Backscatter analysis based algorithms for increasing transmission through highly-scattering random media using phase-only modulated wavefronts

摘要

Recent theoretical and experimental advances have shed light on the existenceof so-called `perfectly transmitting' wavefronts with transmission coefficientsclose to 1 in strongly backscattering random media. These perfectlytransmitting eigen-wavefronts can be synthesized by spatial amplitude and phasemodulation. Here, we consider the problem of transmission enhancement usingphase-only modulated wavefronts. We develop physically realizable iterative andnon-iterative algorithms for increasing the transmission through such randommedia using backscatter analysis. We theoretically show that, despite thephase-only modulation constraint, the non-iterative algorithms will achieve atleast about 25$\pi$% or about 78.5% transmission assuming there is at least oneperfectly transmitting eigen-wavefront and that the singular vectors of thetransmission matrix obey a maximum entropy principle so that they areisotropically random. We numerically analyze the limits of phase-only modulated transmission in 2-Dwith fully spectrally accurate simulators and provide rigorous numericalevidence confirming our theoretical prediction in random media with periodicboundary conditions that is composed of hundreds of thousands of non-absorbingscatterers. We show via numerical simulations that the iterative algorithms wehave developed converge rapidly, yielding highly transmitting wavefronts usingrelatively few measurements of the backscatter field. Specifically, the bestperforming iterative algorithm yields approx 70% transmission using just 15-20measurements in the regime where the non-iterative algorithms yieldapproximately 78.5% transmission but require measuring the entire modalreflection matrix.