The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding

Optical Investigations of Charge Gap in Orbital Ordered La1/2Sr3/2MnO4

Temperature and polarization dependent electronic structure of La1/2Sr3/2MnO4 were investigated by optical conductivity analyses. With decreasing temperature, for E//ab, a broad mid-infrared (MIR) peak of La1/2Sr3/2MnO4 becomes narrower and moves to the higher frequency, while that of Nd1/2Sr3/2MnO4 nearly temperature independent. We showed that the MIR peak in La1/2Sr3/2MnO4 originates from orbital ordering associated with CE-type magnetic ordering and that the Jahn-Teller distortion has a significant influence on the width and the position of the MIR peak.Comment: 10 pages, 4 figure

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 99. DOI: 10.1088/1367-2630/9/4/099A detailed optical study of the iridescent outer-shell of the beetle Plusiotis boucardi has revealed a novel microstructure which controls both the polarization and wavelength of reflected light. A previously unreported hexagonal array across the integument of the beetle exhibits highly localized regions of reflection of only red and green left-handed circularly-polarized light. Optical and transmission electron microscopy (TEM) imaging reveals the origin of this effect as an array of 'bowl-shaped' recesses on the elytra that are formed from a dual-pitch helicoidal layer. Reflectivity spectra collected from the beetle are compared to theoretical data produced using a multi-layer optics model for modelling chiral, optically anisotropic media such as cholesteric liquid crystals. Excellent agreement is obtained between data and theory produced using a model that incorporates an upper isotropic layer (of cuticular wax), followed by a short pitch (310 (± 1) nm) overlying a longer pitch (370 (±1) nm) helicoidal layer of optically anisotropic material. These layers are backed by an absorbing underlayer. Synthetic replication of this form of structure may provide a route to the fabrication of tuneable micro-mirrors for optical applications

Crystalline-to-plastic phase transitions in molecularly thin n-dotriacontane films adsorbed on solid surfaces

doi:10.1063/1.3213642Crystalline-to-rotator phase transitions have been widely studied in bulk hydrocarbons, in particular in normal alkanes. But few studies of these transitions deal with molecularly thin films of pure n-alkanes on solid substrates. In this work, we were able to grow dotriacontane (n-C32H66) films without coexisting bulk particles, which allows us to isolate the contribution to the ellipsometric signal from a monolayer of molecules oriented with their long axis perpendicular to the SiO2 surface. For these submonolayer films, we found a step in the ellipsometer signal at ~331 K, which we identify with a solid-solid phase transition. At higher coverages, we observed additional steps in the ellipsometric signal that we identify with a solid-solid phase transition in multilayer islands (~333 K) and with the transition to the rotator phase in bulk crystallites (~337 K), respectively. After considering three alternative explanations, we propose that the step upward in the ellipsometric signal observed at ~331 K on heating the submonolayer film is the signature of a transition from a perpendicular monolayer phase to a denser phase in which the alkane chains contain on average one to two gauche defects per molecule.This work was supported by the Chilean government through FONDECYT Grant Nos. 1060628 and 7080105 and by CONICYT scholarships (E.A.C., V.d.C. and P.A.S.), and by the U.S. NSF Grant No. DMR-0705974

The anomaly of the oxygen bond-bending mode at 320 cm−1^{-1} and the additional absorption peak in the c-axis infrared conductivity of underdoped YBa2_{2}Cu3_{3}O7−δ_{7-\delta} single crystals revisited by ellipsometricmeasurements

We have performed ellipsometric measurements of the far-infrared c-axis dielectric response of underdoped YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ single crystals. Here we report a detailed analysis of the temperature-dependent renormalization of the oxygen bending phonon mode at 320 cm$^{-1}$ and the formation of the additional absorption peak around 400-500 cm$^{-1}$. For a strongly underdoped YBa$_{2}$Cu$_{3}$O$_{6.5}$ crystal with T$_{c}$=52 K we find that, in agreement with previous reports based on conventional reflection measurements, the gradual onset of both features occurs well above T$_{c}$ at T*$\sim$150 K. Contrary to some of these reports, however, our data establish that the phonon anomaly and the formation of the additional peak exhibit very pronounced and steep changes right at T$_{c}$. For a less underdoped YBa$_{2}$Cu$_{3}$O$_{6.75}$ crystal with T$_{c}$=80 K, the onset temperature of the phonon anomaly almost coincides with T$_{c}$. Also in contrast to some previous reports, we find for both crystals that a sizeable fraction of the spectral weight of the additional absorption peak cannot be accounted for by the spectral-weight loss of the phonon modes but instead arises from a redistribution of the electronic continuum. Our ellipsometric data are consistent with a model where the bilayer cuprate compounds are treated as a superlattice of intra- and inter-bilayer Josephson-junctions

Nematic liquid crystal alignment on chemical patterns

Patterned Self-Assembled Monolayers (SAMs) promoting both homeotropic and planar degenerate alignment of 6CB and 9CB in their nematic phase, were created using microcontact printing of functionalised organothiols on gold films. The effects of a range of different pattern geometries and sizes were investigated, including stripes, circles and checkerboards. EvanescentWave Ellipsometry was used to study the orientation of the liquid crystal (LC) on these patterned surfaces during the isotropic-nematic phase transition. Pretransitional growth of a homeotropic layer was observed on 1 ¹m homeotropic aligning stripes, followed by a homeotropic mono-domain state prior to the bulk phase transition. Accompanying Monte-Carlo simulations of LCs aligned on nano-patterned surfaces were also performed. These simulations also showed the presence of the homeotropic mono-domain state prior to the transition.</p

Highly sensitive label-free in vitro detection of aflatoxin B1 in an aptamer assay using optical planar waveguide operating as a polarization interferometer

This work reports on further development of an optical biosensor for the in vitro detection of mycotoxins (in particular, aflatoxin B1) using a highly sensitive planar waveguide transducer in combination with a highly specific aptamer bioreceptor. This sensor is built on a SiO2–Si3N4–SiO2 optical planar waveguide (OPW) operating as a polarization interferometer (PI), which detects a phase shift between p- and s-components of polarized light propagating through the waveguide caused by the molecular adsorption. The refractive index sensitivity (RIS) of the recently upgraded PI experimental setup has been improved and reached values of around 9600 rad per refractive index unity (RIU), the highest RIS values reported, which enables the detection of low molecular weight analytes such as mycotoxins in very low concentrations. The biosensing tests yielded remarkable results for the detection of aflatoxin B1 in a wide range of concentrations from 1 pg/mL to 1 μg/mL in direct assay with specific DNA-based aptamers