2013/07/31 by Xiaojun Cheng, Chushun Tian, Azriel Z. Genack · 13 citations
Engineering · Mathematics · Physics and Astronomy · #Computer science #Eigenvalues and eigenvectors #Geometry #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Optics #Physics #Quantum mechanics #Random lasers and scattering media #Reflection (computer programming) #Statistics #Surface (topology) #Telecommunications #Terahertz technology and applications #Total internal reflection #Transmission (telecommunications) #Value (mathematics) #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.88.094202
published in Physical Review B 88(9) (American Physical Society)
arxiv created 2013/07/31 · openalex publication_date 2013/09/25 · arxiv updated 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically that the distribution of transmission eigenvalues of diffusive waves exhibits a nonanalytic transition as the strength of surface reflection at one surface passes through a critical value while that at the other is fixed. Above the critical value, the highest transmission eigenvalue is strictly smaller than unity and decreases with increasing internal reflection. When the input and output surfaces are equally reflective, the highest transmission eigenvalue is unity and the transition disappears irrespective of the strength of surface reflection.