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There exist many methods of measuring the refractive index of a material, with various accuracies depending on the method. The best known high-accuracy technique (typically to the 4th decimal place) is the minimum angle technique. This technique requires forming the sample into a highly perfect prism, with extremely accurately characterised angles, such that the entry and exit angles of the probe light source can be measured accurately as it traverses the prism. For fast measurements of the refractive index, for measurements for extremely small samples, or for measurements where the material is hard to prepare into a suitable prism, this method is demanding in time and technology and may even be impossible.

An alternative method, that can provide the same accuracy with a reduced sample preparation is the critical angle method. Here a well characterised reference prism is placed in contact with the sample, and light is introduced along the interface as a parallel beam. This being the critical angle condition, measuring the angle of exit of the light from the reference prism, and knowing its refractive index can give the refractive index of the sample to an accuracy proportional to the accuracy of angular measurement. The most significant advantage is that only one face of the sample need be prepared, by flat-polishing. Where a birefringent sample is used, then several samples corresponding to the principal axes are required, though of course each sample need only have one facet prepared.

In this manner, a high-resolution critical angle experiment has been set up at Warwick, using an optical angle encoder on a PC-driven goniometer arm to measure the exit angle accurately, and with a cubic zirconia reference prism. Light is provided by a mercury-vapour lamp with a telescope and slit assembly to collimate the input light, and with wavelengths selected by appropriate filters from the mercury spectrum. The experiment has been calibrated with reference high-accuracy glasses, and reliably returns refractive indices with errors in the fourth decimal place of order 0.0004.

4.2.2 OPTACT

The optical properties of crystals can be successfully calculated using the established polarisability theory. By using a model where each atomic position of the unit cell is described as a point-dipole oscillator, the optical activity and refractive indices can be found to be in close agreement with experiment. The approach works by calculating the response of each dipole to the propagating light-field and then summing all the responses to give the global optical polarisation. Particularly, from this component-based approximation it is also possible to gain important insights into the source of the materials’ characteristic optical behaviour by identifying the important ionic configurations in the unit cell. Information gained about the linear optical response of a material can, by the Miller rule, be related to the NLO response as well, further extending the value of this kind of simulation.

The OPTACT program, by Devarajan and Glazer7, is a dedicated point-dipole theory program that operates on the polarisation ellipsoid associated with each atomic position in a model unit cell, and was designed to produce accurate optical activity simulation for crystals. The program is a reworking of several successive theories for the computation of optical activity. It is based mainly on the work of Reijnhart“, who applied a theory by Ewald that the response of each atom or ion in a medium to an incident light-field can be considered to be represented by an infinitely small electron-oscillator at its centre. This electron possesses an isotropic free-atom polarisability, and is the basis of the ‘point- dipole’ model. OPTACT achieves its simulation by combining the microscopic analysis (formed from the summation of the point-dipole oscillators) with a macroscopic analysis based on Maxwell’s equations applied to calculating polarisation. This essentially ‘classical’ solution has its own flaws, since it makes no allowance for quantum-mechanical interactions during optical activity, and since in a classical model, all the interaction between dipoles are assumed as the same type. This latter problem causes the calculation to fail in situations where atoms in a crystal see a highly irregular environment.

The program requires an input data set describing the wavelength of the radiation used for calculation*1 , a number of parameters that control the convergence of the summation (in real and reciprocal space, usually set at 7t'2 and the cube-root of the cell-volume). A list of the unit-cell co-ordinates of the crystal is combined with a list of the isotropic polarisability volume (A3) associated with each atom- type. The initial values of these volumes are generally obtained by intuitive guesses based on previous analyses.

Calculation sums the response of the crystal’s point-dipole oscillators, and tries to find an effective polarisability for each atom in the unit cell (an explanation of the mechanisms o f the calculation is beyond the scope of this thesis).

Amongst the output of the program, such as a calculation of the optical rotatory power of the crystal, is a calculation of refractive indices (for each crystal axis) and the associated birefringences the material should possess at the simulated optical frequency. These parameters arc the data of interest here.