Applications Of Linear And Nonlinear Optical Effects In Liquid Crystals

Liquid crystals have been a major subject of research for the past decades. Aside from the variety of structures they can form, they exhibit a vast range of optical phenomena. Many of these phenomena found applications in technology and became an essential part of it. In this dissertation thesis we continue the line to propose a number of new applications of optical effects in liquid crystals and develop their theoretical framework. One such application is the possibility of beam combining using Orientational Stimulated Scattering in a nematic liquid crystal cell. Our numerical study of the OSS process shows that normally this possibility does not exist. However, we found that if a number of special conditions is satisfied efficient beam combining with OSS can be done. These conditions require a combination of special geometric arrangement of incident beams, their profiles, nematic material, and more. When these conditions are fulfilled, power of the beamlets can be coherently combined into a single beam, with high conversion efficiency while the shape and wave-front of the output beam are still of good quality. We also studied the dynamics of the OSS process itself and observed (in a numerical model) a number of notorious instabilities caused by effects of back-conversion iv process. Additionally, there was found a numerical solitary-wave solution associated with this back-conversion process. As a liquid crystal display application, we consider a nematic liquid crystal layer with the anisotropy axis modulated at a fixed rate in the transverse direction with respect to light propagation direction. If the layer locally constitutes a half-wave plate, then the thinscreen approximation predicts 100% -efficient diffraction of normal incident wave. If this diffracted light is blocked by an aperture only transmitting the zero-th order, the cell is in dark state. If now the periodic structure is washed out by applying voltage across the cell and light passes through the cell undiffracted, the light will pass through the aperture as well and the cell will be in its bright state. Such properties of this periodically aligned nematic layer suggest it as a candidate element in projection display cells. We studied the possibility to implement such layer through anchoring at both surfaces of the cell. It was found that each cell has a thickness threshold for which the periodic structure can exist. The anchored periodic structure cannot exist if thickness of the cell exceeds this threshold. For the case when the periodic structure exists, we found the structure distortion in comparison with the preferable ideal sinusoidal profile. To complete description of the electromechanical properties of the periodic cell, we studied its behavior at Freedericksz transition. Optical performance was successfully described with the coupled-mode theory. While influence of director distortion is shown to be negligibly small, the walk-off effects appear to be larger. In summary, there are good prospects for use of this periodically v aligned cell as a pixel in projection displays but experimental study and optimization need to be performed. In the next part we discuss another modulated liquid crystal structure in which the director periodically swings in the direction of light propagation. The main characteristic of such structure is the presence of bandgap. Cholesteric liquid crystals are known to possess bandgap for one of two circular polarizations of light. However, unlike the cholesterics the bandgap of the proposed structure is independent of polarization of normally incident light. This means that no preparation of light is needed in order for the structure to work in, for example, liquid crystal displays. The polarization universality comes at the cost of bandgap size, whose maximum possible value ∆ωPTN compared to that of cholesterics ∆ωCh is approximately twice smaller: ∆ωPTN ≈ 0.58∆ωCh if modulation profile is sinusoidal, and ∆ωPTN ≈ 0.64∆ωCh if it is rectangular. This structure has not yet been experimentally demonstrated, and we discuss possible ways to make it

Beam combining using Orientational Stimulated Scattering in Liquid Crystals

Possibility of beam combining and clean-up using Orientational Stimulated Scattering in a Nematic Liquid Crystal is considered. We numerically study the dynamics of the process and find that back-conversion process tends to limit the effective interaction strength. Instability of the steady state of cross-phase modulation is demonstrated, when both waves have the same frequency. We show that high conversion efficiency can be achieved, and that the shape and wave-front of the amplified output signal are robust with respect to amplitude and phase distortions of the input pump.Comment: 24 pages, 6 figures, will be published in JOSA

Longitudinally Modulated Nematic Bandgap Structure

We discuss a planar nematic liquid-crystal structure with the director periodically twisted in the light propagation direction (periodically twisted nematic) as a medium, which exhibits bandgap and strong reflection for any polarization at normal incidence. This is in contrast to the cholesteric liquid crystals, which reflect only one of the two circular polarizations. The size of the bandgap depends on the modulation profile and amplitude, and its maximal magnitude is smaller, but of the same order as the bandgap of cholesterics with similar material parameters (refractive indices and pitch). The second-order bandgap reflection exhibits polarization universality only for large enough modulation. © 2006 Optical Society of America

Application Of Orientational Stimulated Scattering In Nematic Liquid Crystals For Beam Combining And Clean-Up

Recent experiments demonstrated high conversion efficiency in the process of Orientational Stimulated Scattering (OSS) in nematics. This fact makes OSS attractive for beam combining and clean-up. We consider a scheme for such application and study it by numerically modeling the process. As the process of energy transfer goes, the reverse transfer also begins. However, the region of the back-transfer moves inside the cell with constant velocity in +z direction and given sufficient time, leaves the cell. By modeling the OSS of diffracting one-dimensional beams we show the possibility to obtain a maximum 94% fidelity and 96% power transfer in a numerical experiment with 6 individual overlapping pump beamlets. This means that 90% of the total pump power may be converted into the diffraction-limited output. Remarkably, this output suffers very little cross-phase modulation

Beam Combining Using Orientational Stimulated Scattering In Liquid Crystals

The possibility of beam combining and cleanup using orientational stimulated scattering in a nematic liquid crystal is considered. We numerically study the dynamics of the process and find that backconversion process tends to limit the effective interaction strength. The instability of the steady state of cross-phase modulation is demonstrated, during which both waves have the same frequency. We show that high conversion efficiency can be achieved and that the shape and wavefront of the amplified output signal are robust with respect to the amplitude and phase distortions of the input pump. © 2005 Optical Society of America

Polarization-Universal Bandgap In Periodically Twisted Nematics

Cholesteric liquid crystals are known to possess bandgap and exhibit strong reflection for one of two circular polarizations of light. We suggest a periodically twisted nematic liquid crystal as a medium, which possesses bandgap and exhibits strong reflection for any polarization of normally incident light. Two possible structures are considered: a sinusoidal modulation profile and a rectangular modulation profile. In both cases, the maximum bandgap of a periodically twisted structure is approximately twice as narrow as that of cholesterics. However, the polarization properties of these structures may make them more advantageous than cholesterics in a variety of applications. © 2006 Optical Society of America

Incoherent Spatial Solitons In Nematic Liquid Crystals

We obtain analytical solutions describing spatially incoherent soliton beams in nematic liquid crystal cells. The effects arising from non-locality on the coherence properties of these self-trapped states are systematically investigated and analyzed. © 2005 Optical Society of America

Nonlocal Incoherent Spatial Solitons In Liquid Crystals

We investigate theoretically the properties of spatial partially incoherent solitons in nematic liquid-crystal cells. Following the self-consistent multimode approach, we obtain nonlocal spatial incoherent soliton solutions in such noninstantaneous nonlinear media in closed form. The effect of nonlocality on the coherence properties of these self-trapped states is studied in detail. Pertinent examples are provided. © 2005 Optical Society of America

Incoherent Spatial Solitons In Nematic Liquid Crystals

We obtain analytical solutions describing spatially incoherent soliton beams in nematic liquid crystal cells. The effects arising from non-locality on the coherence properties of these self-trapped states are systematically investigated and analyzed. © 2005 Optical Society of America

Polarization-Controlled Switching Between Diffraction Orders In Transverse-Periodically Aligned Nematic Liquid Crystals

Transverse-periodic-oriented nematic liquid crystals (LCs) are a special type of optical axis grating that are capable of very high efficiency diffraction (theoretically, 100%) in thin layers of materials with thickness comparable to the radiation wavelength. In particular, they fully diffract linearly polarized input beam into circularly polarized +1st and -1st diffraction orders. We experimentally demonstrate switching between diffraction orders of such gratings when the polarization of the incident beam changes from right-circular to left-circular and vice versa with the aid of an electrically controlled LC phase retarder. Such a setup in which the diffraction efficiency and direction are controlled externally, without application of an electric field to the transverse-periodic grating, provides additional control opportunities and does not compromise the quality of the grating. The grating used in the experiment was 1.5m thick and had a period of 4m. The contrast ratio of switching between the +1st and -1st orders was as high as 267:1 for a He-Ne laser beam with a switching time of 6.6 ms. © 2006 Optical Society of America