Transmission eigenvalues in random media with surface reflection

Abstract

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.

References in corpus (3)

• Universal optimal transmission of light through disordered materials
• Filtering Random Matrices: The Effect of Incomplete Channel Control in Multiple Scattering
• Supersymmetric field theory of local light diffusion in semi-infinite media

Cited by in corpus (9)

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• Optical transmission matrix as a probe of the photonic interaction strength
• Controlling transmission eigenchannels in random media by edge reflection
• Invariance principle for wave propagation inside inhomogeneously disordered materials
• Super-universality of eigenchannel structures and possible optical applications
• Energy-leaky modes in partially measured scattering matrices of disordered media
• Impact of surface reflection on transmission eigenvalue statistics and energy distributions inside random media
• Measuring the transmission matrix for microwave radiation propagating through random waveguides: fundamentals and applications
• Scaling theory for anomalous semiclassical quantum transport