Physical bounds, such as the Abbe diffraction limit and the Wheeler–Chu–Harrington bound on the Q factor, have been instrumental in explaining and guiding the designs of optical systems. While multi-channel optical systems offer diverse functionalities, they are also subject to additional constraints absent in single-channel devices. Understanding such constraints can avoid time wasted in blind explorations, guide future work and resource allocations, and sometimes reveal better design strategies that were previously unknown. One direction of our group is finding the physical bounds of multi-channel systems and using them to guide our designs.
The scattering matrix encapsulates the response of multi-channel systems. Once an optical structure’s target function is specified, one can write down the corresponding scattering matrix without having to know the structure itself. We use the rich information in this matrix to derive bounds.
One piece of such information is the degree of nonlocal coupling, which we quantify using how much a localized input spreads laterally when it reaches the output side. Since light must propagate to spread, the amount of lateral spreading puts a bound on the minimal device thickness [1]. This thickness bound generalizes the memory effect in mesoscopic physics and precedes a related bound proposed independently by David Miller.
Another piece of information is the efficiency of transmission. By analyzing the singular values of the transmission matrix, we put a rigorous bound on the maximal channel-averaged transmission efficiency [2].
Beyond setting the limitations of photonic devices, we also introduced a more active way to use theoretical bounds by integrating them into part of the photonic design process. By identifying system parameters that maximize the efficiency bound itself and then performing inverse design, we came up with wide-field-of-view high-numerical-aperture metalens designs with efficiencies greatly surpassing existing records [3].
Related publications
- Thickness bound for nonlocal wide-field-of-view metalenses, Shiyu Li and Chia Wei Hsu. Light: Science & Applications 11, 338 (2022); arXiv:2205.09366.
- Transmission efficiency limit for nonlocal metalenses, Shiyu Li and Chia Wei Hsu. Laser & Photonics Reviews 17, 2300201 (2023).
- High-efficiency high-numerical-aperture metalens designed by maximizing the efficiency limit, Shiyu Li, Ho-Chun Lin, and Chia Wei Hsu. Optica 11, 454–459 (2024).