The propagation of these waves through an isotropic crystal occurs at constant velocity because the refractive index experienced by the waves is uniform in all directions (Figure 5(a)). The lower section of the Michel-Levy chart (x-axis) marks the orders of retardation in multiples of approximately 550 nanometers. One of the images appears as would normally be expected when observing an object through clear glass or an isotropic crystal, while the other image appears slightly displaced, due to the nature of doubly-refracted light. Examples are stretched films and fibers, deformed glass and plastic lenses, and stressed polymer castings. Birefringence is formally defined as the double refraction of light in a transparent, molecularly ordered material, which is manifested by the existence of orientation-dependent differences in refractive index. When these projections are then measured on the vectors, the resultant can be determined by completing a rectangle to the analyzer axis (A). The difference in refractive index, or birefringence, between the extraordinary and ordinary rays traveling through an anisotropic crystal is a measurable quantity, and can be expressed as an absolute value by the equation: where n(e) and n(o) are the refractive indices experienced by the extraordinary and ordinary rays, respectively. 53 0 obj <>stream If the crystal were to be slowly rotated around the letter, one of the images of the letter will remain stationary, while the other precesses in a 360-degree circular orbit around the first. This high level of birefringence is not observed in all anisotropic crystals. Projections of the vectors are dropped onto the axis of the polarizer, and assume an arbitrary value of 1 for both o and e, which are proportional to the actual intensities of the ordinary and extraordinary ray. Stress and strain birefringence occur due to external forces and/or deformation acting on materials that are not naturally birefringent. Non-polarized white light from the illuminator enters the polarizer on the left and is linearly polarized with an orientation in the direction indicated by the arrow (adjacent to the polarizer label), and is arbitrarily represented by a red sinusoidal light wave. The most sensitive area of the chart is first-order red (550 nanometers), because even a slight change in retardation causes the color to shift dramatically either up in wavelength to cyan or down to yellow. Light entering the crystal from the polarizer will be traveling perpendicular to the optical (long) axis of the crystal. Even though the ordinary and extraordinary rays emerge from the crystal at the same location, they exhibit different optical path lengths and are subsequently shifted in phase relative to one another (Figure 4(b)). The net result is that some birefringent samples acquire a spectrum of color when observed in white light through crossed polarizers. These optically anisotropic materials are said to be birefringent (or birefractive). The behavior of an ordinary light ray in a birefringent crystal can be described in terms of a spherical wavefront based on the Huygens' principle of wavelets emanating from a point source of light in a homogeneous medium (as illustrated in Figure 5). The calcite crystal presented in Figure 3(b) is positioned over the capital letter A on a white sheet of paper demonstrating a double image observed through the crystal. Although birefringence is an inherent property of many anisotropic crystals, such as calcite and quartz, it can also arise from other factors, such as structural ordering, physical stress, deformation, flow through a restricted conduit, and strain. The actual division of a light ray into two visible species, each refracting at a different angle, is the process of double refraction. α-BBO (α-BaB2O4) is a negative uniaxial crystal which has large birefringence over a broad transparent range of 190nm to 3500nm. The term anisotropy refers to a non-uniform spatial distribution of properties, which results in different values being obtained when specimens are probed from several directions within the same material.

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