Polarization optical microscopy

In Chapter 2.5.1, the concept of optical birefringence was introduced, and thereby the ex-pression for the transmitted polarized light intensity was presented. Here, we shall look into the experimental aspects of polarization optical microscopy (POM). All experiments were conducted using transmission microscopy, i. e., the light passing through the sample was ana-lyzed. Figure 3.5a presents the overall experimental technique. Unpolarized white light from the microscope illumination source is first passed through apolarizer. A polarizer is an optical filter that converts unpolarized light and passes only a specific linear polarization decided by the polarizer axis (indicated by the double-headed arrow in Fig. 3.5a). The polarized light on reaching the NLC sample is split into the ordinary and extraordinary components as shown in Fig. 2.7. Consequently, an elliptically polarized light is obtained after the LC sample, which then passes through another polarizer, known as theanalyzer, before reaching the microscope

Figure 3.5: Polarization optical microscopy (POM). (a) Schematic representation of the POM principle. (b) Michel-L´evy birefringence chart [148].

ocular or the high-sensitivity CCD camera. In fact, the analyzer is also a polarizer, whose axis can be parallel, perpendicular, or at any intermediate angle relative to the polarizer. In the present setup, both the polarizer and the analyzer could be rotated with a precision of π/180 = 1^◦. When the polarizer and analyzer axes are mutually perpendicular it is termed ascrossed polarizedstate. Additionally, by placing the microchannel on a rotating stage, the angle of the sample relative to the crossed polarizers was changed. When a component of the elliptically polarized light is transmitted through the crossed analyzer, the sample appears bright. No light is transmitted when the optical axis of the NLC is parallel to one of the polar-izer axes. This renders a dark appearance to the sample when observed between the crossed polarizers.

The static and the flow-induced equilibrium director orientation of 5CB in the microchan-nels was determined using a Nikon Eclipse LV100 (Japan) polarizing microscope. Depending upon the region of interest and optical resolution desired, a set of different objectives was used:

5×, 10×, 20×, 40×, 60×, and 100×. Barring the 60× and 100× oilobjectives, the rest were airobjectives. Thenumerical aperture, NA, for lower magnification objectives was typically around 0.5, while for the oil objectives the NA varied from 1.25 to 1.4. In addition to the orthoscopic studies, conoscopy [149] was performed by introducing a Bertrand lens between the analyzer and the ocular. Although conoscopy is a frequently used technique in the field of minerology, it is particularly helpful in the detection of the axiality (uniaxial or biaxial), and the optical characterization (optically positive or negative) of LC samples [72]. Besides

complementing observations from the standard POM methods, the conoscopic technique is also useful in identifying the exact nature of the surface anchoring in the LC samples [150].

In the previous chapter, we have seen that the intensity of the polarized light after the analyzer depends upon the sample birefringence, thickness, and the orientation of the LC optical axis relative to the analyzer axis (see equation 2.30). When the sample is illuminated using white light, one observes a colourful birefringent texture, especially in thin samples.

Michel L´evy, a French geologist, correlated the dependence of the birefringence (and its order) on the sample thickness and presented it using a chart, as shown in Fig. 3.5b.

In a homeotropic sample, the direction of the light propagation coincides with that of the optical axis, i. e.φ=0, and from the equations 2.26 and 2.27:

ne = nkn⊥

Consequently I = 0, the birefringence vanishes for a sample aligned homeotropically. Irre-spective of the sample orientation relative to the crossed polarizers, it appears dark due to complete extinction of the transmitted light. Thus, LC samples aligned homeotropically are also referred to aspseudo-isotropic[72]. On the other hand, for samples aligned unidirection-ally, φ = π/2, and correspondingly ∆n = ne −no = nk−n⊥. The transmitted intensity now varies only withϕ(see equation 2.30). As a result of this, a uniformly aligned sample appears dark (akin to homeotropic) when the optical axis is parallel (or perpendicular) to one of the polarizers. The maximum of the transmitted intensity is obtained at a sample orientation of π/4 relative to the crossed polarizers. The schlieren textures presented in Fig. 2.11 evolves due to different orientations of the nematic director within a confinement possessing random anchoring conditions.

Essentially, rotation of the sample stage or the crossed polarizers forms the first step to-wards reconstruction of the in-plane director field within a nematic sample. Owing to the quadratic dependence of the transmitted intensity, I, onϕ: I ∝ sin²2ϕ, the transmitted signal obtained for symmetrical values of ϕ = ±ϕ₀ cannot be distinguished. For this purpose an opticalretardation platewas used, inserted between the sample and analyzer, at angle ofπ/4 relative to the crossed polarizers. The quartz retardation plate is characterized by two primary

Figure 3.6: Optical retardation using λ plate. (a) Polarized micrographs of a colloid with perpendicular anchoring on its surface, dispersed in a homeotropic matrix of nematic 5CB.

Insertion of theλplate (on the right) helps to distinguish regions of similarly bright intensity (left micrograph). (b) Colour scheme showing LC director field observed with aλplate atπ/4 relative to the crossed polarizers.

axes: fast and slow along which the refractive indices are minimum and maximum respec-tively. In the present work, a retardation plate producing a phase shift of 530 nm was used (also known asλplate). The regions of minimum intensity appear red due to the reduced phase retardation. Correspondingly, the brighter regions acquire different colours depending upon the orientation of the director relative to the fast and slow axes. As an example, the director field around a colloid particle within a homeotropic matrix of 5CB is shown in Fig. 3.6. The bright regions observed between crossed-polarizers show different colours on insertion of the λplate. Figure 3.6b represents the colour scheme expected from different director orientations on introduction of aλplate.