Lecture 3b -- Wave Parameters

This video discusses the parameters we used to describe electromagnetic waves including speed, frequency, wavelength, wave number, refractive index, and impedance.

[@Mohabpiano]

I am currently PhD student and I reviewed this material many times before. Never have I come before a more concise and informative and engaging explanation. Thanks a lot Prof. for making these available here!

[@empossible1577]

Thank you very much!!! I love hearing the materials help people!

[@hjalmarschacht2559]

The BEST description of the wave number / wave vector I've seen. Thank you very much.

[@empossible1577]

You are very welcome! Thank you!

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@Justin Major instablaster :)

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[@jesseinfinite]

This lecture is just phenomenal. I've seen these expressions so many times, but this is the first time I'm seeing all of them connected so beautifully and bringing out the intuitive nature of the "intuitive parameters"

[@empossible1577]

Thank you very much for sharing your thoughts!!! I work hard on the materials and I love hearing how they help people!

[@stevemackay8082]

Dear Prof. You have an exceptional ability to relate the hard reality to intuitive concepts. Thank you hugely. You should be referred to as the Philosopher Prof of Electromagnetics.

[@empossible1577]

That is awesome to hear! You have made my day! Thank you!!

[@PawlTV]

THANK YOU! Very good explanation! :)

[@ahanchakrabortty2254]

BEST

[@ajreenqammar1893]

what if i want to write wave number "k" equations in different medium.lets suppose three medium a metal layer sandwiched between two layers ,one is silica and other is air ?kindly recommend some books to deal with such a problem and some books to learn the basics. thanks

[@empossible1577]

This is a multiple scattering problem. You can see this analysis in Lecture 7f for when there are two interfaces: empossible.net/academics/emp3302/ When there are more than two interfaces, the scattering problem becomes too complex to handle analytically, although there are a few canonical cases that have been handled analytically. Instead, people adopt techniques like transfer or scattering matrices. You may be very interested in learning the transfer matrix method to handle your case. See Topic 2 here: empossible.net/academics/emp5337/

[@ajreenqammar1893]

and please also recommend the sequence in which i can take lectures from your channel from basic to advance

[@empossible1577]

There is a graphic on this page that lays out the courses in a preferred sequence... emlab.utep.edu/academics.htm

[@tsehayenegash8394]

the video is permanently store my mind if you can please upload atmospheric waves like gravity wave, equatorial wave etc. I have also a question why not the frequency is change?

[@empossible1577]

Maybe some day for other types of waves. In most of what you will see frequency does not change because the situations are linear. That is, nothing is moving and the material properties are linear. When the field becomes intense or objects are moving relative to the wave, nonlinear phenomena arise and lost of weird and wonderful things can happen like intensity dependent refractive index, rectification, frequency mixing, and more. It is most common to see nonlinear properties exploit at optical frequencies. You can search for "nonlinear optics" or get a quick overview in Lecture 2h here: empossible.net/academics/emp6303/

[@adamhawkins9829]

I've read that frequency only cancels out of the impedance when conductivity is zero, but I've never seen a good explanation. I didn't see conductivity come up in your impedance calculations. When does conductivity come into play? Do you have a lecture that addresses frequency dependent impedance?

[@empossible1577]

Absolutely. First, let me point to you the official course website. I recommend using that as your main portal to the course. They contain links to the latest versions of notes and videos and there have other learning resources. empossible.net/academics/emp3302/ Lecture 6f - Lossy Dielectrics has what you are looking for. On Slide 16 you will see the equations for complex impedance. You will notice that the frequency term is grouped with the conductivity term. When frequency is zero, the conductivity vanished from the equation. If you understand the derivation of this equation, you will have it figured out. Hope this helps!

[@swapankumarmukherjee8825]

Sir, directs an ignorart towards light

[@user-si1zn3ir7x]

What is the difference between propagation constant and a wave vector? Thank you!

[@empossible1577]

Great question. They are almost the same thing. The wave vector is sort of a generalization to the propagation constant. Propagation constant is a scalar quantity and the direction of the wave is assumed or somehow known, like in a waveguide. A wave vector is when the direction of the wave is not known so the propagation constant is given the direction. This case, the magnitude of the wave vector is the wave number, or propagation constant. Keep in mind some people use the words slightly differently and the propagation constant may be i times to the wave number or something like that. Be cautious with the terminology.

[@mmk34]

Is there any chance you can share how you put together the visualization of the em vector in the slide, I am trying to learn how to do this in MATLAB. Any help or suggestion you can offer is much appreciated.

[@empossible1577]

Happy to help. Can you point to which visualization you are talking about?

[@mmk34]

Yes it's slide 10 that I wanted help with, thank you.

[@empossible1577]

That is a bit of a long story, but I will try to give a short version. For the arrows, I created a function based on cylinder() that creates and draws arrows given a start and end point. I used that to draw the k arrow and the E and H arrows. I used the fill3() command to make the waves. I used the text() command to add the text and equations. I used the line() command to added the 90 degree rectangle indicator. I used camtarget() and camposn() to position the camera and where it is pointed. I created the animation using what I outline on slide 64 of Lecture 2a here: emlab.utep.edu/ee4386_5301_CompMethEE.htm Some time soon I plan on creating a lecture series on MATLAB graphics that would build up to doing things like this.

[@mmk34]

Thank you very much for that, I look forward to your MATLAB graphics lectures, in the meantime I will try out the different functions and techniques that you have detailed above to learn a bit more.

[@sgiri2012]

The speed of light in vaccum is c subscript o. But what's the speed of light in air and how much factor it will be diminished as compared to vaccum. What are the permittivity and permeability of air(o2 and n2 homogeneous mixture). Is it same as compared to the permittivity and permeability in free space. In some texts,they are claiming that the permittivity and permeability are only opted for insulators(i.e., dielectrics). Is it true? Can you clarify me. In some texts,they are also using the same notation for permittivity and permeability for air and free space. Can you throw some light on it ? The flashning occurs due to the dielectric breakdown of the surrounding air. Can we still define permittivity of air ? How permittivity changes before and after dielectric breakdown

[@empossible1577]

For probably 99% of all calculations, the difference between vacuum and air is negligible. The electromagnetic and optical properties of air depend heavily on pressure, temperature, humidity, dust, and other contaminants. Roughly, the refractive index of air at visible wavelengths is 1.00028. How often do you care about the fifth digit of precision in your calculation? There are times when this is significant. For example, optical interferometry. The interference of light is extremely sensitive to optical path length differences and very small changes in refractive index can change the result. There are other examples of highly sensitive optical sensors that will be sensitive to the refractive index of air. The relative permeability will be practically immeasurable above that of vacuum. The relative permittivity is around 1.00056. I think for these reasons, air and vacuum are treated the same. It is only special applications that you really must consider the properties of air. Permittivity, permeability and conductivity are the fundamental electromagnetic parameters. Those that are sticklers for details may also point out some exotic cases, such as bi-anisotropic materials, require additional terms. In the frequency domain, conductivity is usually lumped into a complex permittivity so that there are only permittivity and permeability terms. In this sense, permittivity and permeability can describe everything, not just insulators. I do think it is often more intuitive to talk about conductive materials using conductivity and a real-valued permittivity instead of a complex permittivity. I think this may be where the texts you mention may be coming from. When breakdown occurs, the electric field is intense enough that bound electrons are ripped from the molecules and allow for conduction. This is why you see specific paths during arching. However, after breakdown the properties change significantly because there are free electrons. You can still define a permittivity of air, but it will need to be complex because air is much more conductive during breakdown. Hope this helps!

[@sgiri2012]

@@empossible1577 surely this helped me out. Thank you for your guidance

[@sgiri2012]

@@empossible1577 BTW,would you please take any special course /class on EM waves ?

[@empossible1577]

@@sgiri2012 If there is anything on electromagnetic properties of materials, nonlinear, anisotropic, etc. I think you will find this information very useful.

[@rabiulislamsikder344]

Sir, can you explain what is the effective index of the material?

[@empossible1577]

Did I say "effective index" in this lecture? I did not mean to. The effective index is associated with inhomogeneous things like waveguides or metamaterials. The effective index is sort of an average refractive index of the medium, although there is often more physics involved than just averaging. The concept is that a wave in your inhomogeneous structure would propagate at the same speed and with the same wavelength as a homogeneous material with the effective index.

[@rabiulislamsikder344]

@@empossible1577 Thanks. Effective index is not mentioned in your lecture. I just wanted to know the difference between refractive index and effective index. However, the concept of effective index is not yet clear to me.

[@empossible1577]

@@rabiulislamsikder344 Imagine you could replace an inhomogeneous structure with a homogeneous structure and the wave would behave the same way. That homogeneous material would need to have the effective refractive index as the inhomogeneous material.

[@rabiulislamsikder344]

@@empossible1577 One more question: I am really confused about the modes of an EM wave? Is there any video of yours where it explains the mode and why it is important?

[@empossible1577]

@@rabiulislamsikder344 The concept of modes is confusing because it means different things at different times. Electromagnetic waves have to obey Maxwell's equations so they are not free to look like anything they want. In fact, there is usually only a small set of ways the field can look like. These discrete answers are called modes. For waves in outer space, we would talk about the modes in terms of their polarization. In waveguides, we talk about about the different guided modes. In periodic structures we talk about the Bloch modes. For resonant structures, we talk about resonant modes. They are all just discrete answers to what the fields can look like. As for my videos, I talk about modes differently depending on the topic. I cover polarization modes in Lecture 6d here: empossible.net/emp3302/ For waveguides, I talk about them in Topic 9 at the same link above. Hope this helps!