Monday, September 20, 2010

Nanostructures as optical antennas

My student (with theorist collaborators) had a paper published online in Nature Nanotechnology yesterday, and this gives me an excuse to talk about using metal nanostructures as optical antennas. The short version: using metal electrodes separated by a sub-nanometer gap as a kind of antenna, we have been able to get local enhancement of the electromagnetic intensity by roughly a factor of a million (!), and we have been able to determine that enhancement experimentally via tunneling measurements.

As I've discussed previously, light can excite collective excitations (plasmons) of the electronic fluid in a metal. Because these plasmons involve displacing the electrons relative to the ions, they are associated with local electric fields at the metal surface. When the incident light is resonant with the natural frequency of these modes, the result can be local electromagnetic fields near the metal that can significantly exceed the fields from the incident light. These enhanced local fields can be useful for many things, from spectroscopy to nonlinear optics. One way to get particularly large field enhancements is to look at the region separating two very closely spaced plasmonic structures. For example, closely spaced metal nanoparticles have been used to enhance fields sufficiently in the interparticle gap to allow single-molecule Raman spectroscopy (see here and here).

A major challenge, however, has been to get an experimental measure of those local fields in such gaps. That is where tunneling comes in. In a tunnel junction, electrons are able to "tunnel" quantum mechanically from one electrode to the other. The resulting current as a function of voltage may be slightly nonlinear, meaning that (unlike in a simple resistor) the second derivative of current with respect to voltage (d2I/dV2) is non-zero. From a simple math argument, the presence of a nonlinearity like this means that an AC voltage applied across the junction gives rise to a DC current proportional to the nonlinearity, a process called "rectification". What we have done is turned this around. We use low frequency (kHz) electronic measurements to determine the nonlinearity. We then measure the component of the DC current due to light shining on the junction (for experts: we can do this with lock-in methods at the same time as measuring the nonlinearity). We can then use the measured nonlinearity and photocurrent to determine the optical-frequency voltage that must be driving the tunneling photocurrent. From the tunneling conductance, we can also estimate the distance scale over which tunneling takes place. Dividing the optical frequency voltage by that distance gives us the optical-frequency electric field at the tunneling gap, which may be compared with the field from the incident light to get the enhancement.

It's not at all obvious on the face of it that this should work. After all, the analysis relies on the idea that the tunneling nonlinearity measured at kHz frequencies is still valid at frequencies nearly 1012 times higher. Experimentally, the data show that this does work, however, and our theorist colleagues are able to explain why.

When you think about it, it's pretty amazing. The radiation intensity in the little nanogap between our electrodes can be hundreds of thousands or millions of times higher than that from the incident laser. Wild stuff, and definitely food for thought.


Don Monroe said...

Nice work. It is amazing at first glance that the effect spans such a large range of frequency.

I was wondering: is it reasonable to think of optical antenna effects as a natural, if unrecognized, implication of the 1980-ish research on surface-enhanced Raman scattering?

By the way, this work made the token physics section in EE Times.

Douglas Natelson said...

Hi Don - Thanks. Yeah, it is pretty wild. My coauthor Juan Carlos Cuevas did a great job explaining this to me, since that was one of our major conceptual concerns. The right way to think about the light-driven process is really photon-assisted tunneling (in the presence of the plasmons). It turns out, though, that we are in a happy limit (the plasmon-produced potential between the tips is ~ 20 meV, much smaller than the photon energy of 1.5 eV; and the density of states of gold is boring and smooth over an energy range comparable to the photon energy above and below the Fermi level), and the photon-induced tunneling formula approaches the classical rectification case.

As far as SERS is concerned, it's been known for some time now (going back to the 80s) that these sort of plasmonic effects are exactly what is responsible for much of the enhancement in surface-enhanced Raman. The metal acts like an antenna, giving an enhanced local field to do the Raman process, and then the metal also acts like an antenna to enhance the Raman scattered light. This is now called the "electromagnetic enhancement", to distinguish it from other effects that result from molecule/metal charge transfer ("chemical enhancement").

Schlupp said...

Doug, completely off topic,* there is some new gossip concerning Schoen: He is probably going to get back his PhD.

Not because he is considered innocent or anything, but because the argument for revoking the PhD was legally rather tricky and involved "unworthy" behavior AFTER obtaining it, and not misconduct while working for it. The university of Konstanz does not check the "worthiness" of entering students, which can be taken to suggest that they only care about it in this one single case. Reluctantly, I have to admit that there is some point to it, because PhDs in Germany are next to never revoked for "unworthy" behavior after obtaining them. Singling out one particular case does then appear rather arbitrary, and thus legally questionable.

What annoys me is the paper writing that he has already been punished enough. Huh? He was not allowed to profit from his crime, but that's not a punishment. And he apparently still denies any wrongdoing except "sloppiness".

*Congratulations on the nice work!

Anonymous said...

Very nice work! A couple of questions:

- How extended do you think the plasmon in the electrodes are?

- As far as I recall you are missing the polariton in your series of quasi-particles posts :-) Should one to think of these field enhancements being due to plasmon polaritons or simple plasmons ?


Douglas Natelson said...

Hello Kristen - Numerical modeling (finite element by us w/ commercial software, + FDTD by our colleagues here) suggests that the characteristic length scale for the fields in the gap to drop off laterally is something like the geometric mean of the radius of curvature of the tips and the interelectrode distance. Going into the metal, the length scale to think about is the skin depth (though as we were at pains to explain to the referees, potential drops inside the metal don't affect our results, since what matters is the potential drop relevant to the tunneling electrons).

Regarding the polariton terminology, I guess technically we really are dealing with polaritons here, since it's hard to imagine that the coupling to the field degrees of freedom is weak. I need to think about that some more.... Thanks for making me do so!

Jackson said...

Thank you..