Thanks for the lecture! I do not understand slide 9 on TE and TM mode. Why we analyze magnetic field only for the TM mode? TE and TM mode just different in electric direction, why we do not analyze and compare electric field energy for TE and TM mode? Why magnetic field has anything to do in this analysis on dielectric constant?
Good question! First, the labels "E Mode" and "H Mode" come from my computational electromagnetics courses and is not an industry standard label. If you want more information on that, you may be interested in my book... empossible.net/fdfdbook/ There many different definitions for TE and TM and each leads to different configuration of fields. The short story is that when I see things called "TE" and "TM," I will not immediately know what people are talking about. Be careful with those labels. Now to answer your question. Mathematically, it is possible to express waves completely in terms of just the electric field or just the magnetic field. What I am showing as TE here can be expressed completely in terms of the electric field E, thus the title "E Mode." What I am showing as TM here can be expressed completely in terms of just the magnetic field H, thus the title "H Mode." That is why I analyze these just in terms of either E or H. By the way, I have completely revised and improved the notes for this section. You can find them on the course website that I recommend you use as your main portal to this information. empossible.net/academics/21cem/ Unfortunately, I have not yet re-recorded the videos, but definitely checkout the notes! Hope this helps!
Can/are sub wavelength gratings be used for imaging purposes (i.e., holography)? If yes, what would be the benefit (apart from introducing polarization capabilities)? For the actual image formation ad distance d, I would argue that any feature smaller than the wavelength cannot be propagated from the grating because planar waves describing them will be evanescent by definition.
Grating couplers are often used in holographic glasses to transport light between the source, detector, and eyeball. These are subwavelength to external light but not not internally where they diffract. Otherwise, I am not entirely sure where/why they would be used but I suspect there are applications. A good friend has a book coming out soon on holography and he will have examples and even computer codes about this. Hope this helps! -tip
Thanks a lot for your lecture. It is very informative. Could you give me the reference of some equations that you give in slides like anti reflection layer? Is it right that 1D grating profile containing two dielectric slabs lie alternately, which i mean in fabrication process?
Thanks a lot for these great videos. I have a question on the antireflection layer: why the tapered grating has better performance than binary grating in broadband case? how to design it? Thanks for your help.
The taper is a smooth transition. For design, you can take one of two approaches. First, you can just do any sort of taper. Just about anything works pretty well. Second, you can spend a lot of time optimizing the taper and get a little better performance from it. Unless you really want to improve the angular response, I recommend just incorporating any sort of taper that is maybe 1 to 2 wavelengths large.
On slide 5 you have the figures on the left labeled "Parallel Polarization", but in your dialogue you call that "Perpendicular Polarization". Vice versa for the right figure. Which one is correct? Your slide labeling, or your dialogue?
Sorry if I misspoke! For polarizers, diffraction gratings, and subwavelength diffraction gratings, polarization is defined as the electric field relative to the grating vector K. The grating vector K points in a direction perpendicular to the grating grooves. The TE polarization has the electric field transverse to K which means parallel to the grooves. The TM polarization has the electric field parallel to K which means perpendicular to the grooves. It is very easy to get the words mixed up! Sorry!
If i have a structure of discontinuous arrays of silica with 100 nm period which is 10 nm thick and i hit it with 300 nm em wave, what will happen? Will it diffract? Is it subwavelength?
Would the concept of the spatially varying polarization, say linear to radial, using the form birefringence device, be applicable to EM waves in the microwave region, or would this effect only occur in the optical region? Also would the parameters such as spatial period, and duty cycle scale over in to the microwave region? Great lecture btw.
Thank you...and yes! Electromagnetic waves all behave the same way from radio frequencies to microwave to optical to x-ray frequencies because they are all governed by the same equations, Maxwell's equations. The only reason there are any differences is because the properties of materials can be quite different at different frequencies and the different size scales may limit what we can and cannot built. There is a concept that you eluded to called "scalability." If you find a device of size L that does exactly what you want at frequency f1, you can make it operate at frequency f2 by scaling all dimensions by f1/f2. Very often this leads to devices that are not of practical size when you scale from optical to microwave frequencies. Also, at microwave frequencies, metals exhibit much lower loss so you can often make much smaller and more compact devices than at optical frequencies where metals tend to be avoided as much as possible. BTW, if you are interested in the spatially-variant stuff, take a look at this short course: emlab.utep.edu/scSVL.htm Hope this helps!!
Thank You very much. This is exactly what I have been looking for. I've tried to read some of the literature on space-varying polarization manipulation and PBOE's and the concept of geometric phase kept appearing. It sounded like the geometric phase has to do with light at the photon level but with microwaves I'm not sure if it makes sense to talk about photons.
I am not sure what all you are reading, but space-varying polarization probably refers to the polarization changing as a function of position throughout the cross section of a beam. These are hard to create naturally so we create a linearly polarized beam and convert it to whatever we want using something like a form birefringent wave plate. It does make sense to talk about microwave photons, but it is not that meaningful. The particle nature of a photon is proportional to the wave's energy. The wave's energy is proportional to frequency. Microwaves have a frequency that is orders of magnitude smaller than light so the particle nature of microwave photons are orders of magnitude less significant. Regardless, the particle nature of waves is not needed at all to understand polarization and wave plates.
I see...the material I was reading was called 'Excitation of a single hollow waveguide mode using inhomogenous anisotropic subwavelength structures', and this is where the concept of the geometric phase was mentioned. Regardless, i'll look into your course for spatially varying lattices.
great explanation!!...i have one question. How can one find the effective refractive index of a multilayer (3 layers of different materials) grating? Thanks!
Are you talking about when the layers are along the direction of propagation, like a multilayer film? If so, this doesn't really fit the model of an effective medium unless the layers are very subwavelength. The best way is probably through a simple parameter retrieval. See Lecture 15 in EM21. Also, not sure if you knew it, but you can download the electronic notes for these classes here: emlab.utep.edu/academics.htm
Thank you so much. I didn't know about the notes. Actually I was asking about the grating with coated layers (on material coated on the top of the other) so that we have 3 different material layers in the grating groove height i.e. perpendicular to the grating period axis.
Mahesh Kumar Okay, so instead of a binary grating you have a grating made of three materials. If this is correct, you can derive an analytical equation for this pretty easy. This is what you need to do... emax = f1*er1 + f2*er2 + f3*er3 where f1 + f2 + f3 = 1 are the fill factors. 1/emin = f1/er1 + f2/er2 + f3/er3
At ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-bkLPAL_RLUc.html Why does the length has to be equal to 1/4 wavelength and what happens if you make it shorter or longer? I understand that 1/4 wavelength thickness is good if you want to achieve destructive interference, but I believe that here the goal is to match the effective refractive index closer to that of air, such that the wave essentially penetrates the material instead of reflecting at its interface. Thanks for your help and thanks for this great video!
Great question. First, let me point you to the official course website which has links to the latest videos, electronic notes, and much more. empossible.net/academics/emp6303/ In fact, there are other thicknesses you can choose to get zero reflection. It is just that the quarter-wavelength is the easiest solution and works well. If you want to see a detailed derivation that also identifies how to get other solutions, checkout Lecture 7f Multiple Scattering here: empossible.net/academics/emp3302/ If the wavelength deviates from the design wavelength, reflection is no longer zero. However, there is usually a range of wavelengths where the reflection remains relatively low. If you want zero reflection over a broader range of wavelengths, there are antireflection coatings that have multiple layers.
