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We proposed an effective approach to enlarge the slow light bandwidth and normalized-delay-bandwidth product in an optimized moiré lattice-based photonic crystal waveguide that exhibits intrinsic mid-band characteristics. A flatband corresponding to a nearly constant group index of 34 over a wide bandwidth of 82 nm centered at 1550 nm with near-zero group velocity dispersion was achieved. A large normalized-delay-bandwidth product of 0.5712 with a relative dispersion of 0.114%/µm was obtained, which is a significant improvement if compared with previous results. Our results indicate that the photonic moiré lattice waveguide could advance slow light applications.

Microstrip patch antenna has become more popular recently because of its easy analysis, fabrication, low cost, lightweight, and attractive radiation characteristics. Although a patch antenna has numerous advantages, it also has some drawbacks such as narrow bandwidth, low gain, and a potential decrease and distortion in the radiation pattern. This paper presents the design, simulation, and analysis of rectangular and circular microstrip patch antennas. It discusses antennas' performances based on return loss, reflection coefficient at the input port, bandwidth, 3D radiation pattern, and front-to-back ratio. Designed on an FR-4 substrate of thickness 0.7 mm and relative permittivity (ε r ) of 10, and fed by a 50 Ω microstrip feed line, the antennas are designed to resonate at 1.8GHz. The rectangular patch antenna achieved a bandwidth of 0.17GHz and a gain of 6.37dBi. At the same time, the circular patch antenna exhibits a bandwidth of 0.16GHz and again of 6.53dBi. A comparison of the antenna performances indicates that the rectangular antenna has more bandwidth than the circular antenna. While circular has better gain than rectangular; thus, good matching is better achieved in the circular. Therefore, the antennas can be a good candidate for fixed Point-to-Point link applications.

Slow light waveguides in photonic crystals are engineered using a conventional method or a deep learning (DL) method, which is data-intensive and suffers from data inconsistency, and both methods result in overlong computation time with low efficiency. In this paper, we overcome these problems by inversely optimizing the dispersion band of a photonic moiré lattice waveguide using automatic differentiation (AD). The AD framework allows the creation of a definite target band to which a selected band is optimized, and a mean square error (MSE) as an objective function between the selected and the target bands is used to efficiently compute gradients using the autograd backend of the AD library. Using a limited-memory Broyden-Fletcher-Goldfarb-Shanno minimizer algorithm, the optimization converges to the target band, with the lowest MSE value of 9.844×10−7, and a waveguide that produces the exact target band is obtained. The optimized structure supports a slow light mode with a group index of 35.3, a bandwidth of 110 nm, and a normalized-delay-bandwidth-product of 0.805, which is a 140.9% and 178.9% significant improvement if compared to conventional and DL optimization methods, respectively. The waveguide could be utilized in slow light devices for buffering.