Polarimetry is a highly sensitive method to quantify changes of the polarization state of light when passing through matter and is therefore widely applied in material science. The progress of synchrotron and X-ray free electron laser (XFEL) sources has led to significant developments of X-ray polarizers, opening perspectives for new applications of polarimetry to study source and beamline parameters as well as sample characteristics. X-ray polarimetry has shown to date a polarization purity of less than $1.4\times {10}^{-11}$, enabling the detection of very small signals from ultrafast phenomena. A prominent application is the detection of vacuum birefringence. Vacuum birefringence is predicted in quantum electrodynamics and is expected to be probed by combining an XFEL with a petawatt-class optical laser. We review how source and optical elements affect X-ray polarimeters in general and which qualities are required for the detection of vacuum birefringence.

An experimental study of optical anomalies in solid solutions of alums in relation to their composition, growth temperatures and rates, and hydrodynamic regime was carried out. Theoretical analysis of the data showed that they can be understood in terms of a mechanism of kinetic ordering of the isomorphous atoms (the phenomenon of so-called ‘growth dissymmetrization’). A theoretical model is presented which is supported by data for a number of minerals and synthetic compounds, which are known for their optical anomalies due to growth dissymmetrization.

The origin of anomalous birefringence of grossular–andradite (grandite) garnets from skarns in Mali and Russia was considered. The crystals had complex superposition of two phenomena: mismatch compositional strain (stress birefringence) and growth ordering of atoms (growth dissymmetrization). Study of the crystals using several experimental techniques (optical microscopy, microprobe analysis, X-ray diffraction topography and X-ray single crystal diffraction) as well as calculations of anomalous birefringence has confirmed this hypothesis. Depending on the crystal composition and growth conditions, the relative magnitude of each phenomenon controls the various optical effects. As a result one can see two groups of crystals which are found to have fundamentally different anomalous optical properties: crystals with low (<0.001) and high (0.001–0.015) values of birefringence. The spatial distribution of birefringence within each group is different and this fact is related to different mechanisms causing optical anomalies: stress birefringence and growth dissymmetrization for these two groups, respectively.

We present the results of performance modeling of a diode-pumped solid-state HiLASE laser designed for use in inertial fusion energy power plants. The main amplifier concept is based on a He-gas-cooled multi-slab architecture similar to that employed in Mercury laser system. Our modeling quantifies the reduction of thermally induced phase aberrations and average depolarization in ${\mathrm{Yb}}^{{3+}}$:YAG slabs by a combination of helium cryogenic cooling and properly designed (doping/width) cladding materials.

The crystal structure of one isotropic [(1) Brazil] and three birefringent spessartine samples [(2) California, (3) Tanzania, and (4) Colorado] were refined using the Rietveld method, cubic space group $Ia\overline 3 d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. The results of electron-microprobe analysis (EMPA) indicate homogeneous compositions, in terms of end-members, as follows: (1) Sps54Alm43, (2) Sps90Alm8, (3) Sps64Prp27Grs3, and (4) Sps73Alm19. Their crystal structures were modeled well as indicated by the Rietveld refinement statistics where the reduced χ 2 and overall R (F 2) values for each sample are: (1) 1.395 and 0.0329, (2) 1.082 and 0.0354, (3) 1.025 and 0.0347, and (4) 1.016 and 0.0413. Two cubic phases occur in samples 2–4, and a single cubic phase occurs in sample-1. The dominant cubic phase-1 with locality, weight fraction (%), unit-cell parameter (Å), distances (Å), and site occupancy factors (sofs) are as follows: (1) Brazil: 100%, a = 11.581 54 (1), average <Mn–O> = 2.3156, Al–O = 1.8949 (3), Si–O = 1.6376 (3) Å, Mn(sof) = 0.961(1), Al(sof) = 0.945(1), and Si(sof) = 0.936(1); (2) California: 96.67(7)%, a = 11.613 32(1), average <Mn–O> = 2.3249, Al–O = 1.8956 (4), Si–O = 1.6416 (4) Å, Mn(sof) = 0.951(1), Al(sof) = 0.946(1), and Si(sof) = 0.927(1); (3) Tanzania: 69.46(6)%, a = 11.598 45(1), average <Mn–O> = 2.3199, Al–O = 1.8964 (5), Si–O = 1.6398 (5) Å, Mn(sof) = 0.808(1), Al(sof) = 0.942(1), and Si(sof) = 0.922(1); and (4) Colorado: 98.58(6)%, a = 11.606 89(1), average <Mn–O> = 2.3204, Al-O = 1.8948 (6), Si–O = 1.6450 (6) Å, Mn(sof) = 0.949(1), Al(sof) = 0.967(2), and Si(sof) = 0.913(2). The two-phase intergrowth causes strain that arises from mismatch of the structural parameters and gives rise to strain-induced birefringence.

The structure of a birefringent andradite–grossular sample was refined using single-crystal X-ray diffraction (SCD) and synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Electron-microprobe results indicate a homogeneous composition of {Ca2.88Mn2+0.06Mg0.04Fe2+0.03}Σ3[Fe3+1.29Al0.49Ti4+0.17Fe2+0.06] Σ2(Si2.89Al0.11) Σ3O12. The Rietveld refinement reduced χ2 = 1.384 and overall R (F2) = 0.0315. The HRPXRD data show that the sample contains three phases. For phase-1, the weight %, unit-cell parameter (Å), distances (Å), and site occupancy factor (sof) are 62.85(7)%, a = 12.000 06(2), average <Ca–O> = 2.4196, Fe–O = 1.9882(5), Si–O = 1.6542(6) Å, Ca(sof) = 0.970(2), Fe(sof) = 0.763(1), and Si(sof) = 0.954(2). The corresponding data for phase-2 are 19.14(9)%, a = 12.049 51(2), average <Ca–O> = 2.427, Fe–O = 1.999(1), Si–O = 1.665(1) Å, Ca(sof) = 0.928(4), Fe(sof) = 0.825(3), and Si(sof) = 0.964(4). The corresponding data for phase-3 are 18.01(9)%, a = 12.019 68(3), average <Ca–O> = 2.424, Fe–O = 1.992(2), Si–O = 1.658(2) Å, Ca(sof) = 0.896(5), Fe(sof) = 0.754(4), and Si(sof) = 0.936(5). The fine-scale coexistence of the three phases causes strain that arises from the unit-cell and bond distances differences, and gives rise to strain-induced birefringence. The results from the SCD are similar to the dominant phase-1 obtained by the HRPXRD, but the SCD misses the minor phases.

The cause of birefringence in several garnet-group minerals with general chemical formula, [8]X3 [6]Y2 [4]Z3 [4]O12, which was observed over 100 years ago, is unknown, although many different reasons were proposed, including symmetry lower than cubic. In this study, electron microprobe analyses (EMPA) were obtained for a Ti-rich andradite, ideally Ca3(Fe2 3+)Si3O12, from Magnet Cove, Arkansas, USA, and the results show that the sample is inhomogeneous with two distinct compositions. The crystal structure was refined by the Rietveld method, cubic space group $Ia\overline 3 d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data, which shows a mixture of three distinct cubic phases that are intergrown together and cause birefringence because of strain arising from small structural mismatch. This mixture of three cubic phases was not observed by any other experimental technique. These results have many implications, including garnet phase transitions from cubic to lower symmetry in the mantle, which has important geophysical consequences.

This study was designed to investigate whether a non-invasive birefringence parameter, determined using the Oosight™ imaging system, is useful for estimating the hardness of human zona pellucida (ZP). The value for retardance (R) × thickness (T), but not R or T alone, of ZP was positively correlated (r = 0.92, p < 0.0001) with its hardness estimated by the time required for a 0.1% protease solution to solubilize ZP at 37 °C. In a model experiment to induce ZP puncture by Fluorinert™ fluid microinjection (sham-hatching), the R × T value at the punctured site was positively correlated (r = 0.78, p < 0.01) with the hardness of the ZP as estimated by the maximum expansion rate. The R × T values of ZP in in vitro fertilization-derived embryos (21.6 ± 7.5) and intracytoplasmic sperm injection-derived embryos (20.8 ± 6.3) were significantly higher than that in unfertilized metaphase II oocytes (16.6 ± 6.1; p < 0.05). The R × T value after in vitro hatching of viable blastocysts (10.8 ± 6.2) was significantly lower than that of unexpanded morulae and early blastocysts (19.0 ± 4.0; p < 0.05), while the value of expanding blastocysts (15.3 ± 4.1) was intermediate. In conclusion, hardness of human ZP can be estimated non-invasively by birefringence-based microscopic observation.