Threshold property of a nematic liquid crystal cell with two grating surface substrates

A grating surface can drive the liquid crystal molecules to orientatealong the direction parallel or vertical to the projected plane ofthe grating surface. The nematic liquid crystal (NLC) cellmanufactured with two pre-treated grating surface substrates mayrealize the vertical display, parallel display and twist display. Inthis paper, the threshold property of this NLC cell is investigatedsystematically. With the Frank elastic theory and the equivalentanchoring energy formula of grating surface substrate, the analyticexpressions of the threshold voltage related to three displays areobtained, which are dependent on their geometrical parameters suchas amplitude δ and pitch λ of the grating surfacesubstrate. For a certain anchoring strength, the threshold voltageincreases or decreases with the increase of the valueδ/λ of the different displays.