Transmission channels for light in absorbing random media: from diffusive to ballistic-like transport

While the absorption of light is ubiquitous in nature and in applications, the question remains how absorption modifies the transmission channels in random media. We present a numerical study on the effects of optical absorption on the maximal transmission and minimal reflection channels in a two-dimensional disordered waveguide. In the weak absorption regime, where the system length is less than the diffusive absorption length, the maximal transmission channel is dominated by diffusive transport and it is equivalent to the minimal reflection channel. Its frequency bandwidth is determined by the underlying quasimode width. However, when the absorption is strong, light transport in the maximal transmission channel undergoes a sharp transition and becomes ballistic-like transport. Its frequency bandwidth increases with absorption, and the exact scaling varies with the sample's realization. The minimal reflection channel becomes different from the maximal transmission channel and becomes dominated by absorption. Counterintuitively, we observe in some samples that the minimum reflection eigenvalue increases with absorption. Our results show that strong absorption turns open channels in random media from diffusive to ballistic-like.Comment: 11 pages, 7 figure

Turning Optical Complex Media into Universal Reconfigurable Linear Operators by Wavefront Shaping

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies and reconfigurability. Current designs of custom-tailored photonic devices or coherent photonic circuits only partially satisfy these needs. Here, we propose a way to perform linear operations by using complex optical media such as multimode fibers or thin scattering layers as a computational platform driven by wavefront shaping. Given a large random transmission matrix (TM) representing light propagation in such a medium, we can extract a desired smaller linear operator by finding suitable input and output projectors. We discuss fundamental upper bounds on the size of the linear transformations our approach can achieve and provide an experimental demonstration. For the latter, first we retrieve the complex medium's TM with a non-interferometric phase retrieval method. Then, we take advantage of the large number of degrees of freedom to find input wavefronts using a Spatial Light Modulator (SLM) that cause the system, composed of the SLM and the complex medium, to act as a desired complex-valued linear operator on the optical field. We experimentally build several $16\times16$ complex-valued operators, and are able to switch from one to another at will. Our technique offers the prospect of reconfigurable, robust and easy-to-fabricate linear optical analogue computation units

The Schr\"odinger operator on an infinite wedge with a tangent magnetic field

We study a model Schr\"odinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral quantities coming from the regular case. We are particularly motivated by the influence of the magnetic field and the opening angle of the wedge on the spectrum of the model operator and we exhibit cases where the bottom of the spectrum is smaller than in the regular case. Numerical computations enlighten the theoretical approach