Liquid Crstals
Liquid crystals (LCs) are organic molecules strongly alongated in one direction, characterized by a large anisotropy of their physical properties. They form mesoscopic phases that exist in certain ranges of temperature. Among the most used mesoscopic phases ( display, TV,  screen, projector, etc...) are the nematic LCs. They present a long range orientational order, with all the molecules oriented along a preferential direction, so called nematic director.

From the optical point of view, a nematic LC film behaves as a birefringent plate with the extraordinary (ordinary) index parallel (orthogonal) to the director. Nematics exhibit large birefringence, transparency over a large range of the electromagnetic spectrum (from UV to microwaves), high sensitivity to applied electric and/or magnetic fields. The director orientation can, thus, be driven either electrically, magnetically or optically.
LC can have positive or negative anisotropy, for positive (negative) anisotropy the molecules tend to align parallely (perpendicularly) to the applied field.

Planar aligned liquid crystals cell

The nematic LCs are anchored to the confining walls by a suitable surface treatment that force the director to be parallel to the two cell windows. The inner surface of each window is coated with a transparent conductive layer which allows applying a voltage across the cell, hence, an electric field across the LC film.

Molecules tend to align in such a way to become to the direction of the applied field. The light traversing the LC cell can be decomposed in an ordinary wave, that always sees the same refractive index, and an extraordinary wave that sees a refractive index which depends on the LC molecular orientation.
Based on this mechanism it is possible to modulate the phase of the light phase (by adding polarization element the light intensity is controlled as well).
Liquid crystal light-valves use the same principle but in addition they comprise a photosensitive cell wall.

Homeotropic aligned liquid crystals cell
The LC molecules are aligned perpendicularly to the surface of each windows forming the cell.

In the case of negative electrical anisotropy, when an electric field is applied on the cell the molecules tend to align perpendicular to the field. In this case because the radial symmetry in the nematic configuration, the formation of defects occur.   

Twisted nematic cell (TN)
The cell is planar but the entrance and exit anchoring are orthogonally aligned. The director follow a twist conformation.  

The pitch of the twist is larger than the light wavelenght and the input light polarization follow adiabatically the director orientation (Mauguin regime). At the output the light is perpendicular polarized. By adding an output polarizer the cell is used as intensity light modulator

Cholesteric liquid crystals (CLC)

Liquid Crystals Readings:
  • P. G. De Gennes, and J.Prost "The Physics of Liquid Crystals", Oxford University Press, 1974 (1re édition) 1976 (2e édition).
  • S. Chandrasekhar, Liquid Crystals, Cambridge University Press (1994).
  • I.C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, 2nd edition, Wiley, NJ (2007).
  • G. Chilaya, Cholesteric liquid crystals: optics, electrooptics and photooptics in Chirality in Liquid Crystals, Ch. Bahr, and H. Kitzerow, eds (Springer Verlag, New York, 2000).
  • M. Mitov, G. Weiss, Sensitive Matter: Foams, Gels, Liquid Crystals, and Other Miracles, Harvard University Press (2012).
  • D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices, (John Wiley & Sons, West Sussex, England).