arXiv subjects

Yuxiang Tian

Publications and source records attributed to Yuxiang Tian.

2 recordsLinked to original sources

arXiv2026

Characterize localization length of disordered lattices via critical coupling effect

Light localization by scattering is a fundamental mechanism driving phase transitions of wave transport in disordered systems. Characterizing the localization length in scattering systems is crucial yet challenging. In this Letter, we demonstrate a spatially matched coupling scheme using wavefront shaping to resolve the intrinsic localization length in two-dimensional disordered lattices. By tailoring the incident wavefront, our method facilitates efficient coupling of light to the minimum localized mode. We apply this approach to measure two different self-assembled lattices, and report the first observation of the critical coupling effect, which allows for the direct determination of the characteristic size of minimum localized mode. Our results reveal that for a fixed lattice periodicity, increasing the air-hole diameter significantly reduces this intrinsic localization length. This far-field metrology offers a robust framework for probing wave localization in complex media, which should be useful in various applications such as random lasing and nonlinear optics

physics.optics↗

arXiv2025

Space Complexity of Euclidean Clustering

The $(k, z)$-Clustering problem in Euclidean space $\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error $\varepsilon$, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean $(k, z)$-Clustering and offers both upper and lower bounds. Our space bounds are nearly tight when $k$ is constant, indicating that storing a coreset, a well-known data compression approach, serves as the optimal compression scheme. Furthermore, our lower bound result for $(k, z)$-Clustering establishes a tight space bound of $Θ( n d )$ for terminal embedding, where $n$ represents the dataset size. Our technical approach leverages new geometric insights for principal angles and discrepancy methods, which may hold independent interest.

cs.CG↗