Multiple-scattering Media Research Articles

Nonclassical light manipulation in a multiple-scattering medium.

We investigate the possibility of using a scattering medium as a highly multimode platform for implementing quantum walks. We demonstrate the manipulation of a single photon propagating through a strongly scattering medium using wavefront-shaping technique. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a specific output mode. Using this approach, we show how entanglement of a single photon across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.

Fast wavefront adaptive holography in Nd:YVO4 for ultrasound optical tomography imaging.

Several approaches exist to perform acousto-optic imaging of multiple-scattering media such as biological samples. Up to now, most of the coherent detection methods use holographic setup based on photorefractive crystals such as BSO or SPS. One of the issue of these techniques is the moderate response time compared to the speckle decorrelation time in biological sample. We introduce a new approach for the holographic detection based on two-wave mixing in a Nd:YVO4 gain medium enabling us to perform a fast wavefront adaption (50 μs) of the speckle field from a multiple-scattering sample.

Green's function retrieval and fluctuations of cross density of states in multiple-scattering media

In this work we derive the average and the variance of the cross-correlation of a noise wavefield. The noise cross-correlation function (NCF) is widely used to passively estimate the Green's function between two probes and is proportional to the cross density of states (CDOS) in photonic and plasmonic systems. We first explain from the ladder approximation how the diffusion halo plays the role of secondary sources to reconstruct the mean Green's function. We then show that fluctuations of NCF are governed by several non-Gaussian correlations. An infinite-range correlation term dominates fluctuations of NCF-CDOS and proves that NCF is not a self-averaging quantity with respect to the plurality of noise sources. The link between these correlations and the intensity ones is highlighted. These results are supported by numerical simulations and are of importance for passive imaging applications and material science.

Programming balanced optical beam splitters in white paint

Wavefront shaping allows for ultimate control of light propagation in multiple-scattering media by adaptive manipulation of incident waves. We shine two separate wavefront-shaped beams on a layer of dry white paint to create two enhanced output spots of equal intensity. We experimentally confirm by interference measurements that the output spots are almost correlated like the two outputs of an ideal balanced beam splitter. The observed deviations from the phase behavior of an ideal beam splitter are analyzed with a transmission matrix model. Our experiments demonstrate that wavefront shaping in multiple-scattering media can be used to approximate the functionality of linear optical devices with multiple inputs and outputs.

PARTIALLY PUMPED RANDOM LASERS

Conventional lasers consist of two components: a gain material that is pumped in order to provide amplification of light and a cavity to provide feedback. Random lasers replace the traditional laser cavity with a random, multiple-scattering medium. This can give rise to complex lasing behavior, such as unpredictable multidirectional and multifrequency output. Controlling these systems has proved difficult and, until now, has consisted of material and structural manipulations. In random lasers, the most common pumping mechanism is an optical field, which can be applied uniformly or partially across the scattering medium. Partial pumping, referring to the restricted spatial extent of the pump applied to the gain material, is therefore quite ubiquitous in such systems. In contrast to conventional lasers, however, the impact of partial pumping can be significant in random lasers as a subset of the scattering medium is probed. In this review, we discuss state-of-the-art investigations of partially pumped random lasers. Numerical and experimental investigations of how even a simple spot profile of the pump can dramatically alter random laser output are presented. First, the simple case of partial pumping in strongly scattering systems where laser modes are spatially confined is described. Then the most common but more difficult case of weakly scattering random lasers is considered. Here, modes are spatially extended, forcing greater mode interaction and making the random laser output more difficult to predict. Finally, we review recent works that show how the pumping degree of freedom allows a general increase in control over random lasers.

Optimal control of light propagation through multiple-scattering media in the presence of noise

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.

Filtering Random Matrices: The Effect of Incomplete Channel Control in Multiple Scattering

We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input channels, m1, and output channels, m2, is decreased from unity, the density of the transmission eigenvalues is shown to evolve from the bimodal distribution describing coherent diffusion, to the distribution characteristic of uncorrelated Gaussian random matrices, with a rapid loss of access to the open eigenchannels. The loss of correlation is also reflected in an increase in the information capacity per channel of the medium. Our results have strong implications for optical and microwave experiments on diffusive scattering media.

Penetration of Light into Multiple Scattering Media: Model Calculations and Reflectance Experiments. Part II: The Radial Transfer

In continuation of our contribution to "The Axial Transfer" (Appl. Spectr. 2012. 66(8): 934-943), this paper describes the distribution of localized incident radiation in multiple scattering layers of arbitrary thickness and analyzes the lateral intensity profiles of radiation leaving the sample from its illuminated and non-illuminated surfaces. The theoretical profiles are calculated with different approximations of the equation of transfer. We derive for both non-absorbing and absorbing layers simple analytical expressions and verify their accuracy and range of applicability by comparison with Monte Carlo simulations. Particular emphasis is given to the analysis of the radial absorption, an under-theorized and under-investigated feature that can help to identify weak or hidden absorbers. In addition, we contribute to the description of how the radial reflectance is affected by anisotropy or by error sources like multiple surface reflection for samples in glass cells or deflectance (sideway loss) of radiation in small samples. Finally, the theoretical results are compared with experimental data of radial reflectance for quasi non-absorbing and absorbing powder layers.

Influence of reabsorption and reemission on stimulated Raman scattering of polymethine dyes in multiple scattering media

It is shown that reabsorption of the luminescence radiation in the range of its overlapping with the absorption spectrum and the following reemission to a long-wavelength range may noticeably affect the process of stimulated Raman scattering (SRS) in polymethine dyes in multiple scattering media (MSM). This is related to the fact that SRS in such media occurs jointly with the random lasing (RL), which favors SRS and makes up with it a united nonlinear process. Reemission into the long-wavelength spectrum range amplified in MSM causes the RL spectrum to shift to longer wavelengths and initiates the long-wavelength band of RL, in which a main part of the lasing energy is concentrated. This weakens or completely stops the SRS if the band is beyond the range of possible spectral localisation of Stokes lines. This process depends on the efficiency of light scattering, dye concentration, temperature and pump intensity; hence, there exist optimal values of these parameters for obtaining SRS in MSM.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than , a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 – 5 times . We demonstrate through simulations that as the ratio of the ultrasound focal volume to increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around ; and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110° to 130° when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

Penetration of Light into Multiple Scattering Media: Model Calculations and Reflectance Experiments. Part I: The Axial Transfer

The article presents two general equations of radiation penetration into layers of diffuse reflectors. One of the equations describes the depth origins of reflection, the other the depth profiles of absorption. The equations are evaluated within the theory of radiative transfer applying various degrees of analytical approximations and Monte Carlo simulations. The data are presented for different scattering and absorption coefficients, arbitrary layer thicknesses, collimated and diffused irradiation, and anisotropic forward scattering. The calculated mean depths of reflection are always lower than the mean depths of absorption. For nearly non-absorbing layers, the mean depths of absorption are about one third of the physical layer thickness. In contrast, penetration saturates for strong absorbers at very low depth levels. From the simulated data, methods are derived for the determination of the penetration depth from reflectance and transmittance data of thin layers or from radially diffused reflectance profiles upon spot irradiation. The methods are experimentally verified for a series of metal oxide powders with particle sizes ranging from much smaller to much larger than the wavelength of irradiation and for microcrystalline cellulose stained with different concentrations of an organic dye.

Stimulated resonance Raman scattering from organic dyes in a multiple-scattering medium as a potential method for determining their vibrational spectra

A method is described for deriving Raman spectra of organic dyes from their random lasing spectra. The method was tested using Rhodamine 6G. The Raman spectrum obtained for this dye agrees well with the spectra measured by standard techniques but is more structured, which allows unresolved features to bedetected. The spectrum provides more detailed information owing to the interference between the Raman scattered light and amplified spontaneous emission of the dye molecules within a photon meanfree path. One advantage of the method is that the luminescence of the dye helps to observe Raman lines, which allows one to work in the Stokes region and facilitates the measurement procedure.

Angle-resolved photon-coincidence measurements in a multiple-scattering medium

We present angular-resolved correlation measurements between photons after propagation through a three-dimensional disordered medium. The multiple scattering process induces photon correlations that are directly measured for light sources with different photon statistics. We find that multiple scattered photons between different angular directions with angles much larger than the average speckle width are strongly correlated. The time dependence of the angular photon correlation function is investigated and the coherence time of the light source is determined. Our results are found to be in excellent agreement with the continuous mode quantum theory of multiple scattering of light. The presented experimental technique is essential in order to study quantum phenomena in multiple scattering random media such as quantum interference and quantum entanglement of photons.

Transmission of polarized light through turbid media

The depolarization of light in multiple-scattering media with large (larger than the light wavelength) inhomogeneities is considered. The polarization state of the scattered light is described in the principal-mode approximation. Using the Fokker-Planck model, the polarization and intensity distribution of light are calculated in the vicinity of an inhomogeneity in the shape of an absorbing half-plane. The results of the calculations agree with the experimental data on transmission of light through turbid media.

Two-Photon Imaging in Turbid Media to a Few MM Depths

We present a new detection method for two-photon fluorescence imaging of turbid media that extends imaging depth to few mm. Compared to conventional two-photon microscopy, the imaging depth enhancement is achieved by use of a more efficient detection of fluorescence, propagating in multiple-scattering media. The imaging depth in turbid media depends on two major factors: the ability of the imaging system to deliver necessary excitation light power to a certain depth to induce two-photon fluorescence and the ability of the detection system to collect and detect fluorescence photons scattered by the media. In two-photon imaging, usually, fluorescence is collected by the same microscope objective that is used for excitation. This optical scheme has its principal limitation in efficiency of fluorescence detection because of the narrow angle and area from which fluorescence photons can be collected. As a result, the maximum depth of tissue imaging that was reached so far by two-photon fluorescence microscopy is about 1mm. Our system utilizes for excitation the conventional two-photon microscopy scheme, however, for fluorescence detection we used 1” cathode area PMT directly placed on the turbid sample from the opposite side of excitation. The PMT was equipped with a mechanical shutter and optical filters to reject excitation light and transmit only fluorescence. All optical components of the detector were coupled with index matching compounds to assure refractive index continuity from the sample to the PMT photocathode to minimize light losses due to reflection at boundaries. This detection scheme, while simple in construction and practically not requiring any optics, was proved to be very efficient in the collection of weak fluorescence from a wide area of a turbid sample and allowed to obtain high resolution images at depths up to 3mm.

Taking apart the enhanced backscattering cone: Interference fringes from reciprocal paths in multiple light scattering

We report the decomposition of the enhanced backscattering cone into its constitutive interference fringes. These fringes are due to the constructive interference between reciprocal paths of any multiply scattered wave after ensemble averaging. An optical setup combining a two-point continuous-wave illumination and matching detection allows the observation of the fringes and, therefore, the quantitative characterization of the Green's function for light propagation between the two points in a multiple-scattering media.

Quantum Interference and Entanglement Induced by Multiple Scattering of Light

We report on the effects of quantum interference induced by the transmission of an arbitrary number of optical quantum states through a multiple-scattering medium. We identify the role of quantum interference on the photon correlations and the degree of continuous variable entanglement between two output modes. It is shown that quantum interference survives averaging over all ensembles of disorder and manifests itself as increased photon correlations due to photon antibunching. Furthermore, the existence of continuous variable entanglement correlations in a volume speckle pattern is predicted. Our results suggest that multiple scattering provides a promising way of coherently interfering many independent quantum states of light of potential use in quantum information processing.

Erratum: “Generalized shot noise model for time-reversal in multiple-scattering media allowing for arbitrary inputs and windowing” [J. Acoust. Soc. Am. 125, 3129–3140 (2009)

On page 3138, Fig. ​Fig.6d6d was inadvertently an identical copy of Fig. 6(c). The correct version of Fig. 6(d) is below. All referring text was based on the correct plot. Figure 6d

Generalized shot noise model for time-reversal in multiple-scattering media allowing for arbitrary inputs and windowing

A theoretical shot noise model to describe the output of a time-reversal experiment in a multiple-scattering medium is developed. This (non-wave equation based) model describes the following process. An arbitrary waveform is transmitted through a high-order multiple-scattering environment and recorded. The recorded signal is arbitrarily windowed and then time-reversed. The processed signal is retransmitted into the environment and the resulting signal recorded. The temporal and spatial signal and noise of this process is predicted statistically. It is found that the time when the noise is largest depends on the arbitrary windowing and this noise peak can occur at times outside the main lobe. To determine further trends, a common set of parameters is applied to the general result. It is seen that as the duration of the input function increases, the signal-to-noise ratio (SNR) decreases (independent of signal bandwidth). It is also seen that longer persisting impulse responses result in increased main lobe amplitudes and SNR. Assumptions underpinning the generalized shot noise model are compared to an experimental realization of a multiple-scattering medium (a time-reversal chaotic cavity). Results from the model are compared to random number numerical simulation.

Focal modulation microscopy

We report a novel light microscopy method for high resolution molecular imaging of thick biological tissues with one photon excited fluorescence. Effective optical sectioning and diffraction limited spatial resolution are achieved when imaging deep inside a multiple-scattering medium by the use of focal modulation, a technique for suppressing the background fluorescence signal excited by scattered light. Our method has been validated with animal tissue and an imaging depth around 600 microns has been demonstrated.