In preparation for the next agora on Wednesday
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??
