I’ve joined a group of folks on Twitter who have vowed to read roughly a paper a day for an entire year, and will summarize my reading here occasionally. Part 1 can be read here, and part 2 can be read here. Links are provided for those with university access who are interested in reading more.
One note: I’ve been using twitter, for the most part, to record which papers I’ve read, but I’ve been really bad at it! In some cases, I’ve ended up “filling in” papers that I read to make up for those I’ve lost track of, and the dates between twitter and here may not always agree.
1/31: Rotational frequency shift, I. Bialynicki-Birula and Z. Bialynicka-Birula (1997). I’ve mentioned the “angular Doppler effect” before, in which circularly polarized light undergoes a frequency shift when the source or detector is rotated. It also turns out that vortex beams, with a “twist phase,” experience such a rotational shift as well! This is something I’m gearing up to blog about in the near future.
2/1: Radiation pressure on a free liquid surface, A. Ashkin and J. M. Dziedzic (1973). There is a long-running controversy in optics: does the momentum of light increase, or decrease, on entering a transparent medium? We still don’t have a definite answer, but this paper in the 70s made an ingenious test. By shining a beam of light onto a liquid from above, they found that the liquid bulged outward slightly, suggesting that the momentum increases. Others have found other effects…
2/2: Polarization effects in the diffraction of electromagnetic waves: The role of disclinations, J.F. Nye (1983). I’m currently working on the portion of my book in which I discuss “polarization singularities,” locations where the polarization of light may be mathematically said to have a singular behavior. This paper details a somewhat different class of polarization singularities that are analogous to disclinations — singularities of angle — in crystals.
2/3: Does the glory have a simple explanation? H.M. Nussensveig (2002). Short answer? No! The glory is the rainbow-like halo that appears around a shadow when reflected from a cloud or haze. Though it looks like a rainbow, the physics of the glory is astoundingly complicated and a challenge to explain.
2/4: Real spectra in non-Hermitian Hamiltonians having PT symmetry, C.M. Bender and S. Boettcher (1998). I’ve been telling my optics colleagues for a while that PT symmetry will be a big thing in optics, and they’re not listening! Parity-time symmetry is a property of a medium that looks the same when mirror-imaged and subject to a mathematical time-reversal. In optics, this corresponds to a specific type of medium with both gain and loss. Such PT symmetric structures in optics have interesting properties, such as directional invisibility.
2/5: Lines of circular polarization in electromagnetic wave fields, J.F. Nye (1983). Remember the singularities of polarization I mentioned earlier? Circularly polarized light is “singular” with respect to the orientation direction of elliptical polarization, as a circle has no special orientation. Nye’s paper was the first paper to explore the regular and stable structure of such “C-lines.”
2/6: SUSY-inspired one-dimensional transformation optics, M-A. Miri, M. Heinrich, and D.N. Christodoulides (2014). Another topic that I consider under-explored in optics! This paper studies the application of supersymmetry, typically reserved for particle physics, in optics, and designs these structures using transformation optics, a mathematical tool that has previously been used to design cloaking devices.
2/7: Measurement of the Stokes parameters of light, H.G. Berry, G. Gabrielse, and A.E. Livingston (1977). The “physical” properties of the polarization of light cannot be directly measured, due to the rapid rate of oscillation of light waves. The Stokes parameters, first described by G.G. Stokes, are measurable quantities from which the physical properties can be determined. This paper discusses such measurements in more detail.
2/8: Transmission of light through birefringent and optically active media: the Poincare sphere, H.G. Jerrard (1954). It is possible to “map” every possible polarization state of light to a position on a sphere, with the North Pole being left-hand circular polarization and the South Pole being right-hand circular. This is not only an elegant description, but has surprising physical significance. This paper was one of the first to make people aware of the so-called Poincaré sphere, which had been first visualized 50 years earlier but mostly neglected.
2/9: The wave structure of monochromatic electromagnetic radiation, J.F. Nye and J.V. Hajnal (1987). This paper builds upon Nye’s earlier 1983 paper on C-points and discusses in detail the singularities of polarization and their topology.
2/10: I can’t tell you, ’cause I’m refereeing it for a journal! This paper was one I had to referee for a journal that day, so I counted it for my list! Can’t talk about it until it is published, due to confidentiality stuff.
2/11: Contribution of the electric quadrupole resonance in optical metamaterials, D.J. Cho, F. Wang, X. Zhang, and Y.R. Shen (2008). Most of the time when we consider the response of atoms to electromagnetic waves, we treat them as simple dipoles — a positive and negative charge separated in space. But, with the advent of metamaterials, which use structure to make optical responses not found in nature, the higher-order scattering such as quadrupoles — four charges, two positive, two negative, spatially separated — can become important. I looked up this paper after I independently wondered what such effects would be like.
2/12: The Doppler demon, J. Denur (1981). A thought experiment that dates back to 1867 is Maxwell’s demon, which wonders if it is in principle possible to violate the second law of thermodynamics by having a little demon serve as a gatekeeper to sort high and low energy molecules. It turns out not to be possible, but in 1981 Denur suggested that the use of Doppler shifts might make the demon’s job easier. Also turns out not to be true, but I’ll try & come back to this in a future blog post!
2/13: An angular spectrum representation approach to the Goos-Hanchen shift, M. McGuirk and C.K. Carniglia (1977). The Goos-Hanchen shift is another topic I need to blog about! When a beam of light reflects off of a surface, the light “bounces off” at the same point that it impacts. However, when light is subjected to total internal reflection, the light bounces off shifted from where the incident light hit! This is loosely interpreted as light traveling in the forbidden region before being reflected. This particular paper uses a particular mathematical formalism to analyze the effect.
2/14: Goos-Hanchen shifts from absorbing media, W.J. Wild and C. Lee Giles (1982). Turns out that the Goos-Hanchen shift doesn’t require total internal reflection, as long as light is being reflected off of an absorbing medium.
2/15: Singularities in the transverse fields of electromagnetic waves. I. Theory, J.V. Hajnal (1987). Yet another paper on the topology of singularities in the polarization of light! There’s a lot of subtlety to this phenomenon.
2/16: The topology of symmetric, second-order tensor fields (pdf), T. Delmarcelle and L. Hesselink (1994). This paper, and the two that follow, are all about the mathematics needed to describe the topology of polarization singularities. It is quite unusual and novel math, and I’ve learned a lot in reading about it.
2/17: A Lemon is not a Monstar: visualization of singularities of symmetric second rank tensor fields in the plane, J. Liu, W.T. Hewitt, W.R.B. Lionheart, J. Montaldi and M. Turner (2008). See above! The three fundamental topological structures of polarization singularities are lemons, stars, and a hybrid, the monstar. The monstar is a little mysterious compared to the other two, and this paper tries to sort it out.
2/18: Polarization singularity anisotropy: determining monstardom, M.R. Dennis (2008). A short and elegant paper that ties the rather abstract rules for lemons, stars and monstars to the actual physical properties of the polarization of light.
2/19: Electromagnetic scattering from anisotropic materials, part 1: general theory, R.D. Graglia (1984). Part of my current research interest relates to the scattering of light from materials that possess both electric and magnetic responses; it turns out to be verrrrrry hard to sort things out in this case. This early paper looks at the theoretical aspects of such scattering, building up to computational studies.
2/20: Sharper focus for a radially polarized light beam, R. Dorn, S. Quabis, and G. Leuchs (2003). It is possible to construct light beams that have radial polarization: that is, the axis of polarization points away from the center of the beam at every point in its cross-section. Such beams turn out to work quite well compared to conventionally polarized beams in many applications, including focusing. As this paper shows, radially polarized light actually focuses to a (slightly) smaller spot.
2/21: Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss solution, R.H. Jordan and D.G. Hall (1994). Before people were studying radial polarization in depth, azimuthal polarization (polarization axis pointing around a circle) was being investigated. This paper was the first to derive a simple analytic solution for such azimuthally polarized light, starting an entire subfield of optics.
2/22: Vector-beam solutions of Maxwell’s wave equation, D.G. Hall (1996). Following up on the previous paper, in which one solution for an azimuthal beam was found, this paper constructs a whole family of such solutions.
Whew! That was a lot! Tune in soon for even more #365papers!