We report the first experimental demonstration of combined spatial and
temporal control of light trajectories through opaque media. This control is
achieved by solely manipulating spatial degrees of freedom of the incident
wavefront. As an application, we demonstrate that the present approach is
capable to form bandwidth-limited ultrashort pulses from the otherwise randomly
transmitted light with a controllable interaction time of the pulses with the
medium. Our approach provides a new tool for fundamental studies of light
propagation in complex media and has potential for applications for coherent
control, sensing and imaging in nano- and biophotonics

Ad Lagendijk

Allard P. Mosk

Bergin Gjonaj

J. Shah

Jochen Aulbach

P. Sebbah

Patrick M. Johnson

English

arXiv

We report the first experimental demonstration of combined spatial and temporal control of light transmission through opaque media. This control is achieved by solely manipulating spatial degrees of freedom of the incident wave front. As an application, we demonstrate that the present approach is capable of forming bandwidth-limited ultrashort pulses from the otherwise randomly transmitted light with a controllable interaction time of the pulses with the medium. Our approach provides a new tool for fundamental studies of light propagation in complex media and has the potential for applications for coherent control, sensing and imaging in nano- and biophotonics

Aulbach, Jochen

Gjonaj, Bergin

Johnson, Patrick M.

Mosk, Allard

Lagendijk, Aart

NARCIS 

Control of light transmission through opaque scattering media in space and time

Crossref

Control of Light Transmission through Opaque Scattering Media in Space and Time

University of Twente Research Information

Control of Light Transmission through Opaque Scattering Media in Space and TimeJochen Aulbach,1,2,* Bergin Gjonaj,1 Patrick M. Johnson,1 Allard P. Mosk,3 and Ad Lagendijk11FOM Institute for Atomic and Molecular Physics AMOLF, Science Park 113, 1098 XG Amsterdam, The Netherlands2Institut Langevin, ESPCI ParisTech, CNRS, 10 rue Vauquelin, 75231 Paris Cedex 05, France3Complex Photonic Systems, MESAþ Institute for Nanotechnology and Department of Science and Technology,University of Twente, Post Office Box 217, NL-7500 AE Enschede, The Netherlands(Received 11 November 2010; revised manuscript received 19 January 2011; published 8 March 2011)We report the first experimental demonstration of combined spatial and temporal control of lighttransmission through opaque media. This control is achieved by solely manipulating spatial degrees offreedom of the incident wave front. As an application, we demonstrate that the present approach is capableof forming bandwidth-limited ultrashort pulses from the otherwise randomly transmitted light with acontrollable interaction time of the pulses with the medium. Our approach provides a new tool forfundamental studies of light propagation in complex media and has the potential for applications forcoherent control, sensing and imaging in nano- and biophotonics.DOI: 10.1103/PhysRevLett.106.103901 PACS numbers: 42.25.Dd, 07.60.j, 42.65.kConcentrating light in time and space is critical for manyapplications of laser light. Broadband mode-locked lasersprovide the required ultrashort light pulses for multiphotonimaging [1,2], nanosurgery [3], microstructuring [4], ultra-fast spectroscopy [5,6], and coherent control of moleculardynamics or of nanooptical fields [7–9]. Multiple randomscattering in complex media severely limits the perform-ance of these methods, but often is an unavoidable nui-sance in many systems of interest, such as biological tissueor nanophotonic structures [10]. Spatially, random scatter-ing strongly distorts a propagating wave front, creating thewell-known speckle interference pattern [11]. In the timedomain, ultrashort pulses are strongly distorted and widelystretched due to the broad path length distribution in mul-tiple scattering media [12]. These temporal and spatialdistortions are not separable [13].There is a strong interest in improving applications ofultrashort laser pulses in complex scattering media. Phaseconjugation has been applied to spatially focus light from ashort-pulse laser source through a thin scattering layer[14]. Similarly, phase conjugation is applied to correctdistortions of the ballistic wave front to improve the reso-lution of two-photon microscopy [15]. Coherent control oftwo-photon excitation through scattering biological tissuehas been demonstrated [16]. Those experiments share thecommon limitation that the control is limited only to thosephotons that take the shortest paths through the disorderedmedia and arrive at the target volume without being multi-ply scattered.Recently it was demonstrated that random scattering canactually be beneficial rather than detrimental for the per-formance of optical systems. Applying a shaped wave frontof monochromatic light to a strongly scattering medium,Vellekoop et al. achieved spatially controlled focusing intransmission [17] and on fluorescent molecules inside themedium [18]. These findings have opened new possibilitiesfor imaging in optically thick biological matter [19] andallow trapping particles through turbid media [20]. All ofthese studies used monochromatic light sources, and there-fore only allowed spatial control over the scattered light.Related techniques which allow coherent focusing in scat-tering media are known from ultrasound [21] and micro-waves [22]. The frequency of those types of waves islow enough that electronic transducers can be used totime reverse waves, which redirects the waves towardstheir source. This technique has successfully helped toimprove imaging resolution [23] and communication band-width [24].In this Letter we generalize the concept of wave frontshaping to the regime of broadband light. We report thefirst experimental demonstration of combined spatial andtemporal control of light transmission through randomscattering media. By only controlling spatial degrees onfreedom of the incident wave, we control the field ampli-tude at a selected point in space and time behind thesample. This enables us to create an ultrashort pulse fromthe otherwise randomly transmitted light. We can controlthe amount of time the optimized pulse stays in the sampleand thereby select the path length of the light through themedium.In Fig. 1 we show a simplified scheme of our experi-mental realization. Pulses from a Ti:sapphire laser (dura-tion 64 fs, center wavelength 795 nm) illuminate a two-dimensional phase-only spatial light modulator (SLM).The SLM pixels are grouped into N independent segmentseach of which induces a controllable phase shift i. Thelight is subsequently focused onto a layer of stronglyscattering titanium dioxide pigment (thickness L ¼13:5 m, transport mean free path: lt ¼ 1 m [25]). Thetransmitted light appears as a spatiotemporal speckle pat-tern. In the experiment, we optimize the field amplitude ata selected point in space and time. A pinhole fixes thePRL 106, 103901 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 20110031-9007=11=106(10)=103901(4) 103901-1  2011 American Physical Societyspatial coordinate. To fix the time, the speckle pulse isoverlapped with a reference pulse in a heterodyne detec-tion scheme in a configuration similar to [26]. The hetero-dyne signal exactly corresponds to the cross correlation ofthe speckle pulse and the reference pulse [27]. Effectively,it is an instantaneous measurement of the transmitted fieldamplitude at the delay time of the reference pulse . Thissignal serves as feedback for an optimization algorithm,which controls the incident wave front via the SLM.The principle of the experiment can be described asfollows. Light reflected from a single segment on theSLM is transmitted through the sample, giving rise to thefield EiðtÞ at the detector. Its phase can be modified by atime-independent phase shift i via the SLM. The totalfield scattered into the detector EoutðtÞ is therefore given bythe sum over all segmentsEoutðtÞ ¼XNi¼1EiðtÞeii : (1)Multiple scattering allows us to assume that the contri-butions EiðtÞ from the different segments at every singlepoint in time t are uncorrelated random variables withRayleigh distributed amplitudes jEiðtÞj and uniformly dis-tributed phases iðtÞ [28]. For the nonoptimized case, theresulting field EoutðtÞ can be viewed as the result of arandom walk in the complex field plane. After the optimi-zation, all contributions are in phase, adding up construc-tively. The average amplitude enhancement is givenby [17]hi ¼ hjEoptjirmshjErndjirms ¼4ðN 1Þ þ 11=2 4N1=2: (2)Since the instantaneous field amplitude is optimized, theinstantaneous intensity accordingly increases, with an av-erage intensity enhancement  ¼ 2. The simple modelleading to Eq. (2) does not provide a prediction for theresulting pulse duration. We address this point later in thisLetter.The nonoptimized data were obtained by setting randomphase values to the SLM segments. The optimizationalgorithm adjusts the phase shifts i such that theamplitude of the heterodyne signal is maximized. Weperformed the optimization at 20 equidistant time delaysopt between 1:05 ps to þ13:6 ps. For each opt, theoptimization was performed four times, with N ¼ 12, 48,192, and 300 segments, respectively, each time startingfrom a new random phase pattern.Our main result is displayed in Fig. 2, showing theamplitudes of both the nonoptimized and the optimizedpulses for different time delays opt andN ¼ 300 segmentson the SLM. The long time-tail of the average nonopti-mized transmission reflects the broad path length distribu-tion which has been observed in similar earlier studies [12].The optimized amplitudes show sharp, distinct peaks withdramatically increased amplitudes at the desired time de-lay. We can control the amount of time the optimizedpulses stay in the sample by the time delay opt, and bythat we control the path length of the pulses through thesample. Note that the heterodyne signal is proportional tothe field amplitude, the intensities exhibit even more pro-nounced optimized peaks.The enhancement  versus time delay opt is shown inFig. 3. Its magnitude, depending on the number of seg-ments on the SLM, is constant from zero to several pico-seconds time delay. This result shows that our methodworks for short light paths as well as for light paths morethan 10 times longer than the sample thickness.For long time delays a continuous decrease of  isobserved, which is related to the noise level of the experi-ment. We include a quantitative analysis of this effect inthe supplemental material [27].Figure 4 shows the average enhancement in the constantregime in Fig. 3 versus N together with the enhancementexpected from theory [Eq. (2)], hi ¼ ð4 NÞ1=2. The pre-factor  ¼ 0:90 corrects for the nonuniform illuminationFIG. 2 (color online). Optimized and random speckle pulses.(a) Amplitude of heterodyne signal of a nonoptimized pulse as afunction of time delay, averaged over 50 random speckle pulses.(b) Typical single random speckle pulse. (c)–(g) Amplitudes ofsingle pulses after optimization at different time delays whichare indicated by the dashed arrows. The optimization has beenperformed by dividing the SLM into 300 segments. The opti-mization generates strong, short pulses from diffuse light. Thezero delay position is at the maximum amplitude with no sample.The plotted curves have been normalized to the maximum of theaverage nonoptimized heterodyne signal (factor 1:53 mV1).FIG. 1 (color online). Experimental setup (see text).PRL 106, 103901 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 2011103901-2of the SLM surface with a truncated Gaussian beam, whicheffectively leads to a reduction of the number of usedsegments [27]. Our model matches the data well with noadjustable parameters.The measurement of the output pulse duration reveals aninteresting characteristic the optimization method.Independent of the time delay, the optimized pulses havean (intensity) duration of topt ¼ 115 fs, calculated fromthe average width of the cross-correlation peaks (Fig. 5).The optimized pulses are lengthened compared to the inputpulses (tin ¼ 64 fs). What follows is a qualitative expla-nation of this effect. Further details are included in thesupplemental material [27]. The increased duration corre-sponds to spectral narrowing due to the optimization pro-cedure. Transmission through the random mediumintroduces strong random phase and amplitude fluctuationswithin the laser bandwidth (frequency speckle) [28].This means that a single segment of the SLM, whichadds an almost frequency-independent phase shift, cannotoptimize all frequencies equally well. The optimization isbiased towards frequencies of higher amplitude, since theycontribute higher to the feedback signal. Averaged overmany SLM segments, these are the frequencies in thecenter of the Gaussian spectrum of the laser, resulting ina narrowing of the resulting spectrum. We investigated thedependence of this effect on the number of segments N bya numerical simulation, which generates random spectrabased on the parameters of our experiment. These spectrawere Fourier transformed and their sum optimized in timeto mimic our experimental optimization procedure. For alow number of segments, the spectral amplitude and phaseis dominated by the randomness from the scattering. For anincreasing number of segments, the optimized pulses ex-hibit an increasingly smooth Gaussian amplitude and a flatspectral phase, with a bandwidth narrower than the inputspectrum. The resulting pulse duration converges to 115 fs,in perfect agreement with our experiments. The method iscapable of creating bandwidth-limited pulses, but since it isbased on linear interferometry, the optimization can beequally applied to adapt other pulse shapes or likewise tocompensate material dispersion present in the optical path.The time-integrated intensity (energy) of the pulse withthe highest peak depicted in Fig. 2 is 13.5 times higher thanthe energy of the average nonoptimized pulse. In additionto the temporal optimization, overall more light is trans-mitted into the detected channel, demonstrating that thescattered light is controlled spatially and temporally. ASLM alone, without a random scattering medium, offersonly spatial control, while frequency domain pulse shapingtechniques [29] provide temporal control only. Our methodexploits the mixing of spatial and temporal degrees offreedom by the random medium [13], to control the trans-mitted light in two spatial and one temporal dimension byonly controlling spatial degrees of freedom on the two-dimensional SLM. On the one hand, the conversion of0 2 4 6 8 10 12 140246810121416Time delay τopt (ps) Enhancementα1248192300FIG. 3 (color online). Enhancement  versus selected timedelay opt for different number of segments N on the spatiallight modulator.051015N1/20 5 10 15ExperimentTheory EnhancementαFIG. 4 (color online). Average amplitude enhancement (dots) as a function of the square root of the number of segmentsN. The solid line is given by the expected  ¼ 0:90ð4 NÞ1=2,without any free parameter.0.00.20.40.60.81.01.0 1.5 4.5 5.0 8.0 8.5normalized Amplitude,Time delay (ps)(a) (b) (c)FIG. 5 (color online). Detailed cross-correlation scans afteroptimization with N ¼ 300 segments around the time delaysopt ¼ 1:1 ps (a), 4.8 ps (b), and 8.5 ps (c), together with aGaussian fit (solid lines). The width (FWHM) of the peaks showsno significant dependence on the time delay, with an average ofopt ¼ ð190 7Þ fs.PRL 106, 103901 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 2011103901-3spatial degrees of freedom into temporal ones comes at theprice of a speckle background, which on the other hand iseasily outweighed by the enormous number of degrees offreedom provided by state-of-the-art SLMs. The largenumber of controllable spatial degrees of freedom is agreat advantage over frequency domain pulse shapingtechniques. Spatiotemporal control of the light field allowsa far more generalized application of present coherentcontrol schemes and marks a further step towards opticaltime reversal.In the experimental realization presented here, we opti-mized the pulse front using linear interferometry as a feed-back signal. The optimization of a nonlinear response, likesecond-harmonic generation, will also lead to a compara-bly optimized pulse [30]. Using second-harmonic emissionfrom nanoparticles [14] or two-photon fluorescence fromdyes such as fluorescent proteins [2] would enable focusingultrashort pulses inside complex media such as biologicaltissue, in which the propagation of near-infrared light isdominated by multiple scattering [19]. Given the highsignal-to-background ratio and the enhancement of energydelivered to the selected speckle spot, we envision that ourmethod can improve approaches for selective cell destruc-tion in tissue [31]. In view of its potential for sharp focus-sing, it has potential for nanofabrication, nanosurgery, andother micromanipulation techniques.Up to now we have not discussed the spatial extent of theoptimized pulse. We use a pinhole to select a single specklespot in the Fourier plane of the sample for optimization.We know that transmitted fields in adjacent speckle spotsare uncorrelated [32], from which we can conclude that theoptimization is indeed limited to the selected area. Animportant future direction would be to investigate thespatial extent of the optimized pulse as a function of delaytime. A combination with spatial scanning allows themeasurement of the transmission matrix of the medium[33] in one temporal and two spatial dimensions. ForAnderson-localizing samples [34], the size of the opti-mized speckle should be strongly time dependent [35].In conclusion, we have experimentally demonstratedthat spatial wave front shaping of a pulse front incidenton a strongly scattering sample gives spatial and temporalcontrol over the scattered light. Our approach provides anew tool for fundamental studies of light propagation andhas potential for applications in sensing, nano- andbiophotonics.We thank Timmo van der Beek for the sample fabrica-tion, Kobus Kuipers for providing the AOMs, and HuibBakker for helpful comments on the manuscript. This workis part of the Industrial Partnership Programme (IPP)Innovatie Physics for Oil and Gas (iPOG) of theStichting voor Fundamenteel Onderzoek der Materie(FOM), which is supported financially by NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO).The IPP MFCL is cofinanced by Stichting Shell Research.Note added.—After submission of this Letter, two re-lated preprints appeared [36].*j.aulbach@amolf.nl[1] S.W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).[2] W.R. Zipfel, R.M. Williams, and W.W. Webb, Nat.Biotechnol. 21, 1369 (2003).[3] A. Vogel et al., Appl. Phys. B 81, 1015 (2005).[4] E. N. Glezer et al., Opt. Lett. 21, 2023 (1996).[5] A. H. Zewail, J. Phys. Chem. A 104, 5660 (2000).[6] J. Shah, Ultrafast Spectroscopy of Semiconductors andSemiconductor Nanostructures (Springer, New York, 1999).[7] H. Rabitz et al., Science 288, 824 (2000).[8] J. Herek et al., Nature (London) 417, 533 (2002).[9] M. Aeschlimann et al., Nature (London) 446, 301 (2007).[10] A. F. Koenderink and W.L. Vos, Phys. Rev. Lett. 91,213902 (2003).[11] J. Dainty, Laser Speckle and Related Phenomena(Springer, New York, 1984).[12] A. Z. Genack and J.M. Drake, Europhys. Lett. 11, 331(1990).[13] F. Lemoult et al., Phys. Rev. Lett. 103, 173902 (2009).[14] C. Hsieh et al., Opt. Express 18, 12283 (2010).[15] M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl.Acad. Sci. U.S.A. 103, 17 137 (2006).[16] J.M.D. Cruz et al., Proc. Natl. Acad. Sci. U.S.A. 101,16 996 (2004).[17] I.M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).[18] I.M. Vellekoop et al., Opt. Express 16, 67 (2008).[19] E. J. McDowell et al., J Biomed. Opt. 15, 025004 (2010).[20] T. Cizmar, M. Mazilu, and K. Dholakia, Nat. Photon. 4,388 (2010).[21] A. Derode, P. Roux, and M. Fink, Phys. Rev. Lett. 75,4206 (1995).[22] G. Lerosey et al., Science 315, 1120 (2007).[23] M. Fink and M. Tanter, Phys. Today 63, No. 2, 28 (2010).[24] S. H. Simon et al., Phys. Today 54, No. 9, 38 (2001).[25] O. L. Muskens and A. Lagendijk, Opt. Express 16, 1222(2008).[26] M. Sandtke et al., Rev. Sci. Instrum. 79, 013704 (2008).[27] See supplemental material at http://link.aps.org/supplemental/10.1103/PhysRevLett.106.103901 for an ex-tended technical and analytical description of the experi-ment, including an analysis of the noise level andnumerical simulations of the pulse duration.[28] B. A. van Tiggelen et al., Phys. Rev. E 59, 7166 (1999).[29] A.M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).[30] D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22,1793 (1997).[31] C. Loo et al., Nano Lett. 5, 709 (2005).[32] P. Sebbah, Waves and Imaging through Complex Media(Springer, New York, 2001).[33] S.M. Popoff et al., Phys. Rev. Lett. 104, 100601 (2010).[34] P.W. Anderson, Phys. Rev. 109, 1492 (1958).[35] S. E. Skipetrov and B.A. van Tiggelen, Phys. Rev. Lett.96, 043902 (2006).[36] O. Katz et al., arXiv:1012.0413; D. J. 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Control of light transmission through opaque scattering media in space
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Control of light transmission through opaque scattering media in space and time

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