Sensing the position of a single scatterer in an opaque medium by mutual scattering.

We investigate the potential of mutual scattering, i.e., light scattering with multiple properly phased incident beams, as a method to extract structural information from inside an opaque object. In particular, we study how sensitively the displacement of a single scatterer is detected in an optically dense sample of many (up to N = 1000) similar scatterers. By performing exact calculations on ensembles of many point scatterers, we compare the mutual scattering (from two beams) and the well-known differential cross-section (from one beam) in response to the change of location of a single dipole inside a configuration of randomly distributed similar dipoles. Our numerical examples show that mutual scattering provides speckle patterns with an angular sensitivity at least 10 times higher than the traditional one-beam techniques. By studying the "sensitivity" of mutual scattering, we demonstrate the possibility to determine the original depth relative to the incident surface of the displaced dipole in an opaque sample. Furthermore, we show that mutual scattering offers a new approach to determine the complex scattering amplitude.

Wavefront shaping through a free-form scattering object.

Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are studied are slabs or wave-guides. In this paper, we study how macroscopic changes in the sample shape affect light scattering using the wavefront shaping technique. Using a flexible scattering material, we optimize the intensity of light in a focusing spot using wavefront shaping and record the optimized pattern, comparing the enhancement for different curvatures and beam radii. We validate our hypothesis that wavefront shaping has a similar enhancement regardless of the free-form shape of the sample and thus offers relevant potential for industrial applications. We propose a new figure of merit to evaluate the performance of wavefront shaping for different shapes. Surprisingly, based on this figure of merit, we observe that for this particular sample, wavefront shaping has a slightly better performance for a free-form shape than for a slab shape.

Scaling Theory of Wave Confinement in Classical and Quantum Periodic Systems.

Functional defects in periodic media confine waves-acoustic, electromagnetic, electronic, spin, etc.-in various dimensions, depending on the structure of the defect. While defects are usually modeled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly nontrivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of wave confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities raised to certain powers yield the confinement dimensionality of each band. Our classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave, both quantum and classical, and in any dimension. In the quantum regime, we illustrate our method on electronic confinement in 2D hexagonal boron nitride (BN) with a nitrogen vacancy, in agreement with previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptorlike behavior. We briefly discuss the generalization to quasiperiodic lattices.

X-ray Imaging of Functional Three-Dimensional Nanostructures on Massive Substrates.

To investigate the performance of three-dimensional (3D) nanostructures, it is vital to study their internal structure with a methodology that keeps the device fully functional and ready for further integration. To this aim, we introduce here traceless X-ray tomography (TXT) that combines synchrotron X-ray holographic tomography with high X-ray photon energies (17 keV) in order to study nanostructures "as is" on massive silicon substrates. The combined strengths of TXT are a large total sample size to field-of-view ratio and a large penetration depth. We study exemplary 3D photonic band gap crystals made by CMOS-compatible means and obtain real space 3D density distributions with 55 nm spatial resolution. TXT identifies why nanostructures that look similar in electron microscopy have vastly different nanophotonic functionality: one "good" crystal with a broad photonic gap reveals 3D periodicity as designed; a second "bad" structure without a gap reveals a buried void, and a third "ugly" one without gap is shallow due to fabrication errors. Thus, TXT serves to nondestructively differentiate between the possible reasons of not finding the designed and expected performance and is therefore a powerful tool to critically assess 3D functional nanostructures.

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals.

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size L of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a 1/L scale dependence for crystals in one, two and three dimensions.

Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes.

We study the energy density of shaped waves inside a quasi-1D disordered waveguide. We find that the spatial energy density of optimally shaped waves, when expanded in the complete set of eigenfunctions of the diffusion equation, is well described by considering only a few of the lowest eigenfunctions. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtain the energy density of transmission eigenchannels inside the sample by numerical simulation of the scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results of our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

Observation of intensity statistics of light transmitted through 3D random media.

We experimentally observe the spatial intensity statistics of light transmitted through three-dimensional (3D) isotropic scattering media. The intensity distributions measured through layers consisting of zinc oxide nanoparticles differ significantly from the usual Rayleigh statistics associated with speckle and instead are in agreement with the predictions of mesoscopic transport theory, taking into account the known material parameters of the samples. Consistent with the measured spatial intensity fluctuations, the total transmission fluctuates. The magnitude of the fluctuations in the total transmission is smaller than expected on the basis of quasi-one-dimensional (1D) transport theory, which indicates that quasi-1D theories cannot fully describe these open 3D media.

Diffuse imaging and radius dependent frequency correlations in strongly scattering media.

A new probe of multiple scattering material is demonstrated experimentally. Light from a tunable wavelength source is focused to a point on the surface of an opaque slab. A fraction of this light penetrates into the slab, is multiply scattered, and reemerges at the surface creating a surface speckle pattern. The full spatial and frequency speckle can be easily and quickly recorded using a CCD and an acoustooptical tunable filter. Both the average intensity and frequency correlations of intensity are analyzed as a function of the distance to the source. This method is demonstrated experimentally for white paint. The resulting model yields information about both the static and dynamic transport properties of the sample. The technique has prospects for both static and time resolved diffuse imaging in strongly scattering materials. The setup can be easily used as an add-on to a standard bright field microscope.

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting.

We study the diffuse transport of light through polymer slabs containing TiO(2) scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470-840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 µm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 µm) consist of clusters of small particles (R<0.13 µm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.

Nanophotonic control of the Förster resonance energy transfer efficiency.

We have studied the influence of the local density of optical states (LDOS) on the rate and efficiency of Förster resonance energy transfer (FRET) from a donor to an acceptor. The donors and acceptors are dye molecules that are separated by a short strand of double-stranded DNA. The LDOS is controlled by carefully positioning the FRET pairs near a mirror. We find that the energy transfer efficiency changes with LDOS, and that, in agreement with theory, the energy transfer rate is independent of the LDOS, which allows one to quantitatively control FRET systems in a new way. Our results imply a change in the characteristic Förster distance, in contrast to common lore that this distance is fixed for a given FRET pair.

Non-invasive imaging through opaque scattering layers.

Non-invasive optical imaging techniques, such as optical coherence tomography, are essential diagnostic tools in many disciplines, from the life sciences to nanotechnology. However, present methods are not able to image through opaque layers that scatter all the incident light. Even a very thin layer of a scattering material can appear opaque and hide any objects behind it. Although great progress has been made recently with methods such as ghost imaging and wavefront shaping, present procedures are still invasive because they require either a detector or a nonlinear material to be placed behind the scattering layer. Here we report an optical method that allows non-invasive imaging of a fluorescent object that is completely hidden behind an opaque scattering layer. We illuminate the object with laser light that has passed through the scattering layer. We scan the angle of incidence of the laser beam and detect the total fluorescence of the object from the front. From the detected signal, we obtain the image of the hidden object using an iterative algorithm. As a proof of concept, we retrieve a detailed image of a fluorescent object, comparable in size (50 micrometres) to a typical human cell, hidden 6 millimetres behind an opaque optical diffuser, and an image of a complex biological sample enclosed between two opaque screens. This approach to non-invasive imaging through strongly scattering media can be generalized to other contrast mechanisms and geometries.

Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback.

We experimentally demonstrate spatiotemporal focusing of light on single nanocrystals embedded inside a strongly scattering medium. Our approach is based on spatial wave front shaping of short pulses, using second harmonic generation inside the target nanocrystals as the feedback signal. We successfully develop a model both for the achieved pulse duration as well as the observed enhancement of the feedback signal. The approach enables exciting opportunities for studies of light propagation in the presence of strong scattering as well as for applications in imaging, micro- and nanomanipulation, coherent control and spectroscopy in complex media.

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

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.

Frequency bandwidth of light focused through turbid media.

We study the effect of frequency detuning on light focused through turbid media. By shaping the wavefront of the incident beam light is focused through an opaque scattering layer. When detuning the laser we observe a gradual decrease of the focus intensity, while the position, size,and shape of the focus remain the same within experimental accuracy. The frequency dependence of the focus intensity follows a measured speckle correlation function. We support our experimental findings with calculations based on transport theory. Our results imply wavefront shaping methods can be generalized to allow focusing of optical pulses in turbid media.

Spatial threshold in amplifying random media.

We study experimentally as well as numerically the transport and generation of light in multiple scattering media with optical gain. By imaging the spatial distribution of light escaping from the side of the sample, the propagation depth is analyzed. Far below and far above random laser threshold, the spatial profile of emission light is independent of pump intensity, while around threshold, the spatial distribution of emission light changes profoundly. The experimental results are explained by interpreting the numerical solutions to a set of coupled time-dependent diffusion equations on a nonuniform spatial grid. Our studies provide a new and easily accessible method for observing the random laser threshold.

Observation of multifractality in Anderson localization of ultrasound.

We report the experimental observation of strong multifractality in wave functions below the Anderson localization transition in open three-dimensional elastic networks. Our results confirm the recently predicted symmetry of the multifractal exponents. We have discovered that the result of multifractal analysis of real data depends on the excitation scheme used in the experiment.

Optical anisotropic diffusion: new model systems and theoretical modeling.

We have developed several new experimental model systems that demonstrate anisotropic diffusion of light. These systems, consisting of aligned fibers, stretched plastic foam, and stretched plastic frit, have relatively simple microstructures and are easily sliced, making them ideal for testing theoretical models of diffusion. We demonstrate that the solution to the diffusion equation for arbitrary orientation of the diffusion tensor is consistent with experimental measurements. We also show that simple models of microstructure, based on cylindrical and planar scatterers, are consistent with the experimental results. These models provide simple analytical expressions for predicting the degree of alignment of the scatterers from diffuse transmission measurements. The combination of experimental results and theoretical support demonstrates both the power and the limitations of the diffusion model for providing information about microstructure via simple experiments and modeling.

Varying the effective refractive index to measure optical transport in random media.

We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the effective index of refraction. Experimentally, we measure intensity correlations via spectrally resolved refractive index tuning, controlling the latter via changes in the ambient pressure. Our experimental results perfectly match a generalized transport theory that incorporates the effective medium and predicts a precise value for the diffusion constant. Thus, we directly confirm the applicability of the effective medium concept in strongly scattering materials.

Large photonic strength of highly tunable resonant nanowire materials.

We demonstrate that highly tunable nanowire arrays with optimized diameters, volume fractions, and alignment form one of the strongest optical scattering materials to date. Using a new broad-band technique, we explore the scattering strength of the nanowires by varying systematically their diameter and alignment on the substrate. We identify strong Mie-type internal resonances of the nanowires which can be tuned over the entire visible spectrum. The tunability of nanowire materials opens up exciting new prospects for fundamental and applied research ranging from random lasers to solar cells, exploiting the extreme scattering strength, internal resonances, and preferential alignment of the nanowires. Although we have focused our investigation on gallium phosphide nanowires, the results can be universally applied to other types of group III-V, II-VI, or IV nanowires.

Design of light scattering in nanowire materials for photovoltaic applications.

We experimentally investigate the optical properties of layers of InP, Si, and GaP nanowires, relevant for applications in solar cells. The nanowires are strongly photonic, resulting in a significant coupling mismatch with incident light due to multiple scattering. We identify a design principle for the effective suppression of reflective losses, based on the ratio of the nondiffusive absorption and diffusive scattering lengths. Using this principle, we demonstrate successful suppression of the hemispherical diffuse reflectance of InP nanowires to below that of the corresponding transparent effective medium. The design of light scattering in nanowire materials is of large importance for optimization of the external efficiency of nanowire-based photovoltaic devices.