Lecture 2 (EM21) -- Lorentz and Drude models

This lecture introduces the student to the Lorentz model which describes the dielectric response of materials and Drude model which describes metals. The lecture gives physical insight as to why materials have a dielectric and magnetic response and some implications of this.
Prerequisits: Mechanics and Electromagnetics

[@adilmalik7066]

You are by far the best lecturer for EM and CEM Ive ever seen. Thankyou so much for all your videos. Much appreciated!

[@empossible1577]

Thank you!!!

[@mursalayub5167]

@@empossible1577 true that

[@benjamincordes207]

I want to study plasmonics in graphene. This was a great help. I really like how you build a solid foundation and gradually progresses towards more difficult topics. Very clear and easy to follow, thank you very much!

[@shreyashbhattarai7362]

Amazing lecture! Much better explanation than my professors at UCLA. The world will definitely benefit from more of your videos!

[@leeorshimhoni8949]

like every lecture of Dr Raymond. explicit, logical, well presented and insightful. thank you for this video.

[@empossible1577]

Thank you!

[@danielfwt]

your explanation is very clear and easily understood, thanks for the video!

[@candoga]

He is the best of best EM instructor I've ever seen🤩

[@empossible1577]

Thank you!!

[@TheNomanAhmed]

Very Nice Explanation :) Great work.

[@nooraalameri6938]

thanks Aloooooooooot !!!!This is great effort !

[@svetikdisaster]

Thank you for the nice lectures! I have a question about real part of permittivity of metals at low frequencies. As it is described in Drude model, real part of eps should tend to infinity (slide 49). But very commonly in the literature they are using the formula that describes eps through eps_r and conductivity (slide 48). And there, the real part is equal to 1 (slide 54). Why is it so different? And which answer is closer to the real life: infinity or 1?

[@x.z.487]

Thanks a lot for the lecture! The imaginary part of relative permittivity @45:21 has different sign with Im(eps_r) @43:00. It might be due to inconsistency using the Ansatz in the derivation. Just for information, it took me some time figuring it out:)

[@chang912]

Super clear explanation. Very Very good indeed !

[@empossible1577]

Thank you!

[@skardykats]

@37:23 Is this how they design a -ve dispersion fibre? Which to design it around the resonant frequencies.

[@upasanapanigrahi4796]

Thanks for so wonderful lectures... so beautifully elucidated

[@empossible1577]

Thank you!!! You made my day! :-)

[@live4Cha]

thanks for good lectures :-) i think your use of term "displacement" are ambiguous. At one point (relative phase for resonance) and later for lorentz electron motion. I assume displacement is NOT position but change of position. if we use the equation P = F.v (power J/s = Force (N) x velocity (m/s)) I think the displacement you mean is the term comparable with velocity. I think we can show this - for a harm. osc. can be maximized if phase diff btwn F and V is pi/2. cheers

[@AwesomeAngryBiker]

For continuity put the child back instead of the bowling ball, keeps things consistent

[@anywallsocket]

the point of the bowling ball is twofold: to emphasize the delay between E(t) and P(t), as well as the adsorption induced return to equilibria.

[@prakashranjan6675]

Dear sir Thanks a lot for such a wonderful lecture :) @21:10 Can you explain little more about role of imaginary part of permittivity in the contribution of loss or How does imaginary part of permittivity tell us "Is there is loss"??

[@empossible1577]

That is a good question. I look at mu and eps as the parameters that are most fundamental to Maxwell's equations, but it is hard to understand how they physically affect waves. The refractive index and impedance are the parameters that describe much more effectively what happens to a wave, but they are not fundamental to solve Maxwell's equations. Refractive index is also a complex number. All of the information about the speed of the wave is isolated to the real part of refractive index, called the ordinary refractive index. All of the information related to the decay of a wave (loss) is isolated to the imaginary part of refractive index, called the extinction coefficient. To fully understand how the imaginary part of eps contributes to loss, dig up the equation for the extinction coefficient in terms of epsilon. You will find it to be a weird equation, but you will be able to make two conclusions. First, if the imaginary part of eps is zero, the extinction coefficient is zero and there will be zero loss. Second, if the imaginary part is not zero, the extinction coefficient will not be zero and both the real and imaginary parts of eps contribute to the loss because they both appear in the equation. So, the imaginary part will tell you IF there is loss, but you need both real and imaginary parts of eps to figure out how much loss.

[@nunyabizz3357]

can anyone by any chance clarify around 13:30 why the transform of dr/dt is (-iw)r(w) instead of (+iw)r(w) ?

[@empossible1577]

First, let me point you to the official course website. I recommend using this as your main portal to the videos. This portion of the notes has been considerably revised and improved. You will find the latest version of the notes and videos for this under Topic 2 here: empossible.net/academics/emp6303/ The difference in sign is simply the sign convention (i.e. positive vs negative). For a nice summary of the sign convention, checkout: empossible.net/wp-content/uploads/2018/03/Summary-of-EM-Sign-Conventions.pdf

[@sqrf]

Your expo is really clear... thanks! but how can I interpret and get (or derive) the "parameter" epsilon_{infinite} instead of the one in Drude model. Some texts only said this parameter is related with the background polarization of metal cores.

[@empossible1577]

In principle, the eps_{infinite} is not a physically real number, but it is still very useful to account for very high frequency resonances. Look at the response for a single Lorentz oscillator. Notice that at frequencies much lower than the resonance, it just produces a constant above 1.0. If you are simulating a device over some range of frequencies and are incorporating materials that have their resonances very far above this frequency range, you don't have to account for the dispersion or any other craziness because you are not operating your device there. Instead, you can just lump all of these into a single constant number that we call eps_{infinite}.

[@sqrf]

CEM Lectures Thanks again, you clarify me that parameter more than any textbook or paper where they only use it but no comments about its nature.

[@mursalayub5167]

Is it ok to curve fit the paliks constants for silicon with lorentz fit or is better to use polynomial fit. With the polynomial fit wll the peak at resonance not be missed.

[@empossible1577]

Hard to say. Pretty much anything will work over a limited range of wavelengths or away from resonance.

[@u571lxx]

sehr gut

[@paulamiroy953]

Dear Professor, When refractive index is negative, does it mean the corresponding wave is travelling faster than speed of light in that medium? Thank you.

[@empossible1577]

The sign of refractive index indicates handedness, not speed. The magnitude of refractive index conveys speed. So for the phase velocity to exceed the speed of light you need -1 < n < 1.

[@paulamiroy953]

Thank you Professor. And one more question, in the video are the graphs plotted with Matlab programming?

[@empossible1577]

I think all the plots were generated with MATLAB in all of the lectures. Pictures of devices are sometimes MATLAB and sometimes a CAD tool. Some other things were simply created in PowerPoint.

[@paulamiroy953]

Professor, I have another query, what is the intuitive and physical meaning of negative permittivity?

[@empossible1577]

This means that when an electric field pushes on bound charges, they displace in the opposite direction you think they should. Imagine pushing on a door and it displaces toward you instead of away from you. Weird huh? For bound charges this happens near a resonance when things are phased just right so as to produce this effect.

[@ruiwang9856]

Hi professor, at 54:17, should the sign of imaginary term be negative? It was negative in previous slide. Thanks.

[@empossible1577]

The answer is both! For these slides it should be negative because the positive sign convention is used almost everywhere. However, in a computer code where I used this in a simulation, I used the negative sign convention where the sign in this equation should be positive. Confusing? Sign convention seems simple, but it is the source of a lot of frustrations!

[@ruiwang9856]

@@empossible1577 True, quite confusing, haha

[@nihalfayez1772]

Thanks for lecture. I would ask about how spring represent the polarization, for example what is the physical meaning of damper and what the physical meaning of the parts of the move equations concerning the electron motion. Thanks again

[@empossible1577]

The spring is the restoring force and is analogous to the electrostatic attraction between opposite charges. During the process of displacing charges, some of the energy it took to do that is lost, or converted to other forms like heat. The damper is analogous to these loss mechanisms. The equation is essentially the equation of motion (i.e. balancing all the forces) that quantifies the physical offset of the object suspended by the spring, or offset of the charges.

[@nihalfayez1772]

Thanks alot

[@ruiwang9856]

Hi Professor, at 51:45, it shows higher frequency experiences greater loss. But at 48:13, the absorption decreases with higher frequency. Do those two conclusions conflict? Thanks.

[@empossible1577]

I definitely see how that is confusing. I probably should not have labeled the kappa line as absorption. They are related through alpha = kappa * omega / c0, thus alpha does increase with frequency omega. kappa is very close to pure loss, but it needs to be multiplied by frequency.

[@ruiwang9856]

@@empossible1577 At 49:46, you said metal is very lossy at plasma frequency, do you mean it has a very high alpha, instead of kappa? Thanks.

[@empossible1577]

@@ruiwang9856 I always (at least I mean to always) refer to alpha when it comes to loss.

[@pavelrozov741]

Nice lecture! But what does it mean if the refractive index is less than 1? How can one justify it?

[@empossible1577]

Great question! First, this section of the the course has been pretty significantly revised. Checkout Topic 2 here: empossible.net/academics/emp6303/ A refractive index less than one means the ripples of the wave are propagating faster than light in a vacuum. The answer to this is in Lecture 1b at the same link.

[@pavelrozov741]

@@empossible1577 Thanks! But could you maybe breefly explain why the phase velocity is bigger than c? I read somewhere that it has to do with the fact that when the frequency of the electromagnetic wave is bigger than the resonance frequency of the charged particles, the oscillation of the particles cant follow the frequency of the wave anymore (as you explained by the example with the swing) and therefore the radiated waves from the particles are out of phase with the electromagnetic wave. But how the phase velocity gets bigger than c?

[@kavithasenthilkumar4533]

Sir how did you calculate N for plasma frequency

[@empossible1577]

First, let me point you to the official course website. This is an old video and has been replaced with new ones. At the course website, you can download notes, get links to the latest videos and more. empossible.net/academics/emp6303/ N is essentially the density (atoms/per volume). Perhaps more accurately, N is the number of resonators per volume. Maybe you have a material where not all atoms contribute to a resonance. This is a physical thing determined from the chemistry of the material. Typically, it is the plasma frequency that is measured in the intermediate terms to calculate the plasma frequency are never used.

[@mercedesmalone973]

wow intense lecture.....I had trouble keeping up with it lol

[@empossible1577]

Mercedes Malone LOL. We are trying to keep you challenged.

[@ahmeedbakare828]

Is there a lecture one?

[@empossible1577]

Yes, absolutely. Let me point you to the official course website that has links to the videos, electronic notes, and other resources. emlab.utep.edu/ee5390em21.htm I have made a lot of revisions to the electronic notes so you may notice some differences from the videos.

[@kavithasenthilkumar4533]

In this lecture you had assumed wp=4,wo=2,r=0.1is these values are same for fr-4,and how did you assumed these values.

[@empossible1577]

Every material has its own set of parameters so these are definitely not for FR-4. I just picked some values out of thin air to illustrate the concept and explain the general trends. Usually, the parameters are calculated by fitting the model to measured data. A numerical curve fitting algorithm like nonlinear regression is used.

[@empossible1577]

One more thing, this is an old video. This section of my course has been revised and improved. I suggest accessing the videos through the course website so you always have the latest. See Topic 2 here: empossible.net/academics/emp6303/

[@bewareofthedeceiver]

What metals are dielectric?

[@empossible1577]

This gets into semantics. Loosely, when we say dielectric we mean a material that insulates and has no magnetic response. When we say metal, we mean a material that conducts electrical current very well. However, materials are not binary like this and there is a gradual continuum from perfectly insulating to perfectly conducting. Ignoring permeability, all of these can be treated with a complex permittivity and thus can be thought of as lossy dielectrics. In this sense, all metals are dielectrics. However, I would only say this casual conversation by clarifying what I meant by that.

[@rudolfdelrosario8113]

is there a pdf of this online?

[@empossible1577]

Absolutely. You can get the latest version of all the notes here: emlab.utep.edu/ee5390em21.htm You may notice that the notes have been revised and added to since the recordings.

[@rudolfdelrosario8113]

@@empossible1577 hahaha

[@educativeedge4622]

If u clear the angles between displacement and driving force,then it will b more good, By some draw work,,

[@empossible1577]

I am not sure if I have made all of the revisions you are asking for, but you are looking an old version of these notes. They have been considerably revised. I recommend using the course website as your main portal to the videos. The website has notes you can download, links to the latest version of the videos, and many other learning resources. All of these notes are currently in Topic 2. empossible.net/academics/emp6303/

[@educativeedge4622]

@@empossible1577 Ok thank you! Actually am confuse in swing example,about zero phase,90,or 180 degree.

[@empossible1577]

@@educativeedge4622 Let me now if the new lecture clears that up.