Optical diffraction in chiral smectic-C liquid crystals

[Nature India Special Issue: Lighting the way in physics]

Sir Chandrasekhara Venkata Raman and his student Nagendra Nath published a series of papers in 1936 on the diffraction of light by a liquid in the field of a high frequency sound wave. This was theoretical work developed to explain the observed diffraction pattern obtained for light incident on a liquid medium of periodically varying refractive index arising from the passage of a high frequency sound wave. This is usually referred to as optical diffraction in the phase grating mode since the phase of an incident plane wavefront varies periodically when emerging from the medium without any variations in amplitude.

Thermodynamically, liquid crystals (LCs) are an intermediate phase between a crystal and a liquid phase. LCs are broadly classified into three types: nematic, smectic and cholesteric LC phases. The smectics are further classified into smectic A, smectic B, smectic C and so on. The smectic Cs that are made up of chiral molecules are classified separately as chiral smectic-C LCs (CSLCs). They are structures with a helical stack of layers in each of which molecules are tilted uniformly in a particular direction. The tilt direction spirals about the layer normal. Generally, the tilting of the molecules is coupled to the layer thickness resulting in a local biaxiality in the medium. When light is incident normal to the helical axis or twist axis, such a structure will act as a phase grating for light waves.

In the 1990s, Gobbalipur Shamanna Ranganath and Kattera Appanna Suresh, both then faculty members at the Raman Research Institute, applied Raman and Nath’s theory to optical diffraction in CSLCs. PhD student P.B. Sunil Kumar collaborated with them in these studies. Their calculations implied extra orders which were odd orders in the diffraction pattern. They were always linearly polarised whereas the even orders were elliptically polarised. They also found wandering of intensity from lower orders to higher orders, with variation in the local birefringence of CSLCs (K.A Suresh. and P. B. S. Kumar et al, Liq. Cryst. 1, 73; 1992).

To verify these theoretical results, Suresh and his PhD student Yuvaraj Sah conducted experiments on a commercially available sample BDH-SCE-6 which exhibited a CSLC phase. They aligned the sample appropriately in the phase grating geometry by applying a high magnetic field. This configuration with the laser light (632.8 nm) incident normal to the twist axis of CSLC yielded an excellent diffraction pattern with sharp diffraction spots. Their experimental results turned out to be surprising (K. A. Suresh, Y. Sah, et al. Phys. Rev. Lett. 72, 2863; 1994).

The observed features were very different from the predictions of the original theory as extended to CSLCs in the paper by Suresh and colleagues published in 1992. The various orders in the observed pattern showed some unusual intensity and polarisation features. Depending upon the polarisation geometry, the intensities of some of the higher orders were much higher than that of the lower orders. For the incident linearly polarised light, the diffracted light was linearly polarised in a direction parallel to the twist axis in all the orders. These intensity and polarisation features contradicted the results of the original theory that had been extended to CSLCs.

It was soon realised that the theory was valid only for systems with low birefringence and for small enough sample thickness in which internal diffractions within the medium could be neglected. In reality, the material used in the experiments had a high birefringence and the sample thicknesses were on the higher side. Incorporating the internal diffraction required a more rigorous theory.

Ranganath and Kumar adopted the theory of anisotropic dielectric gratings developed in 1983 (K. Rokushima and J. Yamakita J. Opt. Soc. Am. 73, 7, 901–908; 1983). They applied this theory and formulated equations suitable to the optical diffraction in the CSLC system. Using the material parameters, they computed the intensities of different orders for varying sample thicknesses. The intensity values for proper choice of material parameters agreed well with the experimental results. The computations showed that the theory could also account for the polarisation features seen in the experiments, in the zero and higher orders of diffraction. It was satisfying to note that the experimental results and the theory matched so well.

The experiments and theory have shown that CSLCs can act as an efficient phase grating for light waves. The birefringence of the medium can change by varying the sample temperature. Hence the intensity of the various orders of the optical diffraction can be tuned. This tuning of intensities has wide applications in optical communication.

CSLCs have drawn a lot of attention due to their distinctive helical structure. The existence of ferroelectricity in CSLCs has led to technological applications. The sub-microsecond dynamics and large electro-optic response has been exploited in the fast-switching display devices. Several studies have demonstrated a variety of physical properties exhibited by CSLC. For example, it exhibits pyroelectricity, electroclinical effect, shear-induced polarisation, second harmonic generation and many other interesting phenomena. Even today, the CSLCs are being studied for their fascinating electro-optic and other physical properties.