An Analytical Model of Light Scattering by Birefringent Polycrystalline Dielectrics Using Perturbation of Maxwell & apos;s Equations

Polycrystalline materials have shown promise in advanced optical applications because of their unique optical and mechanical properties. Most polycrystalline materials have non-uniform optical properties due to residual porosity, secondary phases, and/or crystalline anisotropies (e.g., birefringence). These optical inhomogeneities manifest as scattering that reduces the transparency of the polycrystal. Even in the case of a single-phase polycrystal with negligible porosity, birefringence scattering will always be present whenever the crystal is anisotropic (non-cubic). Multiple models for predicting birefringence scattering have been suggested in the literature that are successful in describing scattering loss in specific material systems. Here a first-principles model of birefringent scattering that is applicable to any single-phase, unaligned transparent polycrystal is derived. The model can treat grain size distributions and is not limited to a specific material system. The derivation culminates in an equation that describes birefringence scattering coefficient spectra using the single-crystal refractive index tensor and chord length distribution (measured from a representative polished surface micrograph). The model should be useful for designing materials and characterization. For example, it can be used to predict transmissions of transparent polycrystals for a range of grain sizes or to characterize the average grain size using a transmission measurement. A model is presented for birefringent scattering that is applicable to any single-phase, unaligned transparent polycrystal. The model can treat grain size distributions and is not limited to a specific material system. The derivation culminates in an equation that describes birefringence scattering coefficient spectra using the single-crystal refractive index tensor and chord length distribution. The model should be useful for designing materials and characterization.image