Optica Agora

Last session bringed us to the final part of the paper: we are reaching the experimental part, which is less mathematical and formula than the other parts. So we believe that anyone can (and Should) attend this session.

So please read the last Part IV for next agora!

For the Agora, Aurele 

As you can see, Aurele has extended for the next 2 weeks the discussion regarding optical antennas INCLUDING some related or less related issues which pop up! So perhaps we can get further on Wednesday, perhaps even to section 4 (applications) but also to see if there is further interest in addressing the qualitative discussion in 3.8, and 3.9 (nonlinearity in metals!). We’ll just have to skip past the final sentence of section 3.7 which I still cannot believe and is such an amaxing finding that it should have required its own paper 😉

However last time we did get into a serious discussion of the complex refractive index of metals which goes beyond the question of antennas but is obviously of great importance to anyone who uses metals at optical frequencies (such as Aluminumized mirrors) and wants to understand how they work — quantitatively. In particular there was the issue of epsilon_infinity (assymptotic value at high frequencies well past the plasma frequency): should it be unity, or something else? And if it IS something >1, then does that not affect the plasma frequency?

I had referred to a table in Feynman table 32-3 (in my old edition) taken from Kittel which tabulates the predicted and experimental plasma frequencies of alkalii metals (from an old experiment by Robert Wood, I believe, who realized that metals would become transparent in the far UV). Now I have done a calculation based on the conductivity, valence, and density of Lithium (all well known) but assuming epsilon_infinity = 1 (as Feynman does) and have plotted the result here:

   http://www.strw.leidenuniv.nl/~meisner/LithiumIndexTheory.jpg

This is very consistent with Feynman/Kittel but differs significantly from this reference (which shouldn’t be taken as ABSOLUTELY true, but is the best I can find):

   http://refractiveindex.info/?group=METALS&material=Lithium

Note that he plots Re{n} at the top and Im{n} down below vs. microns, as I do. Comments?

We will organise the next agora meeting, still on wednesday with the continuation of Jeff’s paper! Hopefully we are reaching the experiemental part!

dear Agora follower, we will have the last session from the paper of Jeff, the next wednesday 13 of April at 12.30. Please all join. More will come about this session.

Unless someone can think of a way of adding more days to the month of March, this will unfortunately be our last session on optical antennas. That means that we have a lot of material to cover in one hour! Well actually, most of the detailed math in the paper is behind us, so I’m hoping we can have a more qualitative discussion on sections 3.8 – 3.10 and specially section 4 of the paper. We didn’t go through section 3.6 yet but we can just briefly look at that (and actually I’m more interested in exactly HOW one goes about holding an 80nm gold ball 5 or 10nm from a radiating atom in order to obtain the enhancement shown in figure 6!). The linear dipoles shown in 3.10 seem of somewhat more interest, and in this case he didn’t present any equations for us to ponder. Also I find very surprising him mentioning that metals can have highly non-linear properties discussed in 3.9 — do any of you have experience or knowledge of such nonlinearities and why they aren’t observed in normal situations?

I am still puzzled by one thing I brought up last time, concerning the downwards effective wavelength scaling of very thin linear elements according to eq. (39) which he doesn’t really explain at all. So I did find another paper by the same group (Novotny, Phys. Rev. Let. 98 266802, 29 June 2007) on that subject, and reading it didn’t help much at all. I find number of things troubling, including that the effective wavelength goes o zero for lambda ~= 400nm in silver and gold (unless that is just extending an approximation beyond its validity) as given by eq (39) where _1 < 0. That’s worrisome, especially if I were trying to build one of hese to work in the UV! But my bigger puzzle, if anyone can possibly shed ome light on this, is understanding QUALITATIVELY why there should be any uch reduction in effective wavelength. Why doesn’t this happen at lectronic frequencies? The reduction only becomes significant when the ntenna diameter R is of the order of the penetration depth. But that does NOT happen at RF when you have a very thin wire, so what gives?

Jeff

Jeff is writting to us, regarding the next session of the Agora on Wednesday the 23rd of March:

 This Wednesday 23 March we will try to get a bit further in the Bharadwaj paper on optical antennas. I’d like for us to understand the fundamentals, as we have been doing, but also for us not to get bogged down in a lot of difficult math. Fortunately we have a few people working in this and related fields who have been helpful in the discussions, but that still doesn’t make it easy for the rest of us to understand everything right away! In particular Omar has sent me a copy of a chapter from L. "Principle of nanooptics" by Novotny and B. Hecht (and he said he would make it available to everyone) which explains the derivation of the math in section 3.1 in much more detail, but I find it very difficult reading.

Anyway, last time we got to section 3.3 so I’m hoping that we can quickly review that and get through sections 3.4 and 3.5 (which I think are a little more straight-forward) so that we can get to the concrete application in section 3.6. I don’t know if we can get any further, but I’m interested in  nderstanding equation (39) in section 3.7 which he doesn’t really explain at all. So I’m hoping that some of you experts can help in explaining that!

Sections 3.8 and 3.9 seem less fundamental but also don’t contain much explicit math, so we should be able to get through those, as well as section 3.10, on the following Wednesday, and hopefully talk about some of the interesting applications and future technology in section 4. But since several of you are involved in work with optical antennas, I’m hoping that we can get input on some of those projects as well, even if you’re just beginning the work and don’t yet have any results (or don’t even know where your research is headed!).

And for "extra credit" I’m wondering if anyone can solve this little problem that I mentioned during the discussion last week. In equation (11) he gave an expression for the radiation resistance Re{Z} in terms of the local density of states, but then says that its units are in ohms/m^2. It must be such that (by some definitions) P=J^2 * Re{z}. Now when I worked it out I determined that Z must actually be in ohms-meters and asked about it to the group. Aurele quickly mentioned that P wasn’t power/volume as I had assumed but just power, and that seemed to take care of the m^3 difference, so I figured that explained it. But no, that just makes the discrepancy twice as bad! And P certainly IS the power density, since the current density goes over a volume that is emitting. Is the author wrong: should it indeed be ohms-meters? On the other hand, the right hand side DOES appear to be ohms/m^2. So is the equation wrong, are the definitions wrong, or am I just confused??

On Wednesday 16 March we will have the second (of 4) Agora sessions on optical antennas, again trying to get through the Bharadwaj paper. Don’t worry if you haven’t read much further, because I’m hoping we can still concentrate on the basics in sections 3.1 and 3.2 which were not too clear to all of us last time. In particular I’m trying to appreciate equation (10) and the distinction raised between the classical treatment and quantum mechanical result for radiated power, and also his presentation of Re(Z), the antenna’s radiation resistance in equation (11). Maybe we can also cover section 3.3 and equation (14) which deals with the ability of an antenna to extract more energy from a dipole in an excited state by increasing the spontaneous emission rate with the non-radiative rate remaining the same. Then in section 3.4  the other useful aspect of optical antennas, directivity, is quantified, but I don’t expect we’ll get that far this time.

Jeff 

from Jeff:

For the month of March I was hoping we could discuss the emerging field of Antenna technology applied to optical frequencies. I found this review paper by Bharadwaj et. al. which I’d suggest you start reading. It’s rather long so if you get 1/3 way through it that’s fine. Or if you understand the first 8 or 10 equations you can just stop there and explain them to me 😉

Also, if you have been involved in this field or done any reading on it, I’m particularly interested in your input. Personally I have a good background in classical antenna theory, but no background in quantum mechanics, so parts of this paper went over my head. But hopefully we can concentrate more on qualitative descriptions and applications.

I had a lot of trouble downloading this paper, you can find in the Scratch (the previous link has been removed)

See you all Wednesday at 12:30 (or 13:00 if you want to miss lunch 😉

 jeff

 (posted by Nitish)

The New session for the Agora will be on Wednesday the 9th of March. Jeff will be our session Chair. The paper will be given in due time!

Dear all,

For the last session of Optica agora for this month, I propose to read the following paper.

"Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime". The following paper can be found at

http://pra.aps.org/abstract/PRA/v82/i6/e061801

cheers,

Nitish