How to characterize and calibrate a phase-only SLM

For most applications in complex media, spatial light modulators are used for their ability to control the phase of a laser beam. Whereas deformable mirrors are insensitive to the input polarization, liquid crystal based SLMs need to work with a given input polarization or sometimes a precise combination of input and output polarizations. It is then necessary for LC SLMs to carefully characterize the modulation to find the setup conditions where amplitude variations are minimal and for which the phase range is at least 2π. In any case, for a given wavelength, it is necessary to know the relation between the value given to a pixel on the SLM and the relative phase shift associated. I present here a typical way to characterize the complex modulation of an SLM.

From the bimodal distribution to the quarter circle law

[A. Goetschy and A. D. Stone, Phys. Rev. Lett., 1304.5562, (2013)]

Almost thirty years ago, theoreticians predicted that the distribution of the transmission values of a multiple scattering sample should follow a 'bimodal distribution'.  Physically, that means that, in the diffusive regime, there is a large number of strongly reflected channels - the closed channels - and a small number of channels of transmission close to one - the open channels. The existence of these open channels regardless of the thickness of the medium is of big interest for researchers, especially for imaging or communication applications. Nevertheless, such channels have not yet been directly observed. A investigation on those channels requires a measurement of the entire transmission matrix of a lossless scattering medium. For practical reasons (open geometry, limited numerical aperture, noise...) one usually has access to a subpart of the total transmission matrix. In recent experimental measures of the transmission matrix in optics [S.M. Popoff et al., Phys. Rev. Lett., 104, 100601, (2010)] the distribution of the transmission values follows a 'quarter circle law', characteristic of totally uncorrelated systems. This means that the fraction of the transmission matrix measured shows no effect of the correlations at the origin of the bimodal distribution due to the loss of information. In this paper, A. Goetschy and D. Stone theoretically study the effect of the loss of information or the imperfect control on the statistics of the transmission matrix of a scattering system.

Retrieving an optical scale resolution with light focusing guided by ultrasound

[B. Judkewitz et al., Nat. Photon., 7, 300, (2013)] 

To focus light in or through a scattering medium using wavefront shaping techniques, one needs a way to probe the intensity or the field at the target position. To avoid having to insert a probe in the medium, Xu et al. proposed in 2011 the use of an ultrasonic focused beam to select a target area by photo-acoustic effect [X. Xu, H. Liu and L.V. Wang, Nat. Photon., 5, 154, (2011)]. This technique allows focusing light on a spot of the size of the ultrasound focused beam, which is typically at least one order of magnitude larger than the optical wavelength. In this new study, B. Judkewitz and co-authors used an innovative method to be able to focus light on a much smaller scale.

A pioneering experiment: Focusing through scattering media using wavefront shaping

[I.M Vellekoop and A.P. Mosk, Opt. Lett., 15, 2309, 2007]

In 2007 I.M. Vellekoop and A.P. Mosk published their work on the first demonstration of focusing light through a highly scattering medium. Most techniques to image or focus through scattering media relied on selecting only the part of the light that has not been scattered - the ballistic light. The ballistic signals decay exponentially with the thickness of the medium, limiting drastically the depth at which light can be focused. The idea developed by the authors is to use the scattered waves, that are randomly mixed, to focus light through the medium. A scattering sample illuminated by a coherent wave gives rise to a so-called speckle pattern, that results from the interference of the scattered waves. Using a spatial light modulator (SLM), the authors are able to control independently the phase of the different parts of the incident beam. Each segment gives an output seemingly random complex field. By testing different values of the phase for each segment, they are able to put in phase all the contributions, giving rise to a very bright focus spot.