Slit Diffraction Spectrum Manipulation in Non-Paraxial Regions via the Spatial-Spectral Correspondence Relationship

In the past, a two-dimensional aperture diffraction of light in the non-paraxial region could only be studied using the Huygens integral without functional forms. This work presents a special case—a one dimension slit where the functional form can be obtained. The monochromatic light intensity distributions are investigated in detail. Using the correspondence relationship, the diffracted spectra of polychromatic light in that region can be readily found. Three interesting spectral effects are described: spectral switches, multi-level data transmission, and optical wavelength ruler. Since the functional form is derived without approximation, it is applicable to a region very near to the slit, including the wavelength region or even sub-wavelength scale. Thus, for light with micron-order wavelength (visible to near infrared (NIR) band), these results are valuable to micro- or nano-optics, especially for studies of the spatial intensities or spectral characteristics in the non-paraxial region.

Twisted spectral correspondence and torus knots

Cohomological invariants of twisted wild character varieties as constructed by Boalch and Yamakawa are derived from enumerative Calabi–Yau geometry and refined Chern–Simons invariants of torus knots. Generalizing the untwisted case, the present approach is based on a spectral correspondence for meromorphic Higgs bundles with fixed conjugacy classes at the marked points. This construction is carried out for twisted wild character varieties associated to [Formula: see text] torus knots, providing a colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.

Orientation-Preserving Spectral Correspondence for 3D Shape Analysis

In this article, the authors present an orientation-preserving spectral correspondence for three-dimensional (3D) shape analysis, which is robust and efficient for topological and deformable changes, even for non-isometric shapes. Our technique introduces an optimal spectral representation by combining the eigendecomposition with principal components analysis (PCA) to the heat kernel Laplacian matrix, and we further propose an efficient symmetry detection method based on so-called dominant eigenfunctions. Finally, a 3D descriptor encoding intrinsic symmetry structure and local geometric feature is constructed which effectively reveals the consistent structure between the deformable shapes. Consequently, sufficient orientation-preserving correspondence can be established in our embedding space. Experimental results showed that our method produces stable matching results in comparison with state-of-the-art methods.