Guided Mode Technique Research Articles

Determination of Director Profile in the Vertical Alignment Nematic Liquid Crystal Cell by the Full Leaky Guided Mode Technique

By means of the full leaky guided mode technique, the transmittance of the full leaky waveguide geometry which consists of pyramid, matching fluid of refractivity, the vertical alignment nematic liquid crystal cell are investigated experimentally. The experimental curves with different voltages between polarization-conserving transmittance Tss and the internal angle (the angle of incidence for which light is incident on the vertical alignment liquid crystal cell) are obtained. Comparing these experimental curves with the theoretical curves obtained from multi-layer optics theory, the director profile of vertical alignment nematic liquid crystal cell for different voltages is determined.

Optical anisotropy and liquid‐crystal alignment properties of rubbed polyimide layers

The relation between the optical anisotropy of rubbed polyimide layers and the rubbing process is investigated using the recently developed polarization‐conversion guided mode technique. Results indicate that the effective optical anisotropy of the polyimide layers may be substantially changed by the rubbing process, although this does not significantly influence the ability of the polyimide layers to align liquid crystals.

Nematic Liquid Crystal Optical Dispersion in the Visible-Near Infrared Range

A commercial variable angle spectroscopic ellipsometer from J. A. Woollam Company is modified in order to make possible measurements in guiding structures. The half leaky guided mode technique is realised for liquid crystal optical dispersion measurements. Features and problems related to experimental data interpretation and error sources in the refractive index measurements are carefully analyzed, achieving a final accuracy of ±0.0002. We present the measured optical dispersion curves in the wavelength range from 0.5 to 1.7 μm for two widely studied liquid crystals, namely E7 and 5CB.

Leaky-wave exploration of two-stage switch-on in a nematic pi-cell

The two-stage switch-on dynamics of a nematic pi-cell are explored in detail using a convergent beam fully-leaky guided mode technique. The cell shows an initial switch-on with a time scale in the range several ms to tens of ms (depending on drive voltage) from the symmetrical H state to a new and semistable H state. It then slowly changes (over several hundred ms) to the final stable asymmetrical H state.

Delay effect of switch-on in a supertwisted nematic cell

By using a convergent beam system and the fully leaky guided mode technique the switch-on dynamics of an 180° supertwisted nematic have been studied. Using the Ericksen–Leslie theory and analyzing the guided mode data taken from the cell, the director structure in the cell at different times during switch-on is obtained. For three different applied voltages it is found that the switch-on time is strongly dependent on the applied field—the higher voltage corresponds to faster switching, with no evidence of backflow. A delay at the beginning of the switch-on process has been found and explored for different applied fields. This leads to a suggestion for increasing the switch-on speed of such devices by 25%.

Reply to “Comment on ‘Optical determination of flexoelectric coefficients and surface polarization in a hybrid aligned nematic cell’ ”

In their Comment [G. Barbero and L. R. Evangelista, Phys. Rev. E 68, 023701] on our paper [A. Mazzulla, F. Ciuchi, and J. R. Sambles, Phys. Rev. E 64, 021708 (2001)], Barbero and Evangelista conclude that the procedure followed by us to fit the reflectivity data from the half leaky guided mode technique is questionable. In the absence of a model that is able to reproduce the experimentally obtained tilt angle profiles, their argument is unsubstantiated. To further refute their arguments, we also illustrate and discuss additional experimental data (that were not shown in our paper) that strongly support our conclusions.

FULLY-LEAKY GUIDED MODE MEASUREMENT OF THE FLEXOELECTRIC CONSTANT (e11+e33) OF A NEMATIC LIQUID CRYSTAL

The response to applied voltages of the director profile within an E7-filled Hybrid Aligned Nematic liquid crystal cell has been determined by using the optical wave-guide method known as the Fully-Leaky Guided Mode Technique. Data was collected with applied AC and DC voltages and the measured director profiles were compared with model profiles generated through a minimisation-of-free-energy routine. The sum of the splay and bend flexoelectric coefficients (e11+e33 of E7 was measured as 1.5×10−11Cm−1. Results also show the presence of a DC offset voltage of +0.64 V in the cell.

Optical determination of flexoelectric coefficients and surface polarization in a hybrid aligned nematic cell.

We present an optical study of the influence of both the flexoelectric effect and surface polarization on a hybrid-aligned nematic cell using the half-leaky guided mode technique. Tilt angle profiles, obtained from fits of experimental data (reflectivity curves) taken under applied voltages, are compared with the ones derived by a complete theoretical model. Measurements with an applied alternating voltage allow the evaluation of the anchoring energy by solving the torque balance equation at the planar surface. From measurements with static fields, the sum of flexoelectric coefficients and the surface polarization are determined by numerical solution of Euler-Lagrange equations.

Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique

Optical excitation of half-leaky guided modes has been used to explore the director profile of a thin twisted homogeneously aligned nematic liquid crystal cell (Merck, E7). Twisted alignment is realized by the use of rubbed polyimide layers on both inner walls of the cell. By modelling the optical response of particular director profiles in the cell to fit the halfleaky guided mode reflectivity data, both the thickness and the twist of the director from the top to the bottom of the cell are accurately determined. Then comparing the rubbing directions with the twist of the easy axes, the torsional anchoring coefficient, W T is quantified through a knowledge of the twist elastic constant K 22 of E7. At 24.5°C we find that W T = (5.8 ± 0.4) X 10-5 J m-2.

Quantifying Azimuthal Anchoring of Nematics using In-Plane Fields and Fully-Leaky Guided Modes

In this work we present a new optical guided mode technique which is used to monitor small perturbations to the director twist profile in a conventional liquid crystal cell. The cell is filled with nematic liquid crystal E7 which is homogeneously aligned using rubbed polyimide. Twist distortions are induced via the application of weak in-plane electric fields. Careful analysis of these distortions allows both the twist elastic constant, k22, and the azimuthal anchoring strength, Wa, of the cell to be determined.

Optically resolving dynamic processes in commercial liquid crystal cells

The recently developed fully leaky guided mode technique is a powerful tool for accurately resolving the director profile in standard, commercially fabricated liquid crystal cells. By employing a convergent beam to simultaneously excite many fully leaky guided modes, angular dependent reflectivity and transmissivity data can be captured in a fraction of a millisecond with a charge coupled device array, thus enabling the switching dynamics of the liquid crystal cell to be resolved. A preliminary study of the director profile (optical tensor distribution) during the relaxation of a homogeneously aligned cell (antiparallel rubbed) filled with the nematic material ZLI-2293 is presented here. By resolving the director distribution as a function of time, the time constant for the relaxation process is obtained from which the effective rotational viscosity coefficient γ* is then evaluated.

Groove depth dependence of the anchoring strength of a zero order grating-aligned liquid crystal

The influence of in-plane electric fields on the twist profile of a liquid crystal aligned by nondiffractive (zero order) gratings has been explored using an optical guided mode technique. The liquid crystal is studied in a novel cell geometry comprising one rubbed polyimide alignment layer and one zero order diffraction grating. Comparison of the director-distorted profiles with predictions from elastic continuum theory allow both the twist elastic constant of the bulk liquid crystal and the azimuthal anchoring strengths at the two surfaces to be determined. Experiments have been performed on different depth gratings. Good agreement with the Berreman topological alignment model has been achieved for fairly shallow gratings, but not for gratings with deeper groove profiles. This implies that the theory needs modification to account for deep gratings.

Accurate optical determination of liquid crystal tilt angle by the half-leaky guided mode technique

The first resonant guided mode of P→P reflection in Half-leaky Guided Mode (HLGM) technique is very sensitive to the tilt angle of uniaxial liquid crystals. A formula is presented to describe the relationship between the tilt angle and the incident angle of the first resonant valley point of P→P reflectivity, R pp. This method is suitable to measure tilt angle of any degree, especially 3–85°, with high sensitivity. The great variations of LC layer thickness, LC near-surface sublayers, PI layers, or ITO layers have few effects on the position of the first resonant valley point of R pp. The method can be used to measure tilt angles with high sensitivity, without other influences, and exempt from the time consuming numerical fitting with a complex model, which is needed in other methods by Guided Modes.

Optically guided mode study of nematic liquid crystal alignment on a zero-order grating.

The characterization of a liquid crystal cell, which comprises one zero-order (that is, at the wavelength of study it is nondiffractive) diffraction grating and one rubbed polyimide-coated substrate, has been performed using an optically guided mode technique. The cell is filled with nematic liquid crystal E7 (manufactured and sold by Merck, Poole, U.K.). The excitation of fully leaky guided modes within the liquid crystal layer has allowed the optical director profile to be quantified under the application of weak in-plane electric fields. The fitting of angle-dependent optical data to multilayer optical theory yields the accurate twist profile of the liquid crystal for different field strengths. Comparisons with profiles predicted from elastic continuum theory, assuming a Rapini-Papoular-type anchoring at the surfaces, allow both the azimuthal anchoring strength at each surface and the twist elastic constant of the bulk to be accurately determined. Repeating these measurements as a function of temperature allows the surface and bulk order parameters of the grating-aligned liquid crystal to be deduced.

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.

Convergent beam guided mode technique for use in liquid crystal studies

The use of a convergent beam to excite guided modes in a liquid crystal layer in order to determine the director profile is described. The technique has two main advantages over the conventional collimated beam procedure. First, the convergent beam guided mode (CBGM) technique uses a highly focused beam spot that simultaneously excites many guided modes and produces reflectivity data over a wide angle range. Such reflectivity can be captured in milliseconds with a charge coupled device array and can therefore potentially be used to study cell dynamics. Second, the CBGM technique removes the need to rotate the liquid crystal cell and consequently the focused beam remains completely stationary on the liquid crystal layer, allowing examination of single pixels. The work presented here is a demonstration of the CBGM technique via a study of the static director profile of a homogeneously aligned nematic (E7) liquid crystal layer.

Detailing smectic SSFLC director profiles by half-leaky guided mode technique and genetic algorithm

The genetic algorithm (GA), written to allow automatic analysis of optical reflectivity data obtained from liquid crystal cells using the half-leaky guided mode technique, has been developed to the point where liquid crystal cells can be analysed successfully giving greater detail of optical parameters and director profile than yielded by any other technique. The technique models the liquid crystal layer as a set of discrete, independent sub-layers which can map out the variation of the director through the thickness of the cell. Given sufficient high quality data, it is now possible automatically and accurately to fit the parameters of a complete liquid crystal cell. Using this highly adapted GA, half-leaky guided mode optical reflectivity data from the nematic, smectic A and smectic C* phases of SCE13 in a surface stabilized ferroelectric liquid crystal have been fitted to reveal director profiles and optical parameters of the cell in each phase.

Fitting reflectivity data from liquid crystal cells using genetic algorithms

The half-leaky guided mode technique for quantifying thin optical layers is here combined with a data fitting routine based on a genetic algorithm to provide an immensely powerful procedure for detailing the director profile in liquid crystal cells. This approach not only provides a full description of the optical parameters of the cell, but also gives quantitative uncertainties in these parameters. It is tested here, first by fitting to theoretically produced data and then applied to real experimental data.

Leaky guided wave propagation along imperfectly bonded fibers in composite materials

Leaky guided modes propagating along embedded fibers in a composite material can be used for characterizing the fiber-matrix interface. This principle can be applied to real composites containing small-diameter fibers by using laser interferometric detection of very fine lateral resolution on the order of a few microns. The main purpose of this paper is to develop the analytical tools needed to assess the sensitivity of guided wave inspection to interface properties in composite materials. Typically, the sound velocity is much lower in the matrix than in the fiber and the guided modes are strongly attenuated by leaking their energy into the matrix as they propagate. As a result, the velocity of the lowest-order axisymmetric longitudinal mode decreases while its attenuation increases with increasing interfacial stiffness between the fiber and the matrix. It is shown that loose fibers can be readily identified from early signals produced by fast guided modes. In the case of a well-bonded fiber-matrix interface, these guided modes are slowed down and strongly attenuated by the loading of the matrix depending on the fiber diameter and the interfacial stiffness of the interface. Interestingly, the relative difference between the well-bonded and free fibers is greater at low frequencies. Therefore, good sensitivity to the sought interfacial stiffness can be achieved at a few MHz, i.e., when the fiber diameter is still much smaller than the acoustic wavelength. Our analytical results show that the leaky guided mode technique is mainly sensitive to the transverse interfacial stiffness of the fiber-matrix interface. At typical ultrasonic frequencies between 1 and 20 MHz, the technique works best in the 1011–1013 N/m3 interfacial stiffness range which is one or two orders of magnitude lower than the optimal sensitivity range of the more conventional bulk velocity and reflection methods.

Optical Characterisation of a Homeotropically Aligned Ferroelectric Liquid Crystal Using Half Leaky Guided Modes

Abstract Optical excitation of a half leak guided modes has been used for characterising in detail the optical tensor profile in a homeotropically aligned ferroelectric liquid crystal (SCE8) layer. In the SA phase it is found, by careful fitting of multilayer Fresnel theory to angle dependent transverse magnetic to transverse electric conversion reflectivity data, that at 1°C above the S*C to SA phase transition there is a finite pre-tilt of the SA layers. Further fitting of similarly recorded data in the S*C phase gives details of the cone angle and the chiral pitch of the S*C phase. These results not only serve to obtain material parameters for this S*C phase but also illustratee fully the enormous potential of the half leaky guided mode technique.