Objective Focusing on the insufficient dynamic modulation ability and modulation dimension of planar liquid crystal (LC) devices, we propose a design of planar LC for decoupling control of the amplitude and phase of light, which enables the dual-channel multiplexing display in the near and far fields in a wide band with conjugated image eliminated. Moreover, wavelength-dependent switching control of the display can be achieved by modulating external electric fields. The electronically controlled multiplexing display in the spatial and wavelength dimensions offers a novel approach to expanding the functionality of LC devices. Methods Firstly, Eqs. (3) and (4) show that under the condition of half-wave delay, either linearly polarized or circularly polarized light incident, the same polarization component in the transmitted light field is eliminated. For the horizontally incident light, the local polarization state of the transmitted light field depends on the vector light field of theta. The transmitted light field with the intensity of I=sin(2)(2 theta) can be obtained by the vertical polarization filtering according to Malus'law, and the amplitude modulation can be realized, as shown in Fig. 1. For the left-handed circularly polarized incident light, the transmitted field is a right-handed circularly polarized light with an additional phase of e(i2 theta), where 2 theta is a geometric phase, and thus phase modulation can be achieved. Based on the periodicity of the sine function, a one-to-four mapping was observed between the transmitted light intensity I determined by Malus'law and the orientation angle theta. Based on this degenerate relationship, the decoupling modulation of the amplitude (intensity) and phase of the light field can be realized by selecting an appropriate orientation angle of the LC molecules. With the above amplitude and phase in the decoupling modulation, surface display technology and phase-only hologram were respectively used to design a multiplexing display LC device in the near and far fields, with the working principle shown in Fig. 1(c). Fig. 2 shows the design algorithm of the orientation angle distribution theta(x, y) of the LC molecule in the photo-alignment layer of the LC device. To make up for the lack of molecular orientation accuracy of LC, theta( x, y) needs to be expanded by the two-pixel method. The far-field conjugated images produced by degeneracy problem were effectively reduced by selecting the intensity midpoint and contrast r of the near-field images, as shown in Fig. 3. In addition, by measuring the conversion efficiency of the orthogonal polarization component of the transmitted light field modulated by the polarization grating with voltage, the electronic control ability of the phase delay at different wavelengths was validated in Fig. 4, which provides a theoretical basis for the controllable multiplexing display in wavelength dimension. Results and Discussions The experimental samples, setup, and results are shown in Figs. 5, and 6. We design three samples A, B, and C, with binary, constraint binary, and continuous grayscale in the near field but the same binary image in the far field. Fig. 7 shows the experimental results at 633-nm wavelength, and the near-field and far-field images generated from samples A, B, and C show good quality, indicating that the amplitude and phase modulations are consistent with the expected results. The peak single-to-noise ratios (PNSRs) of the experimental images in the near and far fields are 38.3768, 29.9965, 30.0225, and 37.7480, 30.1558, 30.4755, respectively. The comparison between the near-and far-field images of samples A and B indicates that although the conjugate image is eliminated by introducing the amplitude constraint into the near-field image, the contrast degree of the near-field image is reduced, showing the elimination of the far-field conjugate image at the expense of near-field image contrast degree. Therefore, an appropriate intensity range r of near-field image should be selected based on the performance index of the product in practical application. Figure 8 illustrates the change of near-and far-field display of sample A with the external electric field at 633 nm, 533 nm, and 483 nm wavelengths. It can be seen that the display states of target images switch under different wavelengths with the change of external voltage. When the voltage modulation is set to 2.1 V, 2.4 V, 2.7 V, 3.2 V, 4.0 V, and 4.4 V, various combinations of on and off states of the target image under red, green, and blue light are presented. It means that these LC devices have 6 specific voltages that can control the on and off states of the image at a single or multiple wavelengths, and realize decoupling modulation in the wavelength dimension. Conclusions We study the optical wavefront modulation theory and the electrical modulation law of LC molecules and propose a design of an LC device that can realize continuous intensity display in the near field and holographic display in the far field. To reduce the influence of conjugate images, we propose a method of restricting the intensity of the near-field image to increase phase selectivity. In addition, the device can control the image display in wavelength dimension by adjusting the external field voltage. In general, our work provides a new idea for dynamic and multi-dimensional display.
