Lecture -- Lorentz Model for Dielectrics

This video builds on the previous to cover the dielectric function according to the Lorentz model. Notes and observations are made that are general conclusions about dielectrics including dispersion, permittivity, refractive index, high/low frequency response and what happens around resonance.

[@hamidk4772]

Outstanding 👍.

[@mtfmorsh]

Very helpful explanation ...Thanks

[@dongdongli2431]

hello Professer, do you have any video or informations about the random phase approximation(RPA), I want to calculate the optical conductivity of graphene. I really need some help. Thanks

[@nesslange1833]

14:18 I tampered a little with the parameters (wp, w0, Gamma), but I never received such wild curves for the refraction index on the following slide. How to predict curves with multiple Lorentzian shapes?

[@empossible1577]

That is probably a better question for an expert in spectroscopy. Without being an expert in atomic scale resonances, we as engineers will just measure and then possibly fit a Lorentz model, or multiple Lorentz models to a curve using nonlinear regression or just trial-and-error.

[@HCho-xe1cj]

Thank you so much professor! I’d like to know your thoughts on dielectric function of semiconductors. For some semiconductors, their optical dielectric function is described by the Lorentz model resonance frequency of which is attributed to band transition. In this case, how can I understand the resonance frequency in comparison to that of dielectric materials? Are both these two cases basically the same? And, let’s say there is a semiconductor and its dielectric function is large enough(due to the band transition) to be used as a core material in a slab waveguide. Do you think this guided mode is a result of repeating band transition say, repeating absorption and re-emission as it propagates in the slab?

[@empossible1577]

Hmmm...When it comes to semiconductors I am getting a little outside of what I know well. As I understand it, the periodic nature at the atomic scale is what leads to bandgaps for electrons, but the repetition is too small for photons. Everything can be modeled as Lorentz. Could be wrong!

[@HCho-xe1cj]

@@empossible1577 Thank you so much for your reply :)

[@deborahdeahassiscarneiro2975]

hello, what was the value to ko to plot the constant alfa at minute 13? thank you.

[@empossible1577]

k0 = omega/c, where omega is the radial frequency along the horizontal axis.

[@Sam_Chintapalli]

❤

[@asmaaahmed5755]

excuse me, i need to read more about positive dispersion what do you recommend?

[@empossible1577]

www.amazon.com/Optical-Properties-Solids-Oxford-Physics/dp/0199573379/ref=sr_1_1?crid=27Y6SR0SZ2LZO&dchild=1&keywords=optical+properties+of+solids&qid=1605616351&sprefix=optical+properties+of%2Caps%2C182&sr=8-1

[@hongpan0507]

Water at liquid form doesn't seem to follow this model. Water's dielectric constant starts really high, and then drops off when gets closer to resonance; it levels off at high frequency.. Any idea why?

[@empossible1577]

I suspect because it is partly conductive. Let me point you to the official course website: empossible.net/academics/emp6303/ The next lecture is about the Drude model. I may take a Lorentz-Drude model to fully model water.

[@hongpan0507]

@@empossible1577 Thank you very much! And looking forward to it😀

[@bkahraman99]

which playlist this video is belong to I cannot find

[@empossible1577]

It belongs to EMP 21st Century Electromagnetics. I did not put much effort into organizing the playlists. Instead, I recommend using the course website as your main portal to the materials. You can download the notes, get links to the latest versions, and get links to other learning resources. Here is the link to this course website: empossible.net/academics/emp6303/

[@kutaysagdc6425]

I think the Wp is not always equal to Wo, we can say it should be between Wo and the frequency value which makes Er 0.

[@empossible1577]

The plasma frequency is generally much higher than the resonant frequency. In addition, there is only one plasma frequency while there are many resonant frequencies.

[@pavelrozov741]

Can you explain what is the plasma frequency and how it differs from resonance frequency w0 of the electrons?

[@empossible1577]

Absolutely. First, let me point you to the course website which as links to the latest versions of the notes and videos and has many other resources for you. empossible.net/academics/emp6303/ The plasma frequency is described and even animated in Lecture 2f.

[@pavelrozov741]

@@empossible1577 Thank you! I have another question. How can a material be transmissive below resonance frequency? I read that at frequencies below plasma frequency, total reflexion occurs, since the electrons can follow the oscillations of the wave and thus respond instantaneously to the excitation and the material behaves as a conductor then. Or am I wrong?

[@empossible1577]

@@pavelrozov741 For metals, the plasma frequency is roughly though of this way. Above the plasma frequency the metals are transparent and below the plasma frequency they are good metals. However, the transition at the plasma frequency is not a sharp one. In fact, it is very slow and gradual. Even far below the plasma frequency, metals are never perfect conductors and some amount of the wave can transmit through them. More accurately, they decay very quickly. This leads to the concept of skin depth.

[@pavelrozov741]

@@empossible1577 ok, but how does ist exactly work for dielectrics? As far as I know, the concept of skin depth applies only for metals and not for dielectrics. I know that a material ist never 100% reflective, unless its an ideal conductor. But in the plot for the reflectance it looks like for low frequencies the dielectric is almost as transmissive as for high frequencies (at least much more transmissive as for resonance frequency), but I just cant understand why...

[@empossible1577]

@@pavelrozov741 Strong reflectance happens when a material has rather extreme material properties. The extreme properties could be refractive index or loss. This generally only happens in the vicinity of a resonance and a bit above. It extends a bit above because the loss is rather extreme and extends farther on the high frequency side. Below the resonance and far above the resonance the loss is low so the reflection is low as long as the overall refractive index is also low. Did this help?

[@arfariaz786]

Can you please describe what this resonance is graph means? Thank you

[@empossible1577]

This is covered in a previous video. I recommend accessing the course through the website instead of KZbin so you do not miss anything. See Topic 2 here: empossible.net/academics/emp6303/

[@arfariaz786]

@@empossible1577 ok i'll do this then.. thank you