Fig. 3: Periodic splay-twist stripe domains in planar NF cell at moderate voltages.
From: Periodic splay Fréedericksz transitions in a ferroelectric nematic
a PolScope Microimager texture of stripes with splay regions S; the splay of polarization \({{\bf{P}}}\) in the \({xy}\) plane resembles alternating letters “V” and “Λ”. b Polarizing microscopy shows extinct splay S-regions and bright twist regions of left-handed twist (TL) and right-handed twist (TR). Extinct centers of the S regions prove that \({{\bf{P}}}\) is in the \({{\bf{RE}}}\) plane there. The head of a nail attached to each tilted \({{\bf{P}}}\) vector in the S regions indicates that this end of \({{\bf{P}}}\) is closer to the observer. c Observations with uncrossed polarizers show complementary contrasts of TL and TR regions; monochromatic 485 nm light. d Transmitted light intensity vs. the angle \(\alpha\) between the polarizer and analyzer shows no twist in the S regions and left- and right-handed twists in TL and TR, respectively. Solid lines are numerical fits of the data. The maximum twist angle \({\bar{\varphi }}_{m}\) between \({{\bf{P}}}\) and the \(x\)-axis grows with the voltage. Error bars in (d) show the amplitude of light intensity fluctuations. NF cell in (a–d) with d = (3.1 ± 0.1) μm; 120 °C; 200 kHz, square waveform. e Top of the cell is tilted towards the observer by \(15^\circ\); PolScope Microimager shows optical retardance higher in the splay \({\varLambda }_{{xy}}\) regions than in the \({V}_{{xy}}\) regions. f Splay-canceling geometry of the S-regions explains the difference in the retardance in (e): the horizontal \({\varLambda }_{{xy}}\) splay is accompanied by the vertical splay \({V}_{{xz}}\) which appears more planar and thus of a higher retardance for the obliquely propagating light; in contrast, \({\varLambda }_{{xz}}\) appears more “homeotropic” and of a weaker retardance. Each horizontal splay is accompanied by the vertical splay of an opposite sign so that the splay cancellation condition \(\frac{\partial {P}_{y}}{\partial y}\frac{\partial {P}_{z}}{\partial z} < \, 0\) is fulfilled. In (e, f), \(d=\left(6.5\pm 0.1\right)\,{{\rm{\mu }}}{{\rm{m}}}\); 125 °C. 200 kHz, sinusoidal waveform, 475 nm light.
