Well, I'm home! A hectic final few days at the FiO conference combined with a lack of hotel internet access prevented me from checking the blog very often (I would wander around the Hyatt, where I wasn't staying, looking for a place where I could get a signal -- and the optimal location always changed).

I attended fewer talks on the last couple of days, in large part because I switched into planning collaborative research projects. I attended a few special sessions, however: one on the 200 year anniversary of polarization, and one which encompassed the 'best of topicals'. I briefly summarize these below.

A special session was organized on the polarization of light, to celebrate the 200 year anniversary of the discovery by Etienne-Louis Malus of the phenomenon of polarization. To quote Born and Wolf's Principles of Optics,

Apparently, one evening in 1808, he observed the reflection of the sun from a window pane through a calc-spar crystal, and found that the two images obtained by double refraction varied in relative intensities as the crystal was rotated about the line of sight.

I'll talk more about Malus in future posts. Suffice to say, Malus' observation was hugely important.

The talks of the session included both state-of-the-art polarization research, as well as historical discussions. The talks I attended include:

- Emil Wolf, Recent developments in the theory of polarization of stochastic light beams. Disclosure: I know Emil Wolf quite well! In recent years, Wolf has been developing a unified classical theory of coherence and polarization. Traditionally, the topics have been considered quite independently. Wolf and collaborators have been exploring the most general description of a partially coherent, electromagnetic wave. The talk includes a correction to a result due to the great scientist Stokes, which dates back to 1852!
- Mark Dennis, Polarization patterns in the daylight and cosmic skies. Disclosure: I also know Mark Dennis quite well! Mark is an expert in the study of singularities of optical fields, namely points of a wavefield where standard wave descriptions run into troubles. There are a variety of different types of such singularities, including singularities in the state of polarization of the field, and Mark discussed how such singularities arise in the polarization of light in both the daytime sky, as well as in observations of the cosmos. I'll definitely talk more about optical singularities in future posts.
- Bruce Smith, Polarization in hyper-NA lithography. Optical lithography is the technique by which patterns are written on a photoreactive surface using lasers. When light is tightly focused (i.e. the focal length of the focusing lens is small), polarization effects become important. Smith's talk was a general review of the manipulation of polarization to improve lithography systems.
- Christian Brousseau, Polarization and coherence optics: historical perspective, status and future directions. Brousseau is well-known as an expert not only on polarization but its historical development, thanks in large part to his book Fundamentals of Polarized Light. Brousseau gave a whirlwind tour of the history of polarization, breaking it into 3 phases. The first starts with the discovery by Bartholinus of double refraction in 1669 to the mathematical characterization of polarization produced by Stokes in 1852. The second ranges from the studies of Stokes to the electromagnetics research of Poincaré in 1892. The third phase runs from Poincaré to the discovery by Emil Wolf (1954) that optical coherence functions have wavelike properties. Brousseau also mentioned an interesting debate that I seem to have missed: the speculation that the Vikings may have used iceland spar (which exhibits double refraction) to navigate the oceans using the polarization properties of the sky which Mark Dennis talked about!

Every year now, OSA selects the best talks from the topical meetings it sponsors and arranges them together in a 'best of topicals' session. I attended the first two of these talks, which were very nice.

- Mitsuo Takeda, Coherence holography and spatial frequency comb for 3-D coherence imaging and coherence vortex generation. Disclosure again: I know Takeda! I've talked about OCT in a recent post, which relies upon temporal coherence to image layers of a material. One of the limitations of this technique is optical dispersion, in which the different frequencies of light respond differently to the material, resulting in distortion of the image. Takeda has taken a different approach and is attempting to use a light field which is essentially monochromatic but
*spatially*partially coherent, and he demonstrated some results relating to this. Related to this is a technique he and his collaborators have developed for making holographic images of the coherence function of the field. - Wolfgang Schleich, Factorization of number, Schrödinger cats and the Riemann hypothesis. This was a neat talk! An important problem in mathematical number theory is the determination of factors of large numbers (a trivial example of factorization: 560 = 7 x 8 x 10). The problem becomes ridiculously time consuming for even rather small numbers, and there is a major push to solve the problem quantum-mechanically, i.e. using quantum computing. Schleich reviewed and discussed some extremely devious ways to solve these problems using only the wave nature of light and matter: factorization was achieved using light, cold atoms, and excited protons. Considering modern cryptography essentially depends on the inability of computers to factorize large numbers, these techqniues are directly applicable to that field. I'll have to research and talk about this much more later.

The meeting was an incredibly fruitful one for me! I learned a lot, and 'liveblogging' events actually helped me learn much more than I have in previous years. I've also got a lot of up-to-date research to explore as blog fodder. I planned a number of new collaborations, seem to have been invited to co-author a new review article, and got some informal invitations to visit researchers in various locations, including Japan!

These meetings truly get more fun every year; you meet more interesting people, from all over the world, and make new friends and colleagues. I understand more about the physics and optics with each reexposure to the 'state of the art' research, as well. I can hardly wait for next year's meeting in San Jose!

Your last item reminds me (rather stochastically) about a paper I read which argued for the possibility of proving the Riemann hypothesis by treating the zeros of the Riemann zeta function as energy eigenstates of a "Riemannium" atom and studying their distribution via supersymmetric quantum mechanics. Maybe I should look into that again and see if I can write something about it after I repost my SUSY QM blogo-lessons.

Blake: The work that Schleich described invoked the zeta function, though I don't recall him discussing the Riemann hypothesis in the talk. I'd be interested to read about it, if you write it!

A

guaranteedaudience — ofone! Hooray!🙂

Most of the statistical-physical applications for the Riemann zeta function I can think of offhand involve positive arguments, or if they require analytic continuation, extend only to the negative real line. The Riemann hypothesis

probablydoesn't have adirectbearing on specific physical problems. . . but I've been wrong before this week.Blake wrote: "A guaranteed audience — of one! Hooray!"

Would it help if I absolutely promised to comment on the post, if you write it? 😛