The authors gratefully acknowledge the financial support of the EPSRC A comparison of the flexoelectro-optic effect in the uniform lying helix and standing helix geometries S. M. Morris, F. Castles, B. J. Broughton and H. J. Coles Centre of Molecular Materials for Photonics and Electronics, Electrical Engineering Division, Cambridge University Engineering Department, 9 JJ Thomson Avenue, CB3 0FA, UK BACKGROUNDRESULTS - MODELLING Flexoelectro-optic effect: fast switching (10 – 100  secs) Linear-in-field Deflection of optic axis depends upon polarity Two possible geometries: Uniform lying helix (ULH, in-plane switch) Standing helix geometry (SH, out-of- plane switch) Figure 1. Illustration of the standing helix (SH) and uniform lying helix (ULH) geometries. Figure 2. Coordinate axis for defining q and f. Also shown is an illustration of the rotation of the optic axis with electric field. The helix axis is collinear with the z- axis. THEORY Figure 3. Plots of theta(q) as a function of the distance through the cell for three different electric field strengths. A. One Pitch system Figure 4. Plots of the tilt angle as a function of the distance through the cell for a single pitch system whereby electric field is 3 V  m -1. B. Twenty Pitch system Figure 5. Plots of theta(q) as a function of the distance through the cell for three different electric field strengths. (a)ULH geometry and SH geometry when the direction of the electric field is parallel to the rubbing direction (SH II ) (b) SH geometry when the electric field is perpendicular to the rubbing direction. Variation of  with distance through cell for different electric field strengths Difference in behaviour for the two geometries Tilt angle of the optic axis as a function of position along the helix axis Variation of  with distance through cell for different electric field strengths For a large number of turns there is not a significant difference in behaviour for the two geometries Tilt angle of the optic axis as a function of position along the helix axis – ULH/SH II Figure 6. Plot of the tilt angle as a function of the distance through the cell. Tilt angle of the optic axis as a function of position along the helix axis – SH  Figure 7. Plot of the tilt angle as a function of the distance through the cell. Difference appears to be more of a surface effect. RESULTS – EXPT. Figure 8. The response times as a function of electric field for the ULH and SH II geometry Dynamics Figure 9. The response times as a function of electric field for the ULH and SH II geometry Response is not symmetric in the SH  configuration. CONCLUSIONS Theory predicts that the flexoelectro- optic effect is the same for the ULH and SH II geometry although different for the SH  geometry. Differences decrease with increasing number of pitches. Response times are symmetric for the ULH geometry but asymmetric for the SH  geometry. The expression for the free-energy density that was used can be written as, From the Euler-Lagrange and the free-energy equation we find that the governing equations are given by