Maarten Sluijter

2-D/3-D displays based on switchable lenticulars

— An attractive concept for 3-D displays is the one based on LCDs equipped with lenticular lenses. This enables autostereoscopic multiview 3-D displays without a loss in brightness. A general issue in multiview 3-D displays is their relatively low spatial resolution because the pixels are divided among the different views. To overcome this problem, we have developed switchable displays, using liquid-crystal (LC) filled switchable lenticulars. In this way, it is possible to have a high-brightness 3-D display capable of fully exploiting the native 2-D resolution of the underlying LCD. The feasibility of LC-filled switchable lenticulars was shown in several applications. For applications in which it is advantageous to be able to display 3-D and 2-D content simultaneously, a 42-in. locally switchable prototype having a matrix electrode structure was developed. These displays were realized using cylindrically shaped lenticular lenses in contact with LC. An alternative for these are lenticulars based on gradient-index (GRIN) LC lenses. Preliminary results for such switchable GRIN lenses are presented as well.

General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media

Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem, and most of the theory has been known for at least fifty years. Although the subject appears frequently in the literature, wave propagation through inhomogeneous anisotropic media is rarely addressed. The rapid advances in liquid-crystal lenses call for a good overview of the theory on wave propagation via anisotropic media. Therefore, we present a novel polarized ray-tracing method, which can be applied to anisotropic optical systems that contain inhomogeneous liquid crystals. We describe the propagation of rays in the bulk material of inhomogeneous anisotropic media in three dimensions. In addition, we discuss ray refraction, ray reflection, and energy transfer at, in general, curved anisotropic interfaces with arbitrary orientation and/or arbitrary anisotropic properties. The method presented is a clear outline of how to assess the optical properties of uniaxially anisotropic media.

Switchable lenticular based 2D/3D displays

The use of an LCD equipped with lenticular lenses is an attractive route to achieve an autostereoscopic multi-view 3D display without losing brightness. However, such a display suffers from a low spatial resolution since the pixels are divided over various views. To overcome this problem we developed switchable displays, using LC-filled switchable lenticulars. In this way it is possible to have a high-brightness 3D display capable to regain the full native 2D resolution of the underlying LCD. We showed the feasibility of LC-filled switchable lenticulars in several applications. For applications in which it is advantageous to be able to display 3D and 2D on the same screen, we made a prototype having a matrix electrode structure. A problem with LC-filled lenses is that in the 2D state there is a residual lens effect at oblique angles. This effect and a possible solution are discussed as well.

Ray-tracing simulations of liquid-crystal gradient-index lenses for three-dimensional displays

For the first time, to our knowledge, we report ray-tracing simulations of an advanced liquid-crystal gradientindex lens structure for application in switchable two-dimensional/three-dimensional (3D) autostereoscopic displays. We present ray-tracing simulations of the angular-dependent lens action. From the results we conclude that the lens action of the advanced optical design corresponds to the desired performance for small viewing angles. For oblique viewing angles of approximately 30° and higher, the lens action becomes significantly weaker compromising the 3D performance of an autostereoscopic display. The general approach and the advanced ray-optics analysis procedures presented form a useful tool in the search for improvements for high viewing angles and enable a better understanding of the liquid-crystal technology discussed.

Simulations of a liquid-crystal-based electro-optical switch

We present simulations of a novel liquid-crystal-based electro-optical device that enables a switching effect owing to a backreflection phenomenon. In the simulations, we exploit the optical properties of a liquid-crystal layer with a Freédericksz alignment in an unconventional way. The resulting switching effect of the proposed optical design can be controlled by means of an external electric field. Possible applications of the liquid-crystal device can be found in, but are not restricted to, optical communication systems and lighting applications.

Residual lens effects in 2D mode of auto-stereoscopic lenticular-based switchable 2D/3D displays

We discuss residual lens effects in multi-view switchable auto-stereoscopic lenticular-based 2D/3D displays. With the introduction of a switchable lenticular, it is possible to switch between a 2D mode and a 3D mode. The 2D mode displays conventional content, whereas the 3D mode provides the sensation of depth to the viewer. The uniformity of a display in the 2D mode is quantified by the quality parameter modulation depth. In order to reduce the modulation depth in the 2D mode, birefringent lens plates are investigated analytically and numerically, by ray tracing. We can conclude that the modulation depth in the 2D mode can be substantially decreased by using birefringent lens plates with a perfect index match between lens material and lens plate. Birefringent lens plates do not disturb the 3D performance of a switchable 2D/3D display.

Applicability of geometrical optics to in-plane liquid-crystal configurations

We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices n(o)=1.5 and n(e)=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.

Ray-tracing simulations and applications of liquid crystal beam control devices

We have developed a general ray-tracing method in the geometrical-optics approach which enables the modeling of in general inhomogeneous liquid crystal configurations. In this manuscript, we discuss two prominent examples in which we calculate the optical properties of two liquid crystal configurations. We first present simulations of a liquid crystal-based electro-optical device that enables a switching effect due to a back reflection phenomenon. In these simulations, we exploit the optical properties of a liquid crystal with a special Freedericksz alignment. Secondly we present preliminary results of the optical properties of a liquid crystal-based optical element that can actively control guiding and extraction of light. A promising application of such a device can be found in for example beam control devices for lighting applications or applications that require local dimming and highlighting.

Ray-Tracing Simulations of Liquid-Crystal Devices

In previous work, we have introduced the Hamiltonian method which enables to calculate the ray paths of light rays in inhomogeneous anisotropic media in the geometrical-optics approach. With this method we are able to simulate the effect of optical anisotropy in three dimensions. In this manuscript, we simulate the optical properties of multiple liquid-crystal configurations. We demonstrate the resemblance between the optical properties of a gradient-index fiber and a liquid-crystal layer with a Freédericksz alignment. In addition, we investigate the optical properties of artificial liquid-crystal profiles induced by the electric field of a set of point charges. Altogether, we conclude that, in the geometrical-optics approach, we are able to assess the optical properties of any arbitrary anisotropic optical system.