Liquid Crystals

Chapter 7 - Electromagnetic Formalisms for Optical Propagation


In general, the methods for solving the problem of light propagation through a
medium depend on whether the light–matter interaction is linear or nonlinear. In linear
optics, the light fields (electric or magnetic) are not intense enough to create
appreciable changes in the optical properties of the medium (e.g., refractive index,
absorption or scattering cross sections, etc.) and so its propagation through the
medium is dictated primarily by its properties. In nonlinear optics, the light–matter
interactions are sufficiently intense so that the optical properties of the medium are
affected by the optical fields. For example, the optical field is intense enough to cause
director axis reorientations and so it experiences an ever changing refractive index as
it propagates in the medium. Such coupled interactions give rise to many so-called
self-action effects such as self-focusing, self-phase modulations, stimulated scattering,
etc. These nonlinear optical phenomena and other related processes will be discussed
in Chapters 11 and 12.

In this chapter, we discuss the case of linear optics of liquid crystal structures
extensively used in optical display applications. Such structures usually consist of
various optical phase shifting or polarizing elements in tandem and an aligned liquid
crystal cell serving as an electrically controlled phase-shifting element. In the
previous chapter, we discuss some aspects of the optics of an anisotropic medium
and illustrate mostly on-axis type of propagation and simple director axis reorientation
geometry that allow analytical solutions or conceptual understanding. These
limiting-case studies would suffice if we desired only to grasp the “physics” of the
processes. However, exact quantitative determination of the polarization state of
light and the director axis reorientation profile in a liquid crystal cell under an
applied ac field is mandated by the stringent requirements placed on practical display
devices. More sophisticated models and techniques are needed to calculate
both on-axis and off-axis propagations, inhomogeneous director axis distribution in
conjunction with a multitude of phase plates, filters, retarders, etc. Accordingly, a
detailed exposition of some of the fundamental theoretical formalisms and techniques
currently being used or developed for LC devices will be presented. For
completeness, we shall first review the current understanding of electromagnetic
theories of complex anisotropic media.