A guided-mode-resonance device for both narrowband retroreflection and waveguide input coupling was designed and fabricated for operation wavelength of 1550 nm. It consists of a focusing grating coupler (FGC) integrated in a waveguide cavity resonator constructed by a pair of distributed Bragg reflectors (DBRs) on a reflection substrate. The size of the FGC was 31 × 20 µm 2 . The device was used as a laser mirror of an external cavity laser. The oscillation wavelength was fixed to the retroreflection wavelength, and the laser power was coupled to a waveguide. The coupled power depends on the length of one DBR.The optimal length for the maximum coupling was also discussed theoretically and experimentally.

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Statistically weighted principal component analysis (wPCA) is widely used to reduce the noise of scanning transmission electron microscopy-energy-dispersive X-ray (STEM-EDX) spectroscopic data. It is beneficial to retain the spatial resolution of observation in each step of the analysis, but the direct application of wPCA without preprocessing, such as spatial averaging, often fails against low-count STEM-EDX data. To enhance the applicability of wPCA while retaining spatial resolution, a step-by-step noise reduction method is considered in this study. Specifically, a numerical optimization is developed to simultaneously characterize the smoothness of EDX spectra and the low rankness of the data. In the presented approach, low-count data are first spectrally smoothed by solving this optimization problem, and then further denoised by using wPCA to project onto a subspace rigorously spanned by a small number of components. A challenging example is provided, and the improved noise reduction performance is demonstrated and compared to existing spectral smoothing techniques.