A photonic nanojet (PNJ) is a highly confined light beam that focuses from the shadow side of microparticles. In $46.47\lambda $ this work, we propose a PNJ with ultrahigh quality factor formed by dielectric truncated microtoroid. The key properties of PNJ, such as the maximum intensity, the length of PNJ, the full-width at half maximum (FWHM), are studied in detail using finite-difference time-domain (FDTD) analysis. The results show that a PNJ with an enhanced intensity of 55.21 times to the incident light, superlong length of $46.47\lambda $ and subwavelength FWHM of $0.77\lambda $ is formed by semi-microtoroid, thus, an ultrahigh quality factor of 3308.68 is achieved. More importantly, the properties of the PNJ are tunable by changing the truncated proportions of the microtoroid. The structure we proposed has the advantages of compact structure and simple experimental operation, which is expected to apply in many research fields, including optical detection, optical data storage, super-resolution image, nanopattern, nanolithography, and so on.

In this paper, using the surface plasmon and Fabry–Pérot (FP) cavity, the design of a symmetric silicon grating absorber is proposed. The time-domain finite difference method is used for simulation calculations. The basic unit structure is a dielectric grating composed of silicon dioxide, metal and silicon. Through the adjustment of geometric parameters, we have achieved the best of the symmetric silicon grating absorber. A narrowband absorption peak with an absorption rate greater than 99% is generated in the 3000–5000 nm optical band, and the wavelength of the absorption peak is λ = 3750 nm. The physical absorption mechanism is that silicon light generates surface plasmon waves under the interaction with incident light, and the electromagnetic field coupling of surface plasmon waves and light causes surface plasmon resonance, thereby exciting strong light response modulation. We also explore the influence of geometric parameters and polarization angle on the performance of silicon grating absorbers. Finally, we systematically study the refractive index sensitivity of these structures. These structures can be widely used in optical filtering, spectral sensing, gas detection and other fields.

Neural network training often suffers from spectral asymmetry, where gradient energy is disproportionately allocated to high-frequency components, leading to suboptimal convergence and reduced efficiency. This paper introduces Gradient Spectral Normalization (GSN), a novel optimization technique designed to restore spectral symmetry by dynamically reshaping gradient distributions in the frequency domain. GSN transforms gradients using FFT, applies layer-specific energy redistribution to enforce a symmetric balance between low- and high-frequency components, and reconstructs the gradients for parameter updates. By tailoring normalization schedules for attention and MLP layers, GSN enhances inference performance and improves model accuracy with minimal overhead. Our approach leverages the principle of symmetry to create more stable and efficient neural systems, offering a practical solution for resource-constrained environments. This frequency-domain paradigm, grounded in symmetry restoration, opens new directions for neural network optimization with broad implications for large-scale AI systems.