Optical isotropy in polycrystalline ${\mathrm{Ba}}_2\mathrm{Ti}{\mathrm{Si}}_2{\mathrm{O}}_8$: Testing the limits of a well established concept

We report an optical properties investigation of randomly oriented polycrystalline solids with anisotropic crystal structure. Using fresnoite as the model material, we demonstrate several domain size effects, most notably that a cross-polarization response is observed for the case of large randomly oriented crystallites. We compare our measured results with simulations from several different dielectric models and demonstrate that the appropriate model depends upon the grain size. The results have important implications for the understanding of optical isotropy in polycrystalline materials and bulk vs nanoscale effects.

Figure 1

$300\mathrm{K}$ infrared reflectance spectra of randomly oriented polycrystalline fresnoite with average crystallite diameters $d\approx 10$ $\mu \mathrm{m}$ and $300\mathrm{nm}$. These data were taken with a 20° angle of incidence. Polarizer positions were set for both $s$- and $p$-polarized incident radiation; no analyzer was used. The similarity between the $s$- and $p$-polarized spectra for the small domain material is a consequence of the sample isotropy and the comparably small angle of incidence.

Figure 2

Comparison of the measured $s$- and $p$-polarized reflectance spectra of large domain sized polycrystalline fresnoite with simulated results to test Doll’s hypothesis (Ref. 21). A 20° angle of incidence was employed. Polarization selection ($s$ or $p$) was made on the incident radiation; no analyzer was used.

Figure 3

A comparison of the measured and simulated cross-polarized reflectance spectra of polycrystalline fresnoite consisting of large crystallites. The angle of incidence was 6° in the far infrared, with $s$-polarized incident radiation. The angle of incidence was 20° in the middle infrared, and we show results for both $s$- and $p$-polarized incident radiation. In each case, the analyzer was orthogonal to the polarizer. Note that cross polarization effects are not observed in samples where the randomly oriented domains were small compared with the wavelength of light.

Figure 4

Comparison of the experimental and simulated reflectance spectra of polycrystalline fresnoite consisting of small crystallites. A 20° angle of incidence and $s$-polarized incident radiation were employed for the measurements. The simulation employs a linear combination of the principal dielectric functions of the ${\mathrm{Ba}}_2\mathrm{Ti}{\mathrm{Si}}_2{\mathrm{O}}_8$ single crystal (Ref. 4). Note the poor agreement between the two curves.

Figure 5

Comparison of the experimental and simulated reflectance spectra of polycrystalline fresnoite consisting of small crystallites. A 20° angle of incidence was used for the measurements. Both $s$- and $p$-polarized incident radiation were employed, as appropriate. No analyzer was used. The results of two different simulation methods effective medium approximation (EMA) (upper panel) and average refractive index theory (ARIT) (lower panel), are shown for comparison.