span of frequencies I think you are talking about.

[@anjalibhatia8843]

Oh! OK. Thanks

[@DeisonPreve]

What about a matlab lesson about these??

[@empossible1577]

I can't believe I missed your message about this! I recommend checking out my computational electromagnetic courses: empossible.net/academics/emp5337/ empossible.thinkific.com/bundles/1d-2d-finite-difference-time-domain-with-matlab

[@hamidk4772]

Outstanding ^n