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Jokes like that get you promoted around here.

There is a dot product happening...beta dot r. The dot product of two vectors is a single scalar quantity. Maybe the symbols got messed up in the video render. I will have to check.

No my area, but I suspect just the scalar part I have been showing for EM.

Great question! I was waiting for somebody to ask this... When the iron filings are exposed to a magnetic field, a few things happen. First, like a compass needle, the filings align themselves to the direction of the magnetic field. Second, the filings themselves become magnetized and will attract other filings. Third, the magnetized filings link to each other to form lines. If you want some evidence in this experiment that the magnetic fields lines do not exist, notice when you do this experiment the lines of the filings do not move (unless you shake very hard). However, if you repeat the experiment, the filings form lines in different places. If magnetic field lines really existed, the filings would form the same lines every time. Hope this helps!

@@empossible1577 Thanks for the reply, but I think your answer cannot be correct. Those lines have been the subject of a lot of study, they used to be called "Faraday Tubes" which I really like. But what about a ferrocell? Also, you can do this experiment: use a sensitive microphone and move it through the field of a magnet and hear the static of the field lines, so the point is, there are other ways of detecting those lines other than metal filings so the lines are not the result of the filings themselves becoming magnetized (even if the filings become magnetized, that doesn't explain why they form lines). IMHO ... a magnet field does not exist in a field vacuum, there are many fields around us all the time, including from the planet itself; and the field lines manifest at the constructive/destructive regions of field interference (like a double-slit interference pattern). Also, with large solar eruptions you can clearly see the magnetic field lines visible in the solar plasma. So, I think it is pretty difficult to say that the lines of force do not exist? It's like if I say shadows do not exist, and you say sure they do there's one right there, and I say okay go get me a cup of that shadow so I can take it to my lab and analyze it. Shadows don't exist as principle first-order things, they are an effect from an object blocking light; in the same way field lines of force can be observed in so many ways, they unequivocally do exist, and I believe represent an interference pattern created within field.

I don't think it would get accepted. What I am presenting here is not new or novel. It is just something not discussed or attempted very often because the graphics is very difficult!

Thank you!

Thank you!

Glad you liked it!

I am supposed to be some kind of expert, but I honestly do not know. I am leaning about 60% toward electric and magnetic fields not being physical things. I wish I had a better answer for you!

I have not looked into it much to say anything for sure. But, the few EM phenomena I have looked deeply into can be explained just through Coulomb's law and relativity. I am taking a leap to say all EM phenomena can be explained the same way. However, if this were true it makes me question the objective truth about the existence of E and H fields if they are not needed to explain our observations. If I had any free time, I would dig more deeply into this. Thanks for your comment!

@@empossible1577 haha yes exactly! It seems to me that saying a field is created and then propagates away at c is equivalent to saying the charge distribution changes and then the "state update" is propagating through space at c (weirdly, at a fixed time I think...) The later may be less practical, but seems more intellectually (maybe aesthetically?) pleasing. There's just one force, plus relativity. Thanks for your comment back, I'm kind of the quack at work on this so hearing your thoughts makes me feel like I'm maybe not so off base...

@@Superfungus0 Take pride in being the quack. That is me in every aspect of m life! 🤣

Thank you! My research group is actually developing a ray tracer for simulating metasurfaces right now. That may motivate some videos in the future.

Did I say weight was a scalar? Woops! Thank you!

Thank you! Glad to hear the materials are helping people!

Thank you for the compliment! It is always great to hear this!

No, but that would be cool! The velocity of light is actually a more complicated subject than you may think. For example, which velocity are you asking about, phase velocity, group velocity, or energy velocity? From your equation, that is phase velocity, but it is not exactly correct as you have written it. The more rigorous and intuitive way to calculate this is to first calculate the complex refractive index n = sqrt(ur*er). Second, the phase velocity is v = c0/Re(n). The real operation Re() gets rid of the imaginary part that characterizes loss. BTW, phase velocity can exceed the speed of light in vacuum. The speed of a wave in a rectangular metal waveguide is the classic example of this.

@@empossible1577 thank you for your detailed reply! Metamaterials can have effective properties near zero making nearly infinite phase velocity. Did I understand your video correctly that the group velocity can be made to refract based on the effective properties?

I thought group velocity was the same as the energy velocity. Have you made a video covering differences?

@@egghead55425 Yes. You can predict refraction with effective properties. Remember, phase and power can refract differently! Crazy, huh? The planes of equal phase will refract one way and the beam itself can refract in a different direction. Negative refraction in a photonic crystal is a classic example of that. This is not due to negative refractive index.

They are usually not used and waveguides are most often designed to support only a single mode. That is because the different modes propagate at different speeds and this distorts signals. However, that is not what you asked. There are multimode optical fibers that support hundreds or thousands of modes. It is not so much that the higher order modes have a specific purpose. It is more that it becomes much easier to get light into and out of them. Single mode optical fibers require much more precise alignment. Some people are researching using each mode as a different information channel, effectively extending the bandwidth of a waveguide. The real challenge here is that any imperfection or discontinuity in the waveguide tends to scramble power between the modes, causing cross-channel interference. The fifth (or sixth?) mode of a cylindrical metal waveguide has an azimuthal polarization that propagates with minimal loss. This is used for very high power waveguides and is called and “over moded waveguide.” There are some sensors that make use of coupling between the various modes in a waveguide. Look up “turn around point long period gratings” for one interesting example of this. I am sure there are other applications for the higher order modes that I am not thinking about. Hope this helps!

Any time! 😀

Great to know! My experience with these types of materials is that they are expensive, temperature sensitive, lossy, and highly dispersive (i.e. properties change abruptly with frequency). I don't know specifically about this one. In general, mu=eps materials are very interesting!

@@empossible1577 Z-Phase Hexaferrites are not dispersive or lossy but they are very expensive! Reflection losses are minimized by matching the characteristic impedance to air, but the Brewster angle gets closer to 90 degrees. There are other materials which have much higher indices of refraction with permittivity=permeability at low loss which have recently published. We're able to shrink an antenna/lens by a factor of 10 to 20 while maintaining high efficiency and soon at low-cost!

If you are interested in learning finite-difference time-domain (FDTD), we have a complete free course on the method here: empossible.net/academics/emp5304/ Unfortunately, these are the notes I use when I teach face-to-face so they do not include codes and may be difficult follow. If you want incredibly high-quality instruction along with line-by-line explanation of the code in MATLAB, checkout these online courses on FDTD: empossible.thinkific.com/collections?category=FDTD-in-MATLAB Here is a link to a video showcasing the contents of the 1D FDTD and 2D FDTD courses: ruclips.net/video/uBiprIN8gfY/видео.htmlsi=nrbHirpBctXyqqJ8 Hope this helps!

Pozar is good but you are better

Thank you so much!!! It is great to hear the materials are helping people!

The analysis here assumes the waveguide is uniform along the z direction. It is much more complicated to analyze the case of a discontinuity. In general, any discontinuity will introduce reflections. There are techniques for designing bends and other things while also minimizing reflections. The reason for the reflections is this. At a bend (or other discontinuity), the guided modes change their properties. Continuity of the field requires the tangential components to be continuous. If suddenly the modes change what they look like, there will have to be scattering and/or scrambling of power between the modes to satisfy the continuity of fields. This is important to understand because it is the origin of some ways to mitigate the reflections. For example, think of a horn antenna. The taper smooths the transition between a guided mode and propagating wave.

That derivative was already performed and is the reason the kc parameter appeared. You need to watch the videos leading up to this video because some work was already performed. I recommend accessing the content from the course website so that you can see the organization and get links to the latest version of notes, videos, and other learning resources. Here is the link: empossible.net/academics/emp3302/ I recommend working through Lectures 9a-9h before this video. Hope this helps!

That is awesome to hear! I hope it helped!

For waveguides, I think it is most proper to call them guided modes. I am not entirely sure what a "propagating mode" is. Maybe in a something like a photonic crystal with a band gap you would have propagating modes and cutoff modes. That is just a guess as to what is meant by "propagating mode." If it came up in the context of waveguides, I would probably interpret that is the same as guided mode.

@@empossible1577 Thanks for the clarification, I read thru your reply and I think you're right about not having heard much on "propagating modes" in opposed to a "guided mode" ... most probably was a misnomer from a memory of a conversation that I had a few years back with my graduate advisor in an around the topic. Would you comment a bit on the "cut-off modes" in a photonic crystal? or point me to one of your lectures in which you discuss them. Thanks,

@@rattinyou Modes that are cutoff in waveguides, photonic crystals, or even free space waves (think total internal reflection) all occur with the same physics and properties. Those modes still exist. It is just that they decay quickly. If your photonic crystal slab is thin enough and the cutoff mode does not decay all the way, it will excite a propagating mode on the other side. This is called tunneling. It happens in waveguides, free space waves, and electrons in semiconductors. I don't have much information specifically on the cutoff modes, but all of the advanced topics are covered in my 21st Century Electromagnetics class. here is a link: empossible.net/academics/21cem/ You will find photonic crystals in the Engineered Materials topic. I highly recommend going through Topic 4 first.

@@empossible1577 Thanks Prof. Rumpf, this was quite helpful, I'll follow through with your suggestions.

Thank you Mr. President!

Hmmm...Let me think about that. I suspect your answer lies in the discussion of boundary conditions.

Maybe I could have been more clear in the video. Sorry. Imagine time was frozen and you scanned through the waveguide. That is what you are seeing, not a moving wavefront.

It is great to hear you are getting a lot out of the videos! Thank you!! I think the best way to understand the frequency response of conductivity is through the Drude model. This starts by modeling charges at the atomic scale like a mass on a spring. This is called the Lorentz oscillator model. In conductors, charges are free so the electrostatic restoring force is set to zero and the Lorentz model reduces to the Drude model. As frequency goes to zero, the dielectric properties approach infinity. To learn about this, along with lots of visualizations, checkout Topic 2 in “21st Century Electromagnetics.” Here is a link to that course: empossible.net/academics/21cem/ Impedance is a complex number because it relates the amplitude and phase of the electric and magnetic fields. Without loss (i.e. conductivity), impedance would be purely real. So conductivity absolutely affects impedance. You are watching the correct video about this. See slide 15. You will see conductivity affects both magnitude and phase of impedance. While on this subject, let me point you to the official course website where you can download the notes, get links to the videos and other learning resources. The notes are ahead of the videos in terms of revisions, corrections, and improvements. You are watching a video in Topic 6. Here is the course website: empossible.net/academics/emp3302/

@@empossible1577 Thank you for the response, I will check the resources and try to gain enough knowledge and intuition before I proceed with the online courses. Again I am truly grateful for your effort and dedication to create these videos and also for sharing your astonishing knowledge and experience!

I do not think I am following your question exactly. If by "near side" you mean the other port on the same side as your input port, that typically would not show any power. To get power to that port, there would need to be reflection. It is called directional coupling because the wave keeps moving forward. It is just that the power will transfer between the lines periodically. I am not sure if I answered your question or not.

@@empossible1577 I think you described the very thing that my intuition would (also) expect, but this is the opposite of what actually happens. Let's refer to 6:40 and the coupler on the left side of the slide. If I were to attach a signal generator at 1.83GHz, 0dBm to the In port and terminate Out and Rev ports, I would see about -15dBm at the Fwd port. If I then terminated the Fwd port and monitored the Rev port, I would see -35dBm or something due to leakage and imperfections. In other words, the labels on the board match my experience when taking measurements but they are the opposite of what my intuition says should be the case. I am therefore trying to recalibrate my intuition to match experiment.

@@jjoonathan7178 Hmmm...I wonder if the sharp bends are using reflections to behave how you are saying. Looking at the chamfers, I assumed not. I've simulated tons of things like this, but not that specific design so I guess I cannot say for sure.

@@empossible1577 I just uploaded a video on my channel measuring one that was easy to open (not sure if links are allowed). I don't think it's an artifact of bends or chamfers. It seems to be a thing with coupled-line couplers in general, at least microstrip / stripline / suspended line: all my Krytar and Marki and Anritsu and HP couplers work this way. Near port is coupled, far port is isolated, and this happens even if the thru line has no bends or chamfers like on my Krytar couplers. I can't speak for waveguides. But yeah, what happens is the opposite of what my intuition says should happen, and I've long wanted to clear that up.

Hmmm...I am having trouble picturing what you are saying. To plot the vector fields, I generally use the quiver() function in MATLAB. That is notoriously difficult to use because I use it infrequently enough that I always forget how I got it to work the last time. I usually comes down to the order of X and Y and transposing Ex and Ey in some combination that I always forget and have to figure out again. Can you email me pictures of what you are describing?

@@empossible1577 Yes! I've just now emailed the emprofessor email

@@chasenewberry4357 I replied to your e-mail. Nothing appears to be wrong with your code, but I did suggest some better habits in a few places. Overall, the problem with your plots is how you are setting your color axis limits. The Ex and Ey fields have negative and positive numbers, but your color axis limits will only allow MATLAB to show the positive numbers. I fixed this and your code appears to get the correct result.

@@empossible1577 I received the email and implemented the changes, thank you so much for your help and feedback!

I do not have all of that, but I do have some . Take a look at Topic 7 here: empossible.net/academics/21cem/

Thank you!

For optical frequencies, the short answer is lithography. The longer answer is that there are now also digital manufacturing means such as multi-photon lithography that can make them.

I suspect there is, but I am not aware of it and never looked. With pretty high confidence, I can say the effects will be negligible until those bevels become very large. The power in the mode is far away from the corners so a modest level of rounding would not have a significant effect. Is there a reason you want an analytical solution instead of numerical?

@@empossible1577 Pursuit of beauty, truth and inner meaning of nature perhaps? No, just idle curiosity. I'm manufacturing a series of waveguide to coax transitions for 5.7, 10, 24 and 47 GHz and it appears that for the finished parts, the difference between square corners and a radius has almost no impact other than making the machining simpler. I wondered if there was some deep reason for the results I found and modelled, but I guess it's as you say, in TE10 the energy in the corners is minimal. I'm using OpenEMS FDTD but I just bought your book so I'm looking forward to trying the freq domain approach as well

@@MachiningandMicrowaves I would love to hear your opinion of the book. I have an entire chapter devoted to waveguides.

Glad they are helping you!