Double cone of eigendirections in optically active ethylenediammonium selenate crystals

Abstract

Circular birefringence (CB) is generally responsible for only a small perturbation to the state of light polarization in crystals that also exhibit linear birefringence (LB). As such, the magnetoelectric tensor of gyration, which gives rise to CB and optical activity, is less well determined than the electric permittivity tensor in optical models of the Mueller matrix. To visualize the effect of the magnetoelectric tensor on polarimetric measurements, reported here are experimental mappings of the Mueller matrix and of the CB in a new chiral crystal with accidental null LB at an accessible optical frequency. Single crystals of ethylenediammonium selenate (EDSeO) were synthesized and characterized by X-ray diffraction and Mueller matrix measurements in transmission and reflection. The crystals are isomorphous with the corresponding sulfate salt. They are tetragonal, space group 422. The constitutive relations of EDSeO were recovered using a partial wave summation of incoherent reflections. The extraordinary and ordinary refractive indices cross at 364 nm (3.41 eV), a scenario commonly called the 'isotropic point' or 'iso-index point'. At this wavelength, the magnetoelectric tensor fully describes the polarization transformation, giving rise to a double cone of eigendirections.

Tuning the optical isotropic point of mixed crystals of ethylenediammonium sulfate/selenate

“…Ethylenediammonium forms isomorphous P4 1 2 1 2 crystals with SO 4 2À , SeO 4 2À and BeF 4 2À , and P2 1 2 1 2 isostructural crystals with a variety of other anions (Srinivasan et al, 2013;Nichols et al, 2016;Martin et al, 2017a). Anion substitution in EDSe may lead to a family of isostructural crystals and mixed crystals with physical properties that can be tailored.…”

“…Crystal growth, morphology and optical heterogeneity EDS and EDSe were synthesized as described previously (Cheung et al, 2008;Martin et al, 2017a), and mixed crystals (EDS x Se 1Àx ) were grown from saturated aqueous solutions at room temperature, with the exception of Sample E which was grown at 413 K. The solubility of EDS in deionized water is ca 0.5 g ml À1 at 296 K, while that of EDSe is closer to 1.2 g ml À1 . Crystal growth, morphology and optical heterogeneity EDS and EDSe were synthesized as described previously (Cheung et al, 2008;Martin et al, 2017a), and mixed crystals (EDS x Se 1Àx ) were grown from saturated aqueous solutions at room temperature, with the exception of Sample E which was grown at 413 K. The solubility of EDS in deionized water is ca 0.5 g ml À1 at 296 K, while that of EDSe is closer to 1.2 g ml À1 .…”

“…where the tensor values for the pure crystals were taken from the literature (Nichols et al, 2016;Martin et al, 2017a). Fitted parameters for the eight mixed crystals are outlined in Table 1, along with the corresponding R 2 values which ranged from 0.949 to 0.999.…”

Polarization in France

“…Gibbs 56 first recognized that some achiral crystals could indeed be optically active, and this was stated formally by Voigt. 45,61,62 The story of the discovery of the link between macroscopic and microscopic chirality that Pasteur tells so romantically in 1860 54 fails to mention that along with old Biot who insisted that Pasteur perform his improbable resolution at the Collège de France under the senior colleague's watchful eye, there was another scientist in the room, Henri de Sénarmont. Optical activity was measured in a low symmetry direction of this achiral crystal at a particular frequency at which the refractive indices of eigenmodes in the crystal cross and the linear birefringence drops to zero, leaving only circular birefringence.…”

On the chiroptical properties of racemic crystals

“…Differential absorption maxima through different locations of the same crystal face vary It is conceivable that nonzero CD could be determined by simple measurements of differential absorption of right and left CPL, but only along an optic axis. 21,22 As only one crystallographic direction was probed for each crystal described in Gautier et al, 1 we can be sure that LB and LD were nonzero for some or all of the measured wavelengths. Unfortunately, the crystallographic orientations of the optic axes in biaxial crystals are generally wavelength dependent, so any particular direction chosen for measurement will only coincide with an optic axis for a single wavelength in the spectral region.…”