Inverse-Design Enabled Prototyping of Photonic Metalens for Simultaneous Beam Collimation and Color Mixing in Near-Eye LED Displays

Digital displays (including LCD, OLED, and micro-LED displays) mix light from red, green, and blue sub pixels to generate images. In the state-of-art near-eye displays in AR/VR devices, such as Apple^R Vision Pro^TM, the whole pixel pitch has been reduced to 7.5 microns. Nevertheless, human ocular system can still percept the discretized pixels instead of smooth images, leading to the screen door effect. A direct approach to resolve it could be further increasing the pixel density, but the miniaturized pixel size may cause the divergence angle of emitted light too big to the light coupling optics. At the same time, considering the short illumination distance of typical near-eye displays, an appropriate coloring mixing is also critical to avoid strong color patterns. Hence, precisely engineered beam collimation and color mixing optics are critical to near-eye displays.<br/><br/>Here we proposed a prototyping design of a metalens to achieve simultaneous beam collimation and color mixing. The metalens is discretized into a series of design units, and the material distribution inside the metalens is the design parameter to be optimized. As the dimension of the deign parameters could be large, machine learning based optimization is employed. To achieve this, we employed the adjoint method to evaluate the optical performance of a given design by finite-difference time domain (FDTD) simulations and calculate its derivative with respect to the design parameters. Therefore, the metalens design can be iteratively improved via a gradient descent process.<br/><br/>Specifically, we designed the metalens covering an entire pixel pitch (with a cross section of 4.5 by 4.7 um), consisting of a set of R, G, and B subpixels (the illumination area of a single subpixel measures 1.05 by 3.3 um). The metalens was discretized into 90 * 47 *40 design units. We optimized the capability of the metalens to route vertically incident RGB plane wave sources into corresponding channels, as is described in Zhao, <i>et al.</i>, 2021, <i>Adv. Photonics Res.</i> It should also be noted that while most literatures discussing inverse-design of photonic devices employ finite-difference frequency-domain solvers, we demonstrated FDTD solvers can also solve similar problems and be more adaptive to multi-frequency cases. The metalens optimized in the above-mentioned manner, according to the reciprocity principle of optical system, will convert the RGB lights from their respective channels back into the same planewave-like profile, and thus achieving beam collimation.<br/><br/>Our preliminary results have demonstrated the feasibility of the design concept. The optimized metalens showed the capability of collimating lights from R, G, and B subpixels into a planewave-like profile with divergence angle ~ 5°, while the controlling setup without the metalens showed a divergence angle ~ 20°. The mechanism for the reduction in divergence angle could be explained by the optical/étendue invariant: the optimized metalens defuses the light for the subpixels and increase the cross section of the beam roughly by 6 times, therefore the divergence angle is reduced. The increased cross sections of beams from RGB channels overlap with each other, and naturally achieves color mixing. At the same time, compared to a control setup without the metalens, the optical efficiency is evaluated to be 66%, 78%, and 69% for RGB lights, respectively.<br/><br/>In summary, we demonstrated a design of metalens for beam collimation and color mixing in near-eye LED displays. The design principle of the metalens combines the reciprocity principle of linear optical systems and the adjoint method for optimization, which can be executed in FDTD solvers. We have proved the feasibility of the design concept by simulation results, which indicate a light collimation effect. Future endeavors will focus on further improving the color mixing uniformity, improving the viewing angle tolerance, and integrating the fabrication constrains into the optimization process.