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Liquid crystals are potentially a very exciting technology for creating a real-time high- resolution three-dimensional (3D) display system. There have already been several different attempts to do this including lenticular flat panel displays, autostereoscopic systems and volumetric systems. Recently, amplitude holograms have been used to demonstrate a full-color 3D projection display by Qinetiq1, however this system was bulky, expensive and ultimately limited by the liquid crystal amplitude holograms. For the reproduction of a full 3D image, a fully complex hologram is the ultimate solution, but is very difficult to display using current technology. A purely phase-only hologram (or kinoform) is the best solution that we have for building 3D display at the moment, however there are limits due to the way in which a liquid crystal can be used to modulate a phase-only hologram. We have been developing a new liquid crystal device structure using a vertically grown multi-wall carbon nanotube (MWCNT)2 as a 3D electrode structure which allows a much more complicated phase-only hologram to be displayed using a conventional liquid crystal material.
Conducting MWCNTs can be used as a 3D electrode structure in optically anisotropic media such as liquid crystals, making novel new micro-optical components possible3. Their ability to appear as large (with respect to the size of the liquid crystal molecules) structures within a liquid crystal device means that there is a strong interaction between the nanotubes and the liquid crystal material. This interaction can be interpreted as an optical interaction through the optical anisotropy of the liquid crystal. Hence nano-structures can be used to form defect centers in liquid crystal materials which can be manipulated by applying an external electric field. The nanotubes act as individual electrode sites that spawn an electric field profile, dictating the refractive index profile with the liquid crystal cell. The refractive index profile then acts as a series of graded index profiles that form a phase profile. Changing the electric field applied makes it possible to tune the properties to modulate the light in an ideal kinoform.
The device shown in Figure 1(a) demonstrates a nanotube on the lower electrode and an upper electrode acting as an earth plane for the electric field. This upper electrode is made of transparent conducting material, indium tin oxide (ITO), on glass. A multi-wall carbon nanotube can be likened to a conductive metal rod of nanometer dimensions. When it is embedded between two plane electrodes, the nanotube changes the ideal plane electrostatic field profile. The electric field profile is approximately Gaussian in shape and the liquid crystal molecules will align to this field creating a varying (or graded) refractive index profile across the cell. This graded index is ideal for creating a fully variable phase function or kinoform as used in a 3D hologram. We have demonstrated a new device based on the combination of a sparse array of vertically grown multiwall carbon nanotubes on a silicon substrate to form an electrically reconfigurable micro-optical array as shown in Figure 1(b). This device now is being modified to allow the fields from each MWCNT electrode to overlap to create a full 3D phase profile through the liquid crystal material. The problem is how to address different voltages on the CNTs to make the desired kinoform function.
Liquid crystal over silicon (LCOS) is a perfect platform to create a suitable backplane for a full kinoform display. A typical LCOS backplane chip (Figure 1(c)) contains an array of full HDTV resolution transistors at each pixel that can be used to switch the individual CNT electrodes.
A perfect 3D image can be generated by a computer-generated hologram by using the diffraction of the light from the hologram pixels to create an optical wavefront that appears to come from a 3D object. This is done by a reverse propagation (Fourier transform)-based calculation that reverses the interference process to generate a phase function which, when illuminated with a laser, will regenerate the light from the object in 3D. Figure 2(a) shows how a hologram can be used to generate a 3D image and Figures 2(b) and (c) show an object generated by using binary-phase only holograms on a LCOS microdisplay.