Focusing through a ‘maze’ of strong scattering
One of the broad challenges in a lot of optical applications involving visible light is simply that most materials aren’t particularly transparent.  This is rather obvious, at a glance: materials can be strong absorbers of light, strong reflectors of light, or highly dispersive.  Even materials which do not suffer from these problems can still strongly scatter a light field.  Milk is a good example of this latter case: light can be transmitted through a glass of milk, but seemingly only in a diffuse manner.  No images or bright points of light can be seen through the glass, only a diffuse glow which has little useful purpose.

Researchers at the University of Twente in The Netherlands, however, have demonstrated that it is possible to focus light through a strongly scattering media, in essence by finding special transmission paths through a ‘maze’ of strongly scattering objects, and overall increase the amount of light transmitted through such a scatterer.   Some experimental results were recently reported in Physical Review Letters, and the research seemed cute enough to merit a blog post!

A strong scatterer like milk is essentially a large collection of particles which scatter light around like a ball in a pinball (or pachinko) machine.  If we use a ray picture of light, the path of light through a particulate system might appear as follows:


There are two important lessons to be learned from this picture: 1.  Because of the multiple ‘bounces’ of light, is it impossible to predict the output path of incident light (just like a pachinko machine), and 2.  Light entering the medium at different locations can come out at very different locations and directions.  Light may not even make it all the way through the medium; it may get sent back out the way it came (effectively reflected) or bounce around long enough that it eventually gets absorbed.

It is hopefully obvious why it is difficult to focus light through such a material or transmit any useful information through it by optical means.  It is difficult, but is it impossible?

In large part, the answer to this question depends upon the exact behavior of light in the medium. A model for this behavior was first developed in a rather different field: electrical conductivity.  An electrical conductor, on an atomic level, looks very much like the strong optical scatterers described above.  Electrons flowing through a metal bounce along downstream like the balls in my favorite pachinko analogy.  In 1984, physicist O.N. Dorokhov theorized1 that all possible paths through the metal can be broken into two types: ‘localized’ paths which are in essence dead ends (near zero transmission), and ‘open’ paths for which nearly all electrons pass through (near 100% transmission).  Average electrical resistance, i.e. Ohm’s law, represents the average behavior of electrons, some passing through closed paths, some passing through open paths.

If this theory is correct, a strong scatterer acts very much like a maze: there are a large number of dead ends and a very small number of clear paths.  In reality, though, one of these ‘open channels’ is not found simply by passing a ray of light into the medium at a particular location; rather, a beam with an appropriately shaped phase structure must be shined upon the medium.

The existence of open channels suggests two possibilities: 1.  One should be able to employ the open channels to actually focus light beyond a strong scatterer, and 2.  In principle, one should be able to achieve nearly perfect transmission through a strong scatterer, if the illuminating field perfectly matches one of the open channels.

The first of these possibilities was demonstrated by Vellekoop and Mosk last year in Optics Letters2, the second recently in Physical Review Letters3.  The techniques used were roughly the same in both experiments.  A simplified schematic (excluding standard optical components) is shown below:


Light from a HeNe (helium-neon laser) is passed through a polarizing beam splitter (PBS), which puts different polarization components onto different spatial light modulators (SLM).  The return signals pass through the scattering medium, and then onto a CCD camera.  The spatial light modulators represent a grid of N different segments; adjusting a segment adjusts the phase of the field reflected from that segment.  The shape of the wavefront as a whole can be manipulated by changes in the SLM.

Why two SLMs?  In a strong scattering medium such as the ones considered here, scattering is highly polarization-dependent: the two possible polarizations of the illuminating light field must be corrected independently.

The process for increasing the transmission of light through the system, or making a focal spot, is as follows:  Vary the phase of each element of the SLM individually, selecting the phase which maximizes the intensity in the desired focal region.  A computer-monitored feedback loop between the CCD and the SLMs undertakes this.  The maximum of intensity will presumably occur when the contribution from the SLM element is in phase with the total light field from all other elements.  This process is repeated for all elements, at the end of which one presumably has the fields from all SLM elements in phase in the desired focal region, therefore producing a bright spot.

Results from the PRL are reproduced below:


(Reprinted Fig. 2 with permission from Vellekoop and Mosk, Phys. Rev. Lett. 101 (2008), 120601.  ©2008 by the American Physical Society.4)

Part (a) shows the intensity distribution in a 30 μm x 30 μm square for a nonoptimized illuminating light field.  One can see that only a diffuse speckle pattern appears.  The optimized field appears in part (b), and one can see that a bright intensity spot has been made in the center of the distribution.  Part (c) shows the ‘before’ and ‘after’ intensity, summed in the y-direction.  With an optimized wavefield, significantly more light has passed through the system.  The researchers reported a 35% increase in light throughput for this figure(and a peak intensity that is clearly an order of magnitude larger than the background).

This technique is, in some sense, a strong-scattering relative of the technique of adaptive optics, which is used to correct the distortion of wavefields created by atmospheric turbulence (weak scattering).

These results are significant from both a practical and a physical point of view.  From a physical point of view, the experiment gives good evidence that the open channel theory of Dorokhov is correct.  From a practical point of view, the experiment demonstrates that strong scattering is not necessarily a barrier to making highly concentrated light fields.  It will be interesting to see how the technique develops in future research.


1 O.N. Dorokhov, “On the coexistence of localized and extended electronic states in the metallic phase,” Solid State Commun. 51 (1984), 381.
2 I.M. Vellekoop and A.P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32 (2007), 2309.
3 I.M. Vellekoop and A.P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101 (2008), 120601.
4 Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.


I. M. Vellekoop, A. P. Mosk (2008). Universal Optimal Transmission of Light Through Disordered Materials Physical Review Letters, 101 (12) DOI: 10.1103/PhysRevLett.101.120601

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5 Responses to Focusing through a ‘maze’ of strong scattering

  1. This is really interesting research, but I’m confused by the term “focusing”, because there’s no converging beam. Is there supposed to be a lens system somewhere prior to entering the scattering medium, or are the authors perhaps creating an abstract definition of “focus”, in that an appropriate manipulation of the input phase causes the light to re-converge at the exit?

    Also I assume that this experiment was done using a solid with fixed scattering sites. Do they say anything about applying this to colloid fluids?

    Yeah, yeah, I could look the paper up myself, but it’s so much easier to just ask you… it’s like Reader’s Digest for scientists!

  2. PD: I think the term ‘focusing’ is being used loosely; it would be more accurate to call it ‘concentration of light’, I suppose. The light is focused onto the sample, but it is not obvious that the results would change significantly if the beam was defocused.

    The samples seem to be powdered solids: rutile TiO2, daisy petals and more! The samples are not completely stable, however, and the Opt. Lett. argues that the persistence time of the speckle pattern is a limiting factor on intensity enhancement: the less stable the sample, the less effective the enhancement. Extending the process to a colloid would be in principle possible, I suppose, if one could make the system work fast enough.

  3. stuwat says:

    Dear Reader’s Digest:
    If, as you say, they are using the term ‘focusing’ in a rather loose sense, a better description might be ‘beam steering’. Much like a phased array can be used to steer a beam of microwaves, it appears they are using the same principle to guide a light beam through a highly scattering medium.

  4. LW says:

    I learned something from this post – Pachinko was not invented by the Price is Right!

    I haven’t read all these papers, so i’ll treat this like reader’s digest too: are the algorithms optimal?? if you don’t know the transfer function, i don’t think they can be, so are they just trying random phase patterns and seeing which ones are best? or how do they update the pattern to improve the light ‘concentration’?

    also, has anyone done this with temporally incoherent light? it seems that would be much more robust to speckle issues, but then you can’t just use a phase SLM of course…

    • I learned something from this post – Pachinko was not invented by the Price is Right!


      It’s been a while since I read the papers, but I think that the algorithms are in some sense optimal, at least with respect to the theoretical scattering model being used. That model itself it doubtless an oversimplification of the real media, but a glance back at the original papers suggests they came close to achieving the maximum transmission possible theoretically — at least for a given size & resolution of SLM.

      It does seem that temporal coherence would make the problem more difficult: presumably each frequency of light would have its own optimal “channel” of transmission, and the system would have to adjust each frequency independently.

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