Relationship between lens properties and director orientation in a liquid crystal lens

Lenses with a homogeneously aligned liquid crystal having a Fresnel structure have been prepared by using a nematic with a positive dielectric anisotropy. Their focal length can be varied continuously from the value f_e for an extraordinary ray to f _o for an ordinary ray by applying an electric field across the lens cell. The effective refractive index of the lens where the director is aligned perpendicular to the grooves of the Fresnel structure becomes smaller than when the director is aligned parallel to the grooves. Then the liquid crystal lens has a characteristic aberration which could not be observed in a conventional glass lens; that is, the focal length of the lens becomes different according to the incidence of rays on the different parts of the lens. The properties of the liquid crystal lens can be improved by making the director orientation axially symmetric, in the form of a concentric circle, but the polarization component rotated 90° from the incident extraordinary ray appears when the voltage is applied across the lens cell. This phenomenon is discussed in relation to the optical properties and the director orientation in a liquid crystal prism cell.     

A liquid crystal microlens obtained with a non-uniform electric field

A homogeneously aligned nematic liquid crystal cell with a hole-patterned electrode and with an indium-tin oxide (ITO-) coated counter-electrode has been prepared. A non-uniform electric field can be produced by the asymmetrical electrode structure. The liquid crystal director can be reoriented by applying a voltage across the electrodes, and this produces an axially symmetrical profile of the refractive index. This liquid crystal cell is expected to have a lens effect and so its optical properties have been investigated. The profile of the output light intensity was measured by using a detecting system with an optical fibre. Some relationships between the lens properties, the diameter of the hole and the thickness of the liquid crystal layer have been examined. The liquid crystal cell becomes a convex (converging) lens with a relatively low voltage. A focal length of several millimetres can be obtained by applying voltages of 3-4 V. As the applied voltage increases, the focal length becomes longer, and the cell changes to a concave (diverging) lens when a high voltage is applied (≳ 20 V). These properties are discussed from the viewpoint of the director orientation effects resulting from the non-uniform electric fields in the cell.     

A liquid crystal microlens obtained with a non-uniform electric field

Abstract

A homogeneously aligned nematic liquid crystal cell with a hole-patterned electrode and with an indium-tin oxide (ITO-) coated counter-electrode has been prepared. A non-uniform electric field can be produced by the asymmetrical electrode structure. The liquid crystal director can be reoriented by applying a voltage across the electrodes, and this produces an axially symmetrical profile of the refractive index. This liquid crystal cell is expected to have a lens effect and so its optical properties have been investigated. The profile of the output light intensity was measured by using a detecting system with an optical fibre. Some relationships between the lens properties, the diameter of the hole and the thickness of the liquid crystal layer have been examined. The liquid crystal cell becomes a convex (converging) lens with a relatively low voltage. A focal length of several millimetres can be obtained by applying voltages of 3-4 V. As the applied voltage increases, the focal length becomes longer, and the cell changes to a concave (diverging) lens when a high voltage is applied (? 20 V). These properties are discussed from the viewpoint of the director orientation effects resulting from the non-uniform electric fields in the cell.     

Analysis of the performance of the electric-field-driven liquid crystal lens (ELC Lens) for light of various incident angles

The electric-field-driven liquid crystal lens (ELC) induces the lens effect by the spatially non-uniform distribution of the refractive index. A scheme to analyse the performance of the ELC lens for the lights of various incident angles is devised by the calculation of the phase through the ELC lens and the determination of light ray directions from these phases. The calculated results show that the ELC lens changes the incident light of the plane wave into a focused wave and the focal distance becomes shorter for larger incident angles.     

Experimental investigation of the compressible continuum theory of a homeotropically aligned ferroelectric liquid crystal

The optical tensor configuration in a homeotropically aligned ferroelectric liquid crystal (FLC), SCE13 cell, is investigated by means of optical excitation of half leaky guided modes. A thin slab of FLC is confined between a high index pyramid and a low index substrate whose indices bound those of the liquid crystal. In this geometry there exists a small angle range over which a series of sharp resonant modes may propagate in the liquid crystal. Detecting the angular dependent reflectivity for plane polarized radiation and subsequently fitting the data by iteratively modelling from multilayer Fresnel theory, a full characterization of the tilt and twist profile throughout the cell is achieved. The temperature dependence of the tilt of the principal director, which is related to the smectic cone angle, and of the optical permittivity, as well as the pitch have been obtained. The tilt director profile across the cell is interpreted using a compressible continuum theory for SmC* liquid crystals which includes the possibility of variable cone angle and layer spacing.     

Pulsed voltage studies of electric field effects on the optical permittivity of a nematic liquid crystal

Prism coupling to resonant optical modes in a thin layer of homeotropically aligned nematic liquid crystal has been used to characterize the change in refractive indices which occurs when an electric field is applied. Reflectivity data, recorded over a range of angles of incidence for both TE and TM radiation show sharp minima corresponding to the excitation of optical modes in the liquid crystal layer. Application of a pulsed AC voltage, pulsed to avoid heating, while synchronously monitoring reflectivity changes allows detailed characterization of the shift in the position of these minima due to the influence of the electric field on both the ordinary and extraordinary refractive indices. By fitting theoretical predictions of Fresnel theory a complete characterization of change in both these parameters up to an applied field of some 5 × 10⁶ Vm^-1 is achieved. The refractive index changes recorded are compared with the director fluctuation order parameter theory with which good agreement is found.     

A polarisation-free blue phase liquid crystal lens with enhanced tunable focal length range

A polarisation-free blue phase liquid crystal (BPLC) lens with enhanced tunable focal length range is proposed. A matched conventional glass lens is introduced on a BPLC lens to increase the range of the tunable focal length. The focal length of the BPLC lens can be switched from positive to negative, the negative lens-like phase profile can be neutralised by the conventional glass lens to get an infinity focal length and the positive lens-like phase profile can be enhanced by the conventional glass lens to get a shorter focal length. The minimum focal length can be decreased to almost half of that after the proposed method is adopted in our simulation. Moreover, the proposed BPLC lens exhibits a good polarisation-free feature and the optical effect is relatively good.     

Polymer network liquid crystal grating/Fresnel lens fabricated by holography

In this article, polymer network liquid crystal (PNLC) grating/Fresnel lens is fabricated by holography. The exposure light pattern for the grating is obtained by interfering two planar wave fronts, while the Fresnel pattern is achieved by interfering a planar wave front and a spherical wave front. Owing to the alignment effect and anchoring power of polymer network, the holographic PNLC grating achieves improved diffraction efficiency, and remarkably reduced operation voltage (reduced by 80%) compared with holographic polymer-dispersed-liquid-crystal and holographic polymer-stabilised blue-phase liquid-crystal gratings, while maintaining submillisecond response. Moreover, it achieves high spatial frequency with a 2-μm grating period, thanks to the holographic fabrication. The holographic PNLC Fresnel lens also exhibits attractive electro-optical properties.     

Adaptive nematic liquid crystal lens array with resistive layer

ABSTRACT

We propose an adaptive nematic liquid crystal (LC) lens array using a dielectric layer with low dielectric constant as resistive layer. With the resistive layer and periodic-arranged iridium tin oxide (ITO) electrodes, the vertical electric field across the LC layer varies linearly over the lens aperture is obtained in the voltage-on state. As a result, a centrosymmetric gradient refractive index profile within the LC layer is generated, which causes the focusing behaviour. As a result of the optimisation, a thin cell gap which greatly reduces the switching time of the LC lens array can be achieved in our design. The main advantages of the proposed LC lens array are in the comparatively low operating voltage, the flat substrate surface, the simple electrodes, and the uniform LC cell gap. The simulation results show that the focal length of the LC lens array can be tuned continuously from infinity to 3.99 mm by changing the applied voltage.     

Switchable polarisation-independent blue phase liquid crystal Fresnel lens based on phase-separated composite films

A simple method for fabricating a polarisation independent blue-phase liquid crystal Fresnel lens (BPLCFL) is demonstrated by utilising the photo-polymerisation-induced phase separation. The BPLC/polymer binary Fresnel zones is obtained well by periodic UV illumination with phase separation of the BPLC molecules and UV-curable pre-polymer mixture. The diffraction efficiency can be controlled when applying a uniform electric field which modulates the phase difference between even and odd Fresnel zones. Experimental results show that the maximum diffraction efficiency reaches 24.3%, which is close to the measured diffraction efficiency of the used Fresnel zone-plate mask of 25%. We also characterise the tunable lens performance at different applied voltages.     

A polarisation-independent blue-phase liquid crystal microlens using an optically hidden dielectric structure

A polarisation-independent blue-phase liquid crystal microlens using an optically hidden dielectric structure is proposed. In this design, the non-uniform electric field across the lens aperture is obtained by the modulation of the effective dielectric constant of an optical hidden layer. As the applied voltage varies from 0 to 150V_rms, the focal length of the lens can be tuned from ∞ to 16.6 mm. Simulation results show that this device has a parabolic-like profile and exhibits polarisation-independent property.     

A multifunctional blue phase liquid crystal lens based on multi-electrode structure

A blue phase liquid crystal (BPLC) lens with multifunction using multi-electrode structure and a dielectric layer with high dielectric constant is proposed. The refractive index of the BPLC can be changed flexibly in different regions. Some functional or technical requirements such as switch between positive and negative lenses can be achieved. The lens reveals a good parabolic refractive index distribution and focus adjustment capacity simultaneously. The applied voltage on the electrodes is regular and computable. To decrease the applied voltage of the proposed lens with a large diameter, a drive-type adopted Fresnel lens is introduced.     

Double-layer liquid crystal lens array with composited dielectric layer

ABSTRACT

A double-layer liquid crystal (LC) lens array with composited dielectric layer is proposed. In our design, a spatially non-uniform electric field is generated between the strip electrodes, resulting in a gradient refractive index distribution in the LC layer. Since the upper and lower parts of the LC lens array both adopt a composite dielectric layer, the operation voltage of the LC lens array is effectively reduced. In terms of LC lenslet, the double-layer design doubles the phase difference between the centre and the periphery of the LC layer, thereby reducing the focal length of the LC lens array. In addition, the shortest focal length (~1.78 mm) of the LC lens array is obtained at V = 3.3 V, and the LC lens array has a large focusing range.     

Coaxially bifocal liquid crystal lens with switchable optical aperture

An electrically tunable liquid crystal (LC) lens with dual hole-patterned electrodes is demonstrated. When the LC lens is operated at low voltages, the dual hole-patterned electrodes with different diameters impart the lens with a coaxial bifocal characteristic. At high voltages, the proposed LC lens functions as a conventional lens with a single focal length but with a switchable optical aperture. The demonstrated LC lens is free of disclination lines because of the presence of voltage-assisted high pretilt angles created from the upmost hole-patterned electrode with small diameter.     

A small-angle X-ray scattering study of nanoparticle assembly in an aligned nematic liquid crystal

The assembly of colloidal particles in a nematic liquid crystal has been investigated using small-angle X-ray scattering. The structure and orientation of nanoparticle assemblies in bulk samples of aligned nematic liquid crystal have been determined. The method offers some advantages over optical microscopy, which is usually restricted to investigations of thin cells and micron-sized particles. The scattering from chains of particles has been calculated, and comparison with experimental results has shown that suspensions of 48 and 105 nm diameter silica nanoparticles formed highly ordered structures perpendicular to the liquid crystal director, consistent with quadrupolar defect-induced assembly.     

Anisotropy of non-mesogenic polymer networks dispersed in a liquid crystal matrix

We report here original results characterizing in situ the interactions between a smectic liquid crystal phase and a polymer network dispersed in it. These results have been obtained by neutron scattering on smectic liquid crystal (8CB) samples containing a physical network of 1.5wt% polymer. The samples were polymerized in the isotropic, or in the smectic A phases. For the first time it is experimentally proved that the polymerization of non-mesogenic monomers in an aligned smectic A matrix induces anisotropy in the resulting network. The network becomes elongated along the liquid crystal director. When the polymerization is carried out in the isotropic phase the polymer network has an isotropic distribution even if a magnetic field, which orients the liquid crystal director, is later applied. On the other hand, studies show that after several thermal cycles, the liquid crystal orientational order still remained. Without other external constraints, the polymer network freezes the alignment of the liquid crystal. It is probably imposed by pendant reticulates on the diffuse liquid crystal-polymer interfaces.     

A blue-phase liquid crystal lens array based on dual square ring-patterned electrodes

We propose a blue-phase liquid crystal (BPLC) lens array based on dual square ring-patterned electrodes. A high dielectric constant layer is used to smoothen out the horizontal electric field and reduce the operating voltage. By creating a potential difference between the dual square ring-patterned electrodes, gradient electric fields are generated and lens-like phase profile is obtained. Besides, the focal length of the BPLC lens is adjustable with voltage changes and all simulation results indicate that the BPLC lens array is polarisation-insensitive.     

A polarisation-independent blue-phase liquid crystal lens array using gradient electrodes

A polarisation-independent blue-phase liquid crystal lens array using gradient electrodes is proposed. A high dielectric constant layer helps to smoothen out the horizontal electric field and reduce the operating voltage. With gradient electrodes and a planar top electrode, gradient electric fields are generated and lens-like phase profile is obtained. When the applied voltage is changed, the focal length of the lens can be tuned from ∞ to 5.94 mm. Besides, the simulation results show that the lens is insensitive to polarisation while keeping parabolic-like profile.     

Quantification of the azimuthal anchoring of a homogeneously aligned nematic liquid crystal using fully-leaky guided modes

A novel optical guided mode technique, the fully-leaky guided mode technique, has been used to investigate the director distortion under the application of an in-plane electric field of a homogeneously aligned conventional cell filled with the nematic liquid crystal E7. The liquid crystal is aligned using polyimide rubbed along the direction of the gold electrode edges. A weak field is applied across a 3 mm gap between the gold electrodes to induce small changes in the twist angle of the director. These distortions are determined by fitting to the angledependent reflectivity and transmissivity data and are compared with continuum theory. From careful analysis of the results, both the twist elastic constant, k22, and the azimuthal anchoring strength, Wa, of the system are obtained. At 23.5 C for E7 on rubbed polyimide we find that k22=(6.50 +/- 0.05)x10-12N and Wa=(2.9 +/- 0.2)x10-5 J m-2.     

Liquid crystal Pancharatnam-Berry phase lens with spatially separated focuses

In this paper, we proposed and fabricated a liquid crystal (LC) lens with spatially separated focuses via liquid crystal photoalignment technology. The novel lens is an integration of the polarisation grating and conventional LC lens. The two focuses of that new lens, one of which is real while the other is virtual, can be spatially separated. When combined with normal convex lens and illuminated by a linearly polarised beam, the two emergent light beams become all convergent and the two focuses are separated in three-dimension space. Moreover, the focal lengths of the lens system can be artificially controlled by adjusting the distance between our new lens and the conventional lens. Our results achieve the potential of LC lens’ application in imaging devices such as multifocal cameras, bifocal eyeglasses and so on.