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arXiv:1308.0781 · Physical Review Letters

Coherent Control of Total Transmission of Light through Disordered Media

Sébastien M. Popoff, Arthur Goetschy, S. F. Liew, A. Douglas Stone, Hui Cao

Published Apr 1, 2014• 164 citations
arXivHTMLPDF

Abstract

We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wave front of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results.

DOI
10.1103/physrevlett.112.133903

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•May 21, 1990•25 citations
We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wave front of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results.
Long-range correlation characterizes the nondiffusive scattering paths of light through disordered media, playing an important role in the coherent control of multiply scattered light. Here, we report the long-range correlation of subsets of coherently interacting scattering paths, known as transmission eigenchannels. We find that the high-transmission eigenchannels exhibit a negative long-range correlation, in contrast to conventional positive long-range correlation. Moreover, when the transmission decreases, a prominent negative-to-positive transition of long-range correlation emerges for these eigenchannels. Finally, we demonstrate that this intriguing negative-to-positive transition originates from the characteristic transmission fluctuations of the eigenchannels. Our study provides valuable insights into the long-range correlation of scattered light in disordered media, constituting an important step toward advanced control of scattered light by manipulating the long-range correlation.
We have measured the correlation in frequency-dependent intensity fluctuations in the total transmission through random dielectric samples, using visible light in a (essentially) plane-wave geometry. The correlation function, of which the width at half maximum is proportional to ${\mathit{L}}^{\mathrm{\ensuremath{-}}2}$ (L is the thickness of the sample), decays as (\ensuremath{\Delta}\ensuremath{\omega}${)}^{\mathrm{\ensuremath{-}}1/2}$. This constitutes the experimental proof for the buildup of long-range intensity correlations in the propagation of classical waves by multiple scattering.
This thesis is about coherent control on disordered samples. Coherent control is the steering of processes with light of different frequencies. The relative phases between the frequencies determines in which di- rection the process is steered. When many frequencies are used, the light composes a short pulse. Changing the relative phases of the fre- quencies changes the shape of this pulse. We used such shaped pulses to guide processes on our samples. Pulse shaping and the different disordered samples are introduced in chapter 1, after which chapter 2 proceeds with the experimental details behind our studies. To perform a measurement with a shaped pulse, a nonlinear pro- cess is required. Second-harmonic generation (SHG) is one of the most straightforward nonlinear processes and plays an important role in this thesis. In chapter 3 theory of SHG is developed. Specifically, we deter- mine how to calculate the SHG intensity from shaped pulses on sam- ples with a resonance near the frequency of the illuminating light. We show that two mechanisms that broaden the line width of a resonance can not be distinguished by measuring the SHG signal. In the absence of resonances the maximum SHG intensity is produced by a transform- limited pulse. This pulse shape is required for many nonlinear optical spectroscopies and maximizing the SHG intensity is a useful method to obtain it. For such optimizations, algorithms are used that tune the coefficients for basis functions of the spectral phase. We looked at the fitness landscape of the SHG when a common basis set is used and by inspecting projections of the landscapewe constructed a more efficient basis set, that will make optimizations of SHG more efficient. In chapter 4 we describe simulations of the electric field in a ran- dom electrical network. The electrical network serves as a model for a film of randomly positioned gold islands, which we studied as re- ported in chapter 5. The simulations show that a metal density close to the percolation threshold results in a structure that has favourable properties for selective local excitation of the surface. In chapter 5 we proceed with this experiment on a random gold structure. The structure was coated with a layer of quantum dots. We imaged the fluorescence from this layer with a microscope and in this way were able to detect the local field intensities on the surface. We found that some control on the field intensity is possible, but the effect is minimal compared to the results of the simulations. The reason for this discrepancy is in the radiative damping of the oscillations, which was not included in the simulation. The radiative damping of plas- mons causes dephasing within �20 fs, making control with shaped pulses difficult. We further studied SHG from arrays of sub-wavelength holes in a gold film. The results of this study are presented in chapter 6. The amount of disorder in the positions of the holes in the arrays was var- ied. We found that the the SHG is produced in a resonance with a long lifetime of 55 fs. This lifetime is longer than most plasmonic resonances and shows that the effect of radiative damping is decreased on this structure. Furthermore, the SHG from all the structures has the same features. The disorder does not influence the SHG and the same reso- nance was found on all structures. Thus, it is likely that the resonance is a property of a single hole. Finally, we studied the coherent control of a dye in solution. Here the disorder is not in the structure, but in the transition frequency of the dye. Due to the interaction of the dye with the solvent, this fre- quency is constantly changing. These changes cause coherence to be lost in the system in a short time. We ran a closed-loop optimization to maximize the stimulated emission from the dye. All the pulse shapes tried in the optimization were saved and subsequently tried with the dye dissolved in other solvents. We found that the yield of the opti- mization varied greatly with the used solvent. These results formed a trend with the viscosity of the particular solvents. The viscosity can be related directly to the dephasing time, the time in which coherence is lost in the system. The trend of the optimization yield versus the vis- cosity shows directly that the fluctuations of the solvent are limiting the coherent control of the dye.
We study the prospects of controlling transmission of broadband and bichromatic laser pulses through turbid samples. The ability to focus transmitted broadband light is limited via both the scattering properties of the medium and the technical characteristics of the experimental setup. There are two time scales given by pulse stretching in the near- and far-field regions which define the maximum bandwidth of a pulse amenable to focusing. In the geometric-optics regime of wave propagation in the medium, a single setup can be optimal for focusing light at frequencies $\ensuremath{\omega}$ and $n\ensuremath{\omega}$ simultaneously, providing the basis for the 1+n1+n1+n coherent quantum control. Beyond the regime of geometric optics, we discuss a simple solution for the shaping, which provides the figure of merit for one's ability to simultaneously focus several transmission modes.