Measurement of transmission and reflection from a thick anisotropic crystal modeled by a sum of incoherent partial waves

Abstract

Formulas for modeling ellipsometric measurements of bianisotropic crystals assume perfectly coherent plane wave illumination. As such, the finite coherence of typical spectroscopic ellipsometers renders such formulas invalid for crystals thicker than a few micrometers. Reflection measurements of thick crystalline slabs show depolarization. Researchers have proposed strategies for the full accounting for multiply reflected incoherent waves in anisotropic, arbitrarily oriented crystals [Appl. Opt.41, 2521 (2002).APOPAI0003-693510.1364/AO.41.002521], but to the best of our knowledge these methods have not been tested by explicit measurements. It is shown that by a summation of multiply reflected incoherent waves, transmission and reflection measurements of thick quartz slabs can be interpreted in terms of the constitutive material parameters.

Gyration and Permittivity of Ethylenediammonium Sulfate Crystals

“…Crucial to our approach is an exact treatment of boundary conditions, and the multiple incoherent reflections inside the slab. We applied this method to quartz, and the results were in agreement with published dispersion relations …”

“…Eight unique matrices describe the changes in polarization upon refraction, reflection, or propagation. We provided formulas for their calculation elsewhere …”

“…A model was constructed to fit the Mueller matrix data . The free parameters were the dispersion relations for the components of ε and α , a constant angle of incidence offset, and the crystal miscut.…”

“…We recently developed a new approach that seeks to remedy the shortcomings in the current methods to recover ε and α. 42 From the reflection Mueller matrix of a single cut measured at multiple angles of incidence, the crystal thickness, the exact cut of the crystal, and the dispersion relations for the components of ε and α can be fitted together. Crucial to our approach is an exact treatment of boundary conditions, and the multiple incoherent reflections inside the slab.…”

On the chiroptical properties of racemic crystals

“…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. 26,27 The latter delivers the entire polarization transfer matrix, the 4 × 4 Mueller matrix, without any moving optical parts, a boon for the minimization of instrumental errors that can be as large as the light intensity changes from CB or CD. 18 This is why, even in transparent crystals, measurements of OR along low symmetry directions are extremely challenging, 19,20 with a number of the credible literature examples coming from crystals with accidental linear anisotropy compensation, that is, crystals with LB = 0 at particular frequencies.…”