Liquid Crystals

Chapter 6 - Liquid Crystal Optics and Electro-Optics


Perhaps the most studied and applied property of liquid crystals is their light-scattering
ability. With the aid of an externally applied (usually electric field) field, one can
control or realign the anisotropic liquid crystal axis, thereby controlling the effective
refractive index and phase shift experienced by the light traversing the liquid crystal.
Such electro-optical processes form the basis for various optical transmission, reflection,
switching, and modulation applications. Essentially, the liquid crystal cells are
placed within a stack of phase-shifting (phase retardation) wave plates or polarizing
elements to perform various electro-optical functions,1,2 see Figure 6.1. These operations
usually require a phase shift Δφ on the order of π (e.g., quarter wave plate
requires π/4 and half-wave plate requires π, and so on). Depending on the actual configuration,
the phase shift imparted by the liquid crystal cell Δφ ~ d(Δn)2π/λ, where
d is the path length of the light through the liquid crystal layer, Δn is the birefringence,
and λ is the wavelength.

As seen in previous chapters, liquid crystals are noted for their large birefringence
and easy susceptibility to external field perturbation. To create the required phase
shift for optical application in the visible to near IR regime, only applied voltages of
a few volts and a film thickness of a few microns are required. Since the interaction
of the applied field (usually an ac field) with the nematic, for example, is essentially
a dielectric one, the process of electro-optical control is essentially free of current
flow and dissipation, i.e., very little power is consumed. As a result, liquid crystal has
enjoyed wide spread and an ever increasing demand in various optical display,
switching, information, and image processing industries.

The problem of polarized light propagation in liquid crystals is actually quite
complex, and its quantitative description requires exact treatment of electromagnetic
and anisotropic media. The problem is compounded by the fact that, in general, the
director axis orientation within the cell is inhomogeneous and varies spatially in a
nonuniform manner because of boundary anchoring effects in response to an applied
field. Many sophisticated theoretical techniques and formalisms have been developed
to quantitatively treat the detailed problem of light propagation in these highly



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