Lecture -- Concept of Diffraction From Gratings

[@baigao6062]

Finally I understood what is grating!!!! Thank you sooooooo much!!!!!

[@empossible1577]

Great to hear!

[@parnikagupta1624]

Awesome! It's an in depth analysis

[@empossible1577]

Happy to help!

[@a.vanwijk2268]

What you are saying (between 3:50 and 5:17) basically is: when troughs and peaks align there is light, when they don't there's no light. This is known as constructive and destructive interference, I don't know about your students, but I would imagine most of them have heard that term before. If anything, it wouldn't hurt to introduce these words. After 5:17 the physics become sketchy. A cartoon of Huygens wavelets would be more correct and in the end it comes down to optical path length. In this animation, it seems to me, when the waves align, the screen will be lit evenly from left to right. Fortunately, students will probably remember the cartoon at 12:00, since that comes last :-) Perhaps the array is best ignored here (I meanthe 5:17 thing), then it is just a really nice thought/animation experiment. One last thing to be complete; imo lobes are the measurement results, whereas orders are theoretical in a sense that you can design for a specific order, but lobes just describe the intensity variations that result from an experiment and they appear both on a flat screen and a circular one. Sorry for being a bit nit-picky, but it's easier to learn than to unlearn, right?

[@a.vanwijk2268]

Interesting way of explaining this phenomenon. Personally I wouldn't talk of "allowed" and "not allowed", but rather explain what is physically going on. After all it's not quantum. I wonder what book goes with these lectures, I bet it's not Hecht. The second part about the tripartition is really good stuff.

[@empossible1577]

Thank you! I could perhaps have used better words. I will think about that if I ever rerecord the video. I don't know of any book that covers diffraction gratings very well. Actually, I have never scene diffraction grating described the way I am describing them. I wish I had them taught to me this way a long time ago!

[@koktszfung]

10:50 that sounds just like a random walk! I wonder if that is related to the bell curve envelop of the grating intensity

[@a.vanwijk2268]

Well, it's clearly not random.

[@anywallsocket]

Yeah you're totally right. The Galton board simulates the probability distribution of 'random walks', and you can accomplish the same sort of thing as 'adding redundancies' and 'subtracting differences' by taking an average square. If you compare this as well to Feynman's path integral formulation, you will see there that paths of similar time add, and paths of different times subtract - there is no difference here other than phase is now time, and classical is now quantum. Again, you take the square to get the probability distribution, which will be a bell curve distribution for a symmetric system. You can also make the connection via a simpler route by realizing what's being discussed here is optical dispersion, and that if you have a clump of walkers in 2 or 3 d, over time they will disperse radially (a bell curve of density).

[@maryamfaheem1326]

How do we define this period of a grating or period of any structure?

[@empossible1577]

Think of the grating as a tile pattern. What is the smallest piece of that pattern that you can stack onto itself to perfectly reconstruct the entire grating. That is one unit cell of the grating and its width is the period of the grating.

[@maryamfaheem1326]

@@empossible1577 thank you very much for the reply.Your lecture was very informative.I have learned so much from this video in such a short time

[@empossible1577]

@@maryamfaheem1326 Thank you!!! Here is a link to the course website if you want to see the lectures before or after this one. empossible.net/academics/emp6303/ This video is in Topic 4.

[@maryamfaheem1326]

@@empossible1577 thank you very much for sharing the link.I will definitely watch all the videos related to this topic :). Stay blessed and keep up the good work,sir.

[@rabiulislamsikder344]

In slide 4 in the dielectric function how the term del*epsilon*cos(K*r) came? What grating vector actually implies in the grating structure?

[@empossible1577]

I do not see any equations on Slide 4. I think you are referring to slide 8? The expression for eps(r) just comes from intuition. The relative permittivity of a ruled grating is expressed as some average permittivity plus a varying permittivity of contrast Del_eps. The varying function is cos(K*r) where K is the grating vector. A grating vector is a vector, so it carries two pieces of information. First, the direction of K defines the direction of the grooves. It points perpendicular to the planes (or lines) of the grating. Second, the magnitude K defines the period or spacing of the grating L. The magnitude is actually 2*pi/L. This maybe strange definition lets the variation be calculated with just cos(K*r). The grating vector K is analogous to a wave vector k.

[@rabiulislamsikder344]

@@empossible1577 thanks for your reply

[@ngavu4997]

Do we have other equation of varied relative permittivity? I mean for other periodic surface, is periodic permittivity dependent on the structure of grating?

[@empossible1577]

For the grating equation, the expression used for the permittivity only required that it have the correct period. If the permittivity profile looks completely different but has the same period, the possible diffraction orders will remain the exact same. Changing the permittivity profile will only change how much power gets coupled into each diffraction order and it requires a solution to Maxwell's equations to figure that out. Determining the direction of the possible diffraction orders can be done completely analytically.

[@ngavu4997]

@@empossible1577 thanks a lot for your reply. Can you give me the solution which is how to use Maxwell’s equations to calculate the coupled power on each order? Thanks

[@ngavu4997]

@@empossible1577 sorry, what do you mean “permittivity profile” and how can it change the coupled power for each order?

[@empossible1577]

@@ngavu4997 By "permittivity profile" I mean what the grating actually looks like. As a wave enters the grating, initially it is still just the applied wave. The grating works to gradually couple power from the applied wave into the diffraction orders. What the grating actually looks like controls how quickly this happens and which diffraction orders end up with the most power coupled into them. I cannot look at a diffraction grating and make any kind of intuitive guess about how much power ends up in each diffraction order.

[@empossible1577]

@@ngavu4997There really is no simple equation to use to figure this out, although you may be able to find some approximate equations for simple gratings in the older literature. Instead, you will have to solve Maxwell's equations by simulation. There are many ways to simulate a diffraction grating and don't be too paranoid about picking the absolute best method. They will all get you the correct answer. Certainly rigorous coupled-wave analysis is one of the best and fastest ways to simulate a diffraction grating, but it may be a little challenging to learn and is a bit more cumbersome than other methods for visualizing the fields and simulating things other than diffraction gratings. I personally recommend learning finite-difference frequency-domain (FDFD) as your first numerical method. It is extremely versatile and the fields are easily visualized. The main drawback is its efficiency. RCWA can simulate a diffraction grating in 10 microseconds whereas FDFD might take 100 milliseconds. If you don't mind waiting an extra 99 milliseconds for your answer, you will love FDFD. Here is a website that teaches all of these methods: empossible.net/emp5337/ For FDFD, I have a book coming out soon that teaches this method and caters to the beginner. This will be the official book website: empossible.net/fdfdbook/ Hope this helps!

[@anywallsocket]

he was driving his tesla the whole time

[@empossible1577]

?

[@anywallsocket]

@@empossible1577 Haha, I was making a joke about the noise in the background. It seems to rev up and down like a Tesla. Thanks for your videos btw, very helpful :)

[@empossible1577]

@@anywallsocket I am a poor college professor who cannot afford proper recording equipment! :-( The sound used to be worse. I had a computer with a really loud fan. When people asked, I told them I was recording from an aircraft carrier. LOL

[@anywallsocket]

@@empossible1577 That is as heartwarming as it is depressing. Especially since I'm a physics grad student interested in teaching, but concerned about being poor lol. I respect the honesty though, very much.