Lecture 3h -- Phase Matching & Special Angles

This lecture explains refraction through phase matching instead of Snell's law, and then goes onto to discuss the critical angle and Brewster's angle.

[@mustafakarabiyik]

I have taken various optics, photonics, waveguide, nonlinear optics etc. courses and this is the best-visualized lecture I have ever seen. Really good job.

[@empossible1577]

Thank you!

[@tensorbundle]

You explain very well! Thank you

[@mohammadabdulshukoor7783]

Excellent visualisation of the evanescent fields... Clearly understandable...Thank you for you support prof

[@empossible1577]

Thank you!!

[@fuzzyelectrons]

The visualisations in this video were just brilliant. Thank you so much for putting the time and effort into making this video - and all other ones.

[@empossible1577]

You are welcome!

[@hamsterpoop]

This is excellent! Thanks for the lectures! In this case you are using a plane wave approximation. What would this look like for spherical waves?

[@empossible1577]

Each part of the plane wave is incident on the surface at a different angle so it would reflect at a different angle and also reflect by different amounts. I am not sure there is a way to do this analytically all at once.

[@ZamirWani]

Such a great lecture on the transmissions of fields through a layered isotropic dielectric medias👍🏻 What happens when the second medium is an anisotropic medium, have you any lecture or material. Please help Sir! Your field animations are amazing

[@empossible1577]

I do not have any specific lectures on anisotropic layers, but there are many things that can happen. The main thing is that there may not be any clear TE and TM modes as they become coupled. The case is more difficult to analyze as well. If you want to simulate anisotropic layers, I recommend the transfer matrix method (TMM). I teach this technique in my Computational Electromagnetics class. Here is a link to the course website: emlab.utep.edu/ee5390cem.htm I develop the method for isotropic materials, but I do point to how to generalize the method to anisotropic materials.

[@storytellers2345]

If the wave gets compressed in the high index medium, Does it mean that the light will appear as a different color if we imaged it within the second medium. Let’s say for that matter if a red light is impinged on to a high index medium (glass) from air, should we see a color change of the light when it is traveling in the glass medium?

[@empossible1577]

No. This is because when the light leaves that medium to enter a detector and get absorbed, it is back to the original color. I think it is best to think about color being most fundamentally associated with frequency instead of wavelength.

[@meghjitmajumder3468]

Again thanks for another outstanding lecture!! Especially I was very happy after learning "The Phase Matching" concept. But then again like in most of the cases, I've something to ask as well as say... 1. As I've said earlier, snapshots are not at all useful and I guess you know the reason(in fact, you gave me the explanation in the previous video.I just mention it again just because to remind you that this thing you should consider about in your next videos.) 2.Evanescent Field: I)Would be great if you discuss something about waveguide's evanescent mode also II)You said, "Above the critical angle, penetration is greatest near the critical angle." So should we excite a waveguide right at its cut-off frequency or slightly at a higher frequency? III)"Very high spatial frequencies are supported in material 2 despite the dispersion relation" I didn't understand.

[@empossible1577]

As I revise the slides, I will do my best to make the animations understandable in PDF format. This is good advice! 2.II It is possible to excite waveguides near their cutoff. This is generally not done because the waveguides are very dispersive near the cutoff and signals get distorted. 2.III From the pictures, notice that when a wave is cutoff it still penetrates into the second medium a tiny bit. Therefore, there are still very rapidly varying fields present in the second medium (i.e. high spatial frequencies).

[@meghjitmajumder3468]

@@empossible1577 Thanks Sir

[@dobirhossain3406]

Outstanding lecture and learn a lot from this. Thank you so much. It has been explained that there is no reflection in TM polarization at the Brewster angle, completely TE Polarization. Can I get in the details about it, please?

[@empossible1577]

What details are you looking for?

[@dobirhossain3406]

@@empossible1577 Thank you. Maybe I am wrong. At the Brewster angle, the wave reflected from the surface is entirely TE polarized, the TM component is zero. You mentioned that it is because of the permittivity difference between the materials. My question is, why is TM component zero when there is some permittivity difference?

[@mishuk2008]

I highly wish for once you teach a nonlinear optics course. It will be interesting!

[@empossible1577]

Some day. The closest thing I have is Topic 2 in my 21st Century Electromagnetics course. Specifically, Lecture 2h. empossible.net/academics/emp6303/

[@fuzzyelectrons]

At slide 16 around 21:14, I think you have a small bug: Since n1 > n2, the wavelength should be shorter in the top material than the bottom material. The slides are showing the opposite.

[@empossible1577]

Are you referring to the slide titled "Field Visualization for theta_c = 45 deg?" If so, the slide appears correct to me. On this slide, you are looking at a field on the transmitted side that is either very near cutoff or past cutoff. In this case, the field will have the same wavelength only because it is propagating very nearly parallel to the interface. However, the second medium cannot support such a fast period so the wave is cutoff. Notice you do not see any ripples in the vertical direction. In the horizontal direction you do see oscillations with a wavelength that might seem to be impossible, but that is how a cutoff wave appears. Boundary conditions require that the field be continuous across the interface so it must happen. I think it is very interesting that the wave does actually penetrate some into the second medium even though we say it is total reflected. The evanescent field services as a temporary holding place for field energy that eventually leaves as a reflected wave. Here is another way to think of it...if the field did not actually penetrate into the second medium, how would the field know what was in the second medium in order to know to totally reflect?

[@fuzzyelectrons]

@@empossible1577 But you have a higher refractive index in the top material, wouldn't that imply a shorter wavelength? In each of the four pictures, there's this lambda to the right, indicating that the wavelength is longer in the top material. Now I'm getting a bit confused!

[@empossible1577]

@@fuzzyelectrons Oh dang! How did I miss that? You are correct!!! How embarrassing! LOL I will fix this. Thank you!

[@empossible1577]

@@fuzzyelectrons I have made the corrections to the notes, but not the video. Next time I record the video the correction will be in. You can get links to the latest version of the notes and videos and lots of other learning resources from the course website: empossible.net/emp3302/ Thanks again!

[@fuzzyelectrons]

@@empossible1577 Haha, no worries! I'm glad I could help. :-)