Simultaneous retardation compensation during bending of plastic film coated with a polymer layer of opposite birefringence.
We proposed a method of eliminating the bending-induced retardation of a plastic film by coating it with a polymer layer with an opposite birefringence. We coated a polystyrene (PS) or a poly(methyl methacrylate) (PMMA) layer on a polycarbonate (PC) plastic film. The bare PC film is composed of main-chain-type polymers and showed an increase in retardation with bending. The main-chains of the PC polymer are reoriented along the circular arc direction during bending, resulting in a positive birefringence. In contrast, the 11 wt. % PS-coated and the 19 wt. % PMMA-coated PC films showed minimal change in the retardation regardless of the radius of curvature. The PS and the PMMA polymers are of the side-chain-type, and the side-chains were aligned perpendicular to the circular arc direction during bending, resulting in a negative birefringence. Consequently, the bending-induced retardation of the PC film can be compensated by the PS or the PMMA layer during bending of the film. This method of compensating for the bending-induced retardation of the plastic film can be useful for flexible display applications.
Optimal design of achromatic true zero-order waveplates using twisted nematic liquid crystal.
Phase retarders usually show strong wavelength dependence. A novel and simple configuration with the combination of two twisted nematic liquid-crystal cells is proposed for the design of a true zero-order achromatic quarter-wave plate. The present optimization method considers the material dispersion. Simulation computations show a good achromatic behavior of the optimized waveplate. Compared with other types of broadband quarter-wave plates, the present device is compatible with classical liquid-crystal displays and can be expected to be used in precision polarimeters with low cost and enhanced light efficiency.
Three-dimensional elasticity problems for the prismatic bar
A general solution is given to the three-dimensional linear elastic problem of a prismatic bar subjected to arbitrary tractions on its lateral surfaces, subject only to the restriction that they can be expanded as finite power series in the axial coordinate z. The solution is obtained by repeated differentiation of the tractions with respect to z, establishing a set of sub-problems . A recursive procedure is then developed for generating the solution to from that for . This procedure involves three steps: integration of the stress and displacement fields with respect to z, using an appropriate Papkovich–Neuber (P–N) representation; solution of two-dimensional in-plane and antiplane corrective problems for the tractions in that are independent of z; and expression of these corrective solutions in P–N form. The method is illustrated by an example.