Polarization properties in aperture-less scanning near-field optical microscopy (SNOM) were investigated using the 3D finite-difference time-domain (FDTD) method. We found that scattered light became elliptically polarized with linear or circular-polarized light illumination, and the polarization state of scattered light was preserved. In addition, Jones matrices that express the relationship between incident light and scattered light in terms of the polarization states were successfully obtained. We succeeded in calculating the polarization state of scattered light with arbitrary polarized light illumination by using the Jones matrix method.

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Learning semantic-rich representations from raw unlabeled time series data is critical for downstream tasks such as classification and forecasting. Contrastive learning has recently shown its promising representation learning capability in the absence of expert annotations. However, existing contrastive approaches generally treat each instance independently, which leads to false negative pairs that share the same semantics. To tackle this problem, we propose MHCCL, a Masked Hierarchical Cluster-wise Contrastive Learning model, which exploits semantic information obtained from the hierarchical structure consisting of multiple latent partitions for multivariate time series. Motivated by the observation that fine-grained clustering preserves higher purity while coarse-grained one reflects higher-level semantics, we propose a novel downward masking strategy to filter out fake negatives and supplement positives by incorporating the multi-granularity information from the clustering hierarchy. In addition, a novel upward masking strategy is designed in MHCCL to remove outliers of clusters at each partition to refine prototypes, which helps speed up the hierarchical clustering process and improves the clustering quality. We conduct experimental evaluations on seven widely-used multivariate time series datasets. The results demonstrate the superiority of MHCCL over the state-of-the-art approaches for unsupervised time series representation learning.

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