Spatial resolution of the molecular alignment in electroclinic liquid crystals J. R. Lindle, F. J. Bartoli, a) and S. R. Flom Optical Sciences Division, Naval Research Laboratory, Washington, D.C. 20375-5338 A. T. Harter, B. R. Ratna, and R. Shashidhar Center for Biomolecular Science and Engineering, Naval Research Laboratory, Washington, D.C. 20375-5348 Received 21 November 1996; accepted 21 January 1997 Field induced deformations of the bookshelf geometry in electroclinic liquid crystals are investigated by means of spatially resolved phase retardation experiments. It is found that the triangular deformation model does not adequately describe the optical data, and underestimates the achievable device contrast ratios. To more correctly model the smectic layer deformation, it is necessary to consider a distribution of molecular directors within a stripe domain. © 1997 American Institute of Physics. S0003-69519703012-X Since its discovery by Garoff and Meyer, 1 the electro- clinic effect in chiral smectic-A Sm-A liquid crystals has been extensively investigated. Large electroclinic tilt angles 22.5° and fast electro-optic response 40 s have been reported, 2–5 giving these materials the potential for use as spatial light modulators with gray-scale capability. However, electroclinic liquid crystals ELCs with large induced tilt angles often exhibit a stripe texture when viewed between crossed polarizers. 5,6 Since the presence of periodic stripe domains imposes limitations on achievable contrast ratio, a deeper understanding of the microscopic nature of these do- mains is desired. The formation of the stripe texture in ELCs has been attributed to a field-dependent deformation of the bookshelf geometry, and the stripe width was observed to be roughly comparable to the cell thickness. 5–9 This texture has often been depicted see inset to Fig. 1 as a periodic triangular deformation of the Sm A* planes, having a uniform but dis- tinct molecular alignment in adjacent regions. X-ray mea- surements support this picture, showing a bimodal distribu- tion of smectic A layers in KN125 5 and W317. 6 However, no attempts to measure the spatial uniformity of the molecular directors within a stripe domain have been reported, and the triangular deformation model has not been rigorously tested. In this study, the stripe deformation in the smectic A* phase of KN125, whose structure and physical properties are discussed elsewhere, 5 is studied by means of spatially re- solved, phase-retardation experiments capable of probing in- dividual stripe domains. The optical experiments reveal sig- nificant features of the stripe deformation not observed in x-ray measurements. It is found that a simple triangular de- formation model does not accurately describe the optical data, and it is necessary to consider a distribution of molecu- lar directors within a stripe domain. The results should per- mit better predictions of the optical performance of ELCs. Micron-scale spatial resolution is achieved by inserting focusing and recollimating lenses between polarizers, plac- ing the sample at focus, and measuring the light transmitted by the analyzer as a function of sample position, polarization direction, and applied field. The cell surface defines the x-z plane and the field is applied in the y direction, the direction of light propagation. The stripes in the homogeneously aligned samples are parallel to z, the unperturbed smectic layer normal. The transmitted intensity for a birefringent sample between crossed polarizers is given by 10 I  =I 0 sin 2   /2 sin 2  2   , 1 where I 0 is the incident intensity,  is the angle between the molecular director and the light polarization P, and  =2   nd /  is the phase angle, d the sample thickness,  the wavelength, and  n the birefringence. As illustrated in the inset to Fig. 1,  varies with x because of the layer deforma- tion and may be written as  ( x ) = + ( x ) + ,where  is the polarization angle relative to the z axis,  ( x ) is the angle between the z axis and the local layer normal, and the elec- troclinic tilt angle  is the angle between the local layer normal and the molecular director. When the focused laser beam is scanned perpendicular to the stripes, i.e., along x, the spatial variation in molecular director due to layer deformation produces peaks and valleys in the transmission corresponding to the light and dark stripes observed using a polarizing microscope. 5 If one as- sumes a triangular-wave layer deformation,  ( x ) is constant within a given stripe and its sign alternates between adjacent stripes. The orientation of the molecular director in each re- gion may be determined by positioning the focused beam within a stripe domain and tuning the polarization angle to a a Electronic mail: bartoli@v6550c.nrl.navy.mil FIG. 1. X scan, transmitted signal as a function of x, for a 15-m-thick KN125 sample placed between crossed polarizers; the inset illustrates the experimental geometry not to scale. 1536 Appl. Phys. Lett. 70 (12), 24 March 1997 0003-6951/97/70(12)/1536/3/$10.00 © 1997 American Institute of Physics