This weekend was a little light in comparison to some of the previous ones. It was still obnoxiously hot on Saturday, so I wasn't motivated to do much. Sean and I walked around Rue d'Alesia doing some (unsuccessful) souvenir shopping, and then stopped at the creperie on the corner of Blvd Jourdan by the hotel to eat dinner and watch Germany destroy beat Argentina. I went to place d'Italie by myself afterwards to try and find stuff for people at home. Apparently this is massive sale week/month, as a lot of stores have stuff up to 50% off. I wound up finding a gift for a friend and buying an athletic shirt for myself, but I still have no clue what to get for my parents.

Sunday, Sean and I went to Fontainbleu with some of the other Cité residents. It was kind of a last minute invitation, so only the two of us went from the REU group. It was a 40 minute ride on the RER D followed by a 15 minute bus ride to get there, but admission was free since it was the first sunday of the month. The place is very pretty, but I'm not sure it measures up to Versailles. It's not quite as opulent, but some of the touches (stone walls painted to look marble) were cool.

Also, in a move demonstrating vast intelligence and foresight, the Cité people gave us card access to the buildings for 1 month, despite our being residents for two. We got this straightened out on Thursday night or so, but it also happened that they gave us wifi for one month instead of two as well, which we didn't notice until Friday night after "business hours". Luckily, one of the other residents let me copy here wifi code and we all have access now (and will try to get ours back tonight), but the oversight reeks of stupidity.

At work today, Bianca told me that the thunderstorm that forcibly retired out laboratory pursuits Friday also knocked out the climate control in the lab, which renders the laser kaput until the control is fixed. We're hoping to be back online by Wednesday, but it looks like my goal of ablating something before the date Michael did last summer (7/9) is not going to be met.

So instead of doing laboratory work, I read 3 articles today.

Short-Pulse Laser Heating on Metals

TQ Qiu and CL Tien, Int. J. Heat Mass Transfer., Vol 35, No 3, 1992

The authors discuss a two-step process for the laser heating of metals, namely:

(1) The incident laser pulse excites free electrons to high energies and

(2) said electrons collide with the phonons, and the phonons experience heat transfer through collisions

In the limit of long pulses (longer than the electron-phonon thermal relaxation time), the model treats the light as heating up the metal directly.

I have mentioned this scheme before. This is the second time I've tried to read this paper; the authors hand-wave a little in places, which is unfortunate, but I believe I've gotten the gist out of this article.

The author starts with two heat transfer equations:

where the first equation corresponds to the electron gas and the second to the lattice phonons (thus the 'e' and 'l' subscripts). The 'G' term represents the electron-phonon coupling, while the Q term is a source term designed to represent the laser. The authors make several simplifying assumptions:

~G depends weakly on Te (meaning that Te is neither terribly small nor terribly large)

~the number of free electrons is 1/atom

~The source term is of modest intensity (.1-100 MW/cm^2)

~The laser pulse duration is longer than the electron-phonon collision time (.02ps)

~The optical properties of the material depend weakly on temperature.

The authors then proceed to solve the differential equations numerically after switching to dimensionless equations, and find that their simulations (surprisingly) agree with experimental data. 

Simulation Study and Experiment on Laser-Ablation Surface Cleaning
Zhou et al, Optics & Laser Technology Vol 33 Issue 3 April 2001

This paper wasn't so useful from an understanding point of view but as a reference point of view. The authors basically amalgamate the results of a few different papers into their own model without much explanation, but they do provide the references to papers which hopefully will go into the derivation in more detail. I won't summarize the paper because I didn't get very much out of it conceptually, and the context in which laser cleaning is utilized is quite different (nuclear decontamination) but I intend to follow up on the sources cited.

Ultrafast Dynamics of Femtosecond Laser-Induced Periodic Surface Pattern Formation on Metals
Jincheng Wang and Chunlei Guo (yeah, U of R!), Applied Physics Letters 87 (2005)

The authors revisit the formation of periodic structures on metals after ablation (discussed by Fauchet among others in several papers in the early 80s. I had started reading one of them a few weeks ago and found that it drew heavily on a paper pretty far removed from my project. I later started reading the latter paper in my free time, but I'm not finished yet). The general theory is this: incident pulsed light strikes surface defects or nonuniformities on the material to be ablated. The light is then scattered along the surface, where it interferes with the incident light. Periodic structure formation is evident on the material from this interference.

The authors investigate structure formation on three different metals: Cu, Ag, and Au, in order of decreasing threshold fluence. By the old theory, one would expect to see stronger surface formation on the gold material since the abation threshold is lower and structure would form more easily. However, what the authors found was that Au had the least defined periodic structure formation and that copper had the strongest. The authors then conclude that there are two competing processes involved in the formation of the periodic structures, or more precisely, electrons lose energy by two processes: electron-lattice coupling, the efficiency of which is described by a coupling constant, g, and diffusion to a lower temperature region. Structures are formed via the first mechanism. Thus, materials with higher g values would be more likely to exhibit periodic structures. Copper's g constant is more than twice that of silver and almost five times that of gold, (10 vs 3.6 and 2.1 x10^16 respectively), which supports the authors' theory. The authors do not, however, go on to predict more explicitly the relationship between g and structure formation.

My next move is to read some of the sources for the second paper. Perhaps I should also set traps for small animals to sacrifice to the laser gods so that the system can become operational again.

As a total aside (now that the US is out of the world cup after playing hideously against Ghana, I seem to have less of these) I've been watching a bunch of badminton videos on youtube at Cité. I want to be able to do this when I grow up...