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Optical manifestations and bounds of topological Euler class

We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined optical weights of the Euler bands at different dopings and further restrict the size of the adjacent band gaps. In this process, we also consider the associated interband contributions to dc conductivities in the flat-band limit. We physically validate these results by recasting the bound in terms of transition rates associated with the optical absorption of light, and demonstrate how the Euler connections and curvatures can be determined through the use of momentum and frequency-resolved optical measurements, allowing for a direct measurement of this multiband invariant. Additionally, we prove that the bound holds beyond the degenerate limit of Euler bands, resulting in nodal topology captured by the patch Euler class. In this context, we deduce optical manifestations of Euler topology within k·p models, which include quantized optical conductivity, and third-order jerk photoconductivities. We showcase our findings with numerical validation in lattice-regularized models that benchmark effective theories for real materials and are realizable in metamaterials and optical lattices. Published by the American Physical Society 2025

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Effect of stimulus size on chromatic discrimination

In psychophysical experiments, discrimination thresholds were measured in different directions around points in the MacLeod–Boynton chromaticity diagram, while the eye was maintained in a state of constant adaptation to a metamer of D65. A spatial forced-choice procedure was used: a brief (150 ms) disk divided into four sectors was presented, and the observers’ task was to detect the sector that differed from the other three. The diameter of the test disk varied from 32 min to 2.4∘ of visual angle. Sensitivity was probed at several different referent positions in the chromaticity diagram, including the adapting chromaticity. The data for each referent were fitted with ellipses. In the case of the largest test size (2.4∘ diameter), ellipses were predominantly oriented so that their longer axis was aligned with the line connecting the center of the ellipse to the chromaticity of D65 (the adaptation point). Along such radial lines, colorimetric purity varies, and the orientation of the ellipses reflects reduced sensitivity to saturation differences compared to hue differences. With decreasing test size, the ellipses change their orientation so that their longer axis is rotated toward a tritan direction, and the detection of changes in chromaticity depends primarily on the activity of long- and middle-wave cones. However, these general principles must be modified in several ways according to the region of the chromaticity diagram that is being probed.

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Compact deep-groove-assisted bends on SiN platform for monolithic integrated laser

To build a photonic integration platform that incorporates monolithically integrated light sources which require minimized loss and reflection, a micro-meter scale passive layer is needed in addition to the III-V layer. Low temperature plasma-enhanced chemical vapor deposition (PECVD) silicon nitride (SiN) is a promising candidate, owing to its back-end-of-line (BEOL) integration capabilities, along with its amorphous structure that allows the growth of defect-free thick layers. In view of the III-V layer stack, the optimized SiN waveguides are thick and in a rib formation. However, bends on this thick SiN platform suffer from high radiation losses, resulting in the need for a bending radius as large as 800 µm that poses challenges for compact photonic integrated circuits (PICs). This paper describes and demonstrates a novel SiN bending structure with a deep etched groove along the outer side. This structure significantly reduces the bending radii to 37 µm with a bending loss of 0.1 dB/90°. A compact micro-ring resonator (MRR) with deep etched grooves is also investigated, exhibiting a substantial enhancement in the free spectral range (FSR) compared with the rib waveguide MRRs, while offering a passband of 39.1 GHz. These notable performance improvements pave the way for compact integrated emitters on a single substrate.

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