When a thin film that is prepared in a step form on a substrate and coated uniformly with a reflective material is illuminated by a parallel coherent beam of monochromatic light, the Fresnel diffraction fringes are formed on a screen perpendicular to the reflected beam. The visibility of the fringes depends on film thickness, angle of incidence, and light wavelength. Measuring visibility versus incident angle provides the film thickness with an accuracy of a few nanometers. The technique is easily applicable and it covers a wide range of thicknesses with highly reliable results.
We introduce a relatively simple and efficient optical technique to measure nanoscale displacement based on visibility variations of the Fresnel diffraction fringes from a two-dimensional phase step. In this paper we use our technique to measure electromechanical expansions by a thin piezoelectric ceramic and also thermal changes in the diameter of a tungsten wire. Early results provide convincing evidence that sensitivity up to a few nanometers can be achieved, and our technique has the potential to be used as a nanodisplacement probe.
X-ray microdiffraction utilizing Fresnel zone plate focusing optics has been used to study microstructural properties of individual 90 degree ferroelectric domains in BaTiO3. Diffraction measurements at a microfocused spot resolution of 0.3 microm over domain widths of approximately 10 microm unambiguously reveal features of lattice buckling, rotation, and strain near domain boundaries. Our results may be understood within the context of bound residual strain due to lattice mismatch and elastic interactions between neighboring domains.
When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.
We investigate lattice orientation and strain fields across ferroelectric domain walls in a single crystal lithium tantalate using x-ray diffraction imaging ͑topography͒. The sample is an actual voltage-operated optical switch consisting of a series of triangular polarization-inverted domains formed in an originally poled single crystal. By applying an electric field only about 2% of the coercive field in the forward and reverse directions, we observed asymmetric lattice rotation of about 10 −6 rad, and normal strain variation in the order of 10 −5 with reference to the zero-field state. Our results confirm that in congruent LiTaO 3 crystals there is unexpectedly large strain field expanding several micrometers across the domain walls, in contrast with the widely accepted theoretical fact that in this material the polarization reversal establishes over only a few lattice constants, resulting in small and localized lattice distortions.
In this work we present the theoretical background and experimental procedure to measure the thickness of thin films by analyzing Fresnel diffraction patterns obtained from polychromatic illumination of phase-step samples. As examples of this technique, we measured the thicknesses of thin aluminum layers on glass substrates using three different broad-spectrum light sources. The results are in excellent agreement with independent interferometric measurements within less than 5% relative uncertainties.
Ellipsometry is an important and non-destructive technique to measure the optical constants and thicknesses of layered materials. This technique is based on the simple idea of changes in the polarization state of light upon reflection from the sample surface. However, commercial ellipsometers are rather complicated and expensive devices that are not the best choice for learning the principles of ellipsometry. They usually require precise measurements of the angular position of polarization-sensitive components, such as polarisers and wave retarders. In this paper we demonstrate a simple ellipsometer which uses the concept of Stokes parameters to fully determine the polarization state of the reflected light by measuring the relative intensities at four positions of the analyser. We also describe the essential steps in analysing the ellipsometry data, and provide three real-world examples. The film thickness and index of refraction of layered samples are measured with reasonable accuracy. This work is the result of a graduate-level physics project and can easily be implemented in an educational optics laboratory to help graduate students better understand and use the concepts of light polarization, Stokes parameters, and ellipsometry.
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