Measuring large optical transmission matrices of disordered media.

We report a measurement of the large optical transmission matrix (TM) of a complex turbid medium. The TM is acquired using polarization-sensitive, full-field interferometric microscopy equipped with a rotating galvanometer mirror. It is represented with respect to input and output bases of optical modes, which correspond to plane wave components of the respective illumination and transmitted waves. The modes are sampled so finely in angular spectrum space that their number exceeds the total number of resolvable modes for the illuminated area of the sample. As such, we investigate the singular value spectrum of the TM in order to detect evidence of open transmission channels, predicted by random-matrix theory. Our results comport with theoretical expectations, given the experimental limitations of the system. We consider the impact of these limitations on the usefulness of transmission matrices in optical measurements.

[1]  S. Popoff,et al.  Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. , 2009, Physical review letters.

[2]  A. Genack,et al.  Transmission eigenvalues and the bare conductance in the crossover to Anderson localization. , 2011, Physical review letters.

[3]  Yongkeun Park,et al.  Active spectral filtering through turbid media. , 2012, Optics letters.

[4]  A. Mosk,et al.  Universal optimal transmission of light through disordered materials. , 2008, Physical review letters.

[5]  S. Skipetrov,et al.  Information transfer through disordered media by diffuse waves. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Ko,et al.  Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems. , 1988, Physical review. B, Condensed matter.

[7]  Thomas G. Bifano,et al.  Vector transmission matrix for the polarization behavior of light propagation in highly scattering media. , 2012, Optics express.

[8]  A. Lagendijk,et al.  Observation of weak localization of light in a random medium. , 1985, Physical review letters.

[9]  K. Stetson,et al.  Progress in optics , 1980, IEEE Journal of Quantum Electronics.

[10]  B. M. Fulk.  MATH , 1992 .

[11]  J. Baik,et al.  The Oxford Handbook of Random Matrix Theory , 2011 .

[12]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[13]  Michael S Feld,et al.  Overcoming the diffraction limit using multiple light scattering in a highly disordered medium. , 2011, Physical review letters.

[14]  A. Goetschy,et al.  Filtering random matrices: the effect of incomplete channel control in multiple scattering. , 2013, Physical review letters.

[15]  H. J. Choi,et al.  Wide spectral bandwidth electro-absorption modulator using coupled micro-cavity with asymmetric tandem quantum well. , 2012, Optics express.

[16]  Sylvain Gigan,et al.  Image transmission through an opaque material. , 2010, Nature communications.

[17]  Jing Wang,et al.  Transport through modes in random media , 2011, Nature.

[18]  Quantum interference and entanglement induced by multiple scattering of light. , 2010, Physical review letters.

[19]  Wolf,et al.  Weak localization and coherent backscattering of photons in disordered media. , 1985, Physical review letters.

[20]  E. G. van Putten,et al.  Scattering lens resolves sub-100 nm structures with visible light. , 2011, Physical review letters.

[21]  Li,et al.  Correlation in laser speckle. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.