Understanding Nanoparticle Interaction with Cell Membranes

(left) Sabina Tatur, 
(right) Marco Maccarini











Authors: Sabina Tatur¹, Marco Maccarini²

Affiliation: 
¹Department of Physics, University of Illinois at Chicago, USA 
²CEA Grenoble, France.

Although metallic nanoparticles – small entities with dimensions of just a few nanometers – have already been used for the fabrication of lustre decorations in medieval ceramics from Mesopotamia [1], it took another millennium until Michael Faraday provided a first scientific description of their optical properties in his 1847 lecture [2]. But only the emergence of modern experimental techniques - developed in the past thirty to forty years - triggered a boost in the interdisciplinary area of research, development and industrial activity of nanotechnology and nanoscience [3]. Today, metallic nanoparticles, made of noble metals, magnetic or semiconducting materials are added to many consumer goods to revolutionize the product with unique properties.

The skyrocketing progress in nanotechnology in recent years promises a great benefit for our civilization. Yet, there is, at the same time, an increasing concern about their potential harmful side effects on health and environment, and too little research has been conducted in this field so far. One might suppose that the principal determinants of hazardous materials are the surface properties and the surface area to which organisms are exposed. However, a general extrapolation from known hazardous or non-hazardous materials is impracticable since the physicochemical properties of many nanomaterials and nanoparticles deviate considerably from those of bulk or molecular materials.

The first contact that nanomaterials have with any living organism, is always the plasma membrane, a ~5 nm thick lipid bilayer surrounding each animal or plant cell [4]. Lipid membranes are therefore biologically relevant models to study nanomaterial-cell interactions. Understanding the interaction between nanoparticles and cell membranes has two-fold importance in terms of the evaluation of nanosafety as well as the effectiveness of nanoparticles in medical applications.

In this context, we recently studied the interaction of gold nanoparticles (AuNPs) with model cell membranes and focused our research on the effect of surface charge on AuNP destiny and membrane integrity. Previous research in this field showed that the degree of membrane disruption by AuNPs depend on their concentration, size, surface modification and charge, as well as on the phase state of the lipid bilayer (gel or liquid phase) [5-9]. These studies were, however, only symptomatic and missing the attempt to understand the link between surface characteristics of cell membrane and AuNPs to the final destination of the AuNPs.

To provide insight into the fate of AuNPs and their impact on cell membrane integrity, we analyzed the interaction of cationic ammonium AuNPs and anionic carboxy AuNPs with model membranes of only one lipid component. The single component membranes allowed us to focus on the interaction of the AuNPs with the lipid phases, avoiding complications arising from changes in structure and organization of the lipid membrane as a result of additional components in the membrane. To further bypass the electrostatic interactions between the solid substrate, onto which the lipid membrane was deposited, and the lipid bilayer itself, we prepared double lipid bilayers, in which a second lipid bilayer floats on top of the first one. This kind of membrane system gave us access to a highly hydrated, fluctuating bilayer with dynamic properties comparable to natural cell membranes [10] and was, therefore, our model of choice for the examination of the structural integrity of the model membrane with insight into the fate of the AuNPs by neutron reflectometry.

Figure 1a: The sketch shows structural details of the lipid double bilayer after addition of 1 mg/ml (left) and 0.1 mg/ml (right) of cationic AuNPs. The addition of the higher concentration causes a disruption of the membrane, whereas the addition of the lower one causes the AuNPs to incorporate into the hydrophobic moiety of the membrane.

We found that the AuNPs functionalized with cationic head groups penetrated into the center of the lipid bilayers and caused membrane disruption (see Figure 1a) [11]. In contrast, the AuNPs functionalized with anionic head groups did not permeate through the membrane but rather impeded the disruption of the lipid bilayer at alkaline pH (see Figure 1b).

Figure 1b: The sketch shows structural details of the lipid double bilayer after the addition of 0.01 mg/ml of anionic AuNPs. At alkaline pH, the NPs shield the membrane from disintegration that would usually happen under these conditions.

We are now working on understanding the mechanism of this interaction and hope that our approach can provide a strategy for a prospective nanoparticle risk assessement based on a surface charge evaluation and can contribute to nano-safety considerations during their design.

By understanding how nanoparticles affect our environment and taking precautions accordingly, not only will we revolutionize our products but we will be able to benefit from them yet another millennium.



References:
[1] Philippe Colomban, “The use of metal nanoparticles to produce yellow, red and iridescent colour, from bronze age to present times in lustre pottery and glass: solid state chemistry, spectroscopy and nanostructure”, Journal of Nano Research, 8, 109-132 (2009). Abstract.
[2] Michael Faraday, “The Bakerian lecture: experimental relations of gold (and other metals) to light”, Philosophical Transactions of the Royal Society of London, 147, 145-181 (1847). Full Text.
[3] Chris Toumey, “The man who understood the Feynman machine”, Nature Nanotechnology, 2, 9-10 (2007). Abstract.
[4] Jeremy M Berg, John L Tymoczko, and Lubert Stryer, “Biochemistry”, W.H.Freeman and Company, 5th edition (2002). [5] Ralph A. Sperling, Pilar Rivera Gil, Feng Zhang, Marco Zanella, Wolfgang J. Parak, “Biological applications of gold nanoparticles”, Chemical Society Reviews, 37, 1896-1908 (2008). Abstract.
[6] Alaaldin M. Alkilany, Pratik K. Nagaria, Cole R. Hexel, Timothy J. Shaw, Catherine J. Murphy, Michael D. Wyatt, “Cellular Uptake and Cytotoxicity of Gold Nanorods: Molecular Origin of Cytotoxicity and Surface Effects”, small, 5, 701-708 (2009). Abstract.
[7] Nikolai Khlebtsov, Lev Dykman, “Biodistribution and toxicity of engineered gold nanoparticles: a review of in vitro and in vivo studies”, Chemical Society Reviews, 40, 1647-1671 (2011). Abstract.
[8] Pakatip Ruenraroengsak, Pavel Novak, Deborah Berhanu, Andrew J. Thorley, Eugenia Valsami-Jones, Julia Gorelik, Yuri E. Korchev, Teresa D. Tetley, “Respiratory epithelial cytotoxicity and membrane damage (holes) caused by amine-modified nanoparticles”, Nanotoxicology, 6, 94-108 (2012). Abstract.
[9] Atsushi Hirano, Hiroki Yoshikawa, Shuhei Matsushita, Yoichi Yamada, and Kentaro Shiraki, “Adsorption and Disruption of Lipid Bilayers by Nanoscale Protein Aggregates”, Langmuir, 28, 3887-3895 (2012). Abstract.
[10] Giovanna Fragneto, Thierry Charitat, Jean Daillant, “Floating lipid bilayers: models for physics and biology”, European Biophysics Journal, 41, 863-874 (2012). Abstract.
[11] Sabina Tatur, Marco Maccarini, Robert Barker, Andrew Nelson, Giovanna Fragneto, “Effect of functionalized gold nanoparticles on floating lipid bilayers”, Langmuir, 29, 6606-6614 (2013). Abstract.

Profiting from Nonlinearity and Interconnectivity to Control Networks

(left) Adilson Motter, (right) Sean Cornelius














Authors: Sean P. Cornelius¹ & Adilson E. Motter^1,2

Affiliation:
¹Department of Physics & Astronomy, Northwestern University, USA.
²Northwestern Institute on Complex Systems, Northwestern University, USA.

The concept of a complex network---a set of “nodes'” connected by “links” that represent interactions between them---pervades science and engineering, describing systems as diverse as food webs, power grids, and cellular metabolism [1]. Due to the interconnected nature of such systems, perturbations that affect one or more nodes can propagate through the network and potentially cause the system as a whole to fail or change behavior. But our study, recently published in Nature Communications [2], shows that this principle can be a blessing in disguise, giving rise to a new strategy to control network behavior.

Past 2Physics article by Adilson E. Motter:
July 01, 2012: "First Material with Longitudinal Negative Compressibility"
by Zachary G. Nicolaou and Adilson E. Motter.

A hallmark of real complex networks, both natural and engineered, is that their dynamics are inherently nonlinear [3]. It is this nonlinearity that permits the coexistence of multiple stable states (some desirable, others not), which correspond to different possible modes of operation of a real network. Because of this, when a network is perturbed, it can spontaneously go to a “bad” state even if there are “good” ones available. The question we asked is: can this principle be applied in reverse? In other words, can we perturb a network that is in (or will approach) a “bad” state in such a way that it spontaneously evolves to a target state with more desirable properties?

Our research was motivated by recent case studies in our research group, which showed how networks damaged by an external perturbation can, counter-intuitively, be healed by intentionally applying additional, compensatory perturbations. For example, bacterial strains left unable to grow in the wake of genetic mutations can be made viable again by the further knockout of specific genes [4], while extinction cascades in ecological networks perturbed by the loss of one species can often be mitigated by the targeted suppression of additional species [5]. However, a systematic extension of such a strategy to general networks remained an open problem, partly due to system-specific constraints that restrict the perturbations one can actually implement. Indeed, in most real networks there are constraints on the potential compensatory perturbations one can implement in the system, and these generally preclude bringing the system directly to the target, or even to a similar state. In food-web networks, for instance, it may only be possible to suppress (but not increase) the populations of certain species (e.g., via hunting, fishing, culling, or non-lethal removals), while some endangered species can't be manipulated at all. Similarly, one can easily knock down one or more genes in a genetic network, but coordinating the upregulation of entire genetic pathways is comparatively difficult.

The critical insight underlying our research is that even when a desired stable state of a dynamical system can't be reached directly, there will exist a set of other states that eventually do evolve to the target---the so-called basin of attraction of that state. If we could only bring the system to one of those states through an eligible perturbation, the system would subsequently reach the target on its own, without any further intervention. A core component of our work is thus the introduction of a scalable algorithm that can locate basins of attraction in a general dynamical system [2] (for a Python implementation of the algorithm, see Ref. [6]). Figure 1 presents a visual illustration of this approach for transitions between patterns stored in an associative memory network, in which the control intervention (downward arrows) causes the network to spontaneously transition to the next pattern under time evolution (diagonal arrows).

Figure 1: Patters representing the letters of the word “NETWORK” are stored as different stable states in an associative memory network. The example shows how our algorithm induces transitions between consecutive letters by only perturbing “off” pixels.

A remarkable aspect of this approach is its robustness. In the example just mentioned, the control procedure succeeds in driving the system to the target or to a similar pattern with a small number of binary errors (gray pixels). Thus, even if the target state cannot be reached by any eligible perturbation, it may nonetheless be possible to drive the network to a similar state using this control procedure. This would not be possible if the dynamics were linear, since in that case the nonlocal nature of the control trajectories may prevent numerical convergence to the desired target even when the initial state is already close to the target [7].

The approach is based on casting the problem as a series of constrained nonlinear optimization problems, which enables systematic construction of compensatory perturbations via small imaginary changes to the state of the network. Prior to the introduction of this technique there were no systematic methods for locating the portions in the attraction basins that can be reached by eligible perturbations in general high-dimensional dynamical systems, short of conservative estimates and brute-force sampling. The latter requires an amount of computation time exponential in the number of dynamical variables of the system, which is notoriously large for complex networks of interest. In contrast, the running time of our approach scales only as the number of variables to the power 2.5.

There are numerous potential applications for the above control approach. As an example, we considered the identification of candidate therapeutic targets in a form of human blood cancer caused by the abnormal survival of cytotoxic T-cells. Here, normal and cancer states correspond to two different types of stable steady states [8]. Potential curative interventions are those that bring the system from a cancerous or pre-cancerous network state to the attraction basin of the normal state, which then leads to programmed cell death. We demonstrate that 2/3 of all such compromised states can be rescued through perturbations limited to network nodes not previously identified as promising candidate targets for therapeutic interventions. Furthermore, we show that perturbing an average of only 3.4 of them suffices to control the entire network. The effectiveness of many approved drugs relies on their being multi-target, temporary, and tunable, which are precisely the characteristics of the type of control interventions introduced by our study, making such predictions attractive for future experimental exploration [9].

This work illustrates how interconnectedness and nonlinearity---unavoidable features of real systems commonly thought to be impediments to their control---can actually be turned to our advantage. This has broad implications and may in particular shed new light on the requirements on the observability of real networks to allow their real-time control (for recent studies on network observability, see Refs. [10, 11]).

Our approach is based on the systematic construction of compensatory perturbations to the network, and, as illustrated in our applications, can account for both rather general constraints on the admissible interventions and the nonlinear dynamics inherent to most real complex networks. These results provide a new foundation for the control and rescue of network dynamics and for the related problems of cascade control, network reprogramming, and transient stability. In particular, we expect these results to have implications for the development of smart traffic and power-grid networks, of new ecosystem and Internet management strategies, and of new interventions to control the fate of living cells.

The research was supported by NSF (Grant DMS-1057128), NCI (Grant 1U54CA143869), and a Northwestern-Argonne Early Career Investigator Award.

References:
[1] Mark Newman, "The physics of networks", Physics Today, 61(11), 33 (2008). Full Article.
[2] Sean P. Cornelius, William L. Kath, Adilson E. Motter, "Realistic control of network dynamics", Nature Communications, 4, 1942 (2013). Abstract.
[3] Adilson E. Motter and Réka Albert, "Networks in motion", Physics Today 65(4), 43 (2012). Full Article.
[4] Adilson E Motter, Natali Gulbahce, Eivind Almaas & Albert-László Barabási, "Predicting synthetic rescues in metabolic networks", Molecular Systems Biology, 4, 168 (2008). Full Article.
[5] Sagar Sahasrabudhe & Adilson E. Motter, "Rescuing ecosystems from extinction cascades through compensatory perturbations", Nature Communications, 2, 170 (2011). Abstract.
[6] Sean P. Cornelius & Adilson E. Motter, "NECO - A scalable algorithm for NEtwork COntrol", Protocol Exchange, Nature Protocols (2013), doi:10.1038/protex.2013.063. Link.
[7] Jie Sun and Adilson E. Motter, "Controllability transition and nonlocality in network control", Physical Review Letters, 110, 208701 (2013). Abstract.
[8] Ranran Zhang, Mithun Vinod Shah, Jun Yang, Susan B. Nyland, Xin Liu, Jong K. Yun, Réka Albert, Thomas P. Loughran, Jr. "Network model of survival signaling in large granular lymphocyte leukemia". Proceedings of the National Academy of Sciences of the United States of America, 105, 16308 (2008). Abstract.
[9] Peter Csermely, Tamás Korcsmáros, Huba J.M. Kiss, Gábor London, Ruth Nussinov, "Structure and dynamics of molecular networks: A novel paradigm of drug discovery", Pharmacology & Therapeutics, 138, 333 (2013). Abstract.
[10] Yang Yang, Jianhui Wang, and Adilson E. Motter, "Network observability transitions", Physical Review Letters, 109, 258701 (2012). Abstract.
[11] Yang-Yu Liu, Jean-Jacques Slotine, and Albert-László Barabási, "Observability of complex systems", Proceedings of the National Academy of Sciences of the United States of America, 110, 2460 (2013). Abstract. 

Acoustically Invisible Walls

(left) Oliver Wright
(right) Sam Lee

Authors: Oliver B. Wright¹ and Sam Hyeon Lee²

Affiliation:
¹Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan
²Institute of Physics and Applied Physics, Yonsei University, Seoul, South Korea

Physicists in a Korea-Japan collaboration have devised a way to make hard walls transmit sound almost perfectly[1], which could prove useful for developing new types of windows or acoustic concentrators. Based on solid walls of metal or plastic perforated by small holes containing stretched membranes made of humble kitchen cling film, the collaboration have imaged sound travelling unimpeded through them. Sound in such structures, known as metamaterials, resonates strongly with the structure at certain frequencies, allowing counterintuitive effects such as zero sonic reflection. This is an example of a phenomenon known as extraordinary transmission, first demonstrated in the field of optics, whereby light waves are squeezed through sub-wavelength holes more efficiently than expected [2,3].

In the design presented, a tiny force from the sound wave is sufficient to launch a large motion of the membranes, a situation that mimics the air in the hole moving as if with zero mass. Sam Lee of Yonsei University, Kong-ju Bok Lee of Ehwa Women’s University and Oliver Wright of Hokkaido University speculate that this sonic invisible wall could be used for security glass, for example in banks or taxis, that allows you to talk across it, but protects you from any mechanical intrusion.

Figure 1: (left) Single hole with membrane in a cylindrical duct; (right) metamaterial wall consisting of an array of holes containing membranes.

In the first experiments done, sound was incident in a cylindrical tube of diameter 100 mm on a wall blocking the tube containing a single hole of diameter 17 mm mounted with a tight membrane, as shown in Figure 1. It was found that 90% of the acoustic amplitude was transmitted at the audio frequency of 1.2 kHz, in spite of only 3% of the area of the wall being open.

The team also demonstrated a giant concentration up to a factor of 5700 with smaller holes, and that the acoustic energy is effectively transmitted for any angle of incidence, as shown in the example of Figure 2. Figure 1 also shows an example of how a wall of membrane-covered holes could be constructed, effectively constituting a metamaterial wall that transmits sound effectively. This “extraordinary-transmission” phenomenon can be used over a wide range of frequencies. So the method would work equally well for ultrasound, for which preliminary experiments have been reported at lower efficiencies using resonances in bare holes [4]; this could be exploited to concentrate ultrasonic energy through tiny holes, forming novel lenses useful for high resolution ultrasonic imaging.

Figure 2: (Bottom image) Pressure map obtained in the audio-frequency extraordinary-acoustic transmission experiment at 1.2 kHz on an acoustic metamaterial consisting of tight membranes in 4 tiny holes, showing a giant acoustic concentration of 5700 in intensity with an areal coverage ratio of only 0.03. (Top image) Image for holes with no membranes.

References:
[1] Jong Jin Park, K. J. B. Lee, Oliver B. Wright, Myoung Ki Jung, and Sam H. Lee, "Giant Acoustic Concentration by Extraordinary Transmission in Zero-Mass Metamaterials", Physical Review Letters, 110, 244302 (2013). Abstract.
[2] R. Ulrich, in Optical and Acoustical Microelectronics, edited by J. Fox, page 359 (Polytechnic, New York, 1974).
[3] T.W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays", Nature, 391, 667 (1998). Abstract.
[4] Bo Hou, Jun Mei, Manzhu Ke, Weijia Wen, Zhengyou Liu, Jing Shi, and Ping Sheng, "Tuning Fabry-Perot resonances via diffraction evanescent waves", Physical Review B, 76, 054303 (2007). Abstract.

Mesoscopic Interference and Light Trapping in Semiconductor Nanowire Mats

[From left to right clockwise] Claire Blejean, Otto Muskens, Tom Strudley, Tilman Zehender, Erik Bakkers

Authors: Tom Strudley¹, Claire Blejean¹, Tilman Zehender², Erik P.A.M. Bakkers^2,3, Otto L. Muskens¹,

Affiliation: 
¹Faculty of Physical and Applied Sciences, University of Southampton, UK
²Dept of Applied Physics, Eindhoven University of Technology, Netherlands
³Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.

For many years the field of mesoscopic physics, defined as the interface between the microscopic and macroscopic worlds, has been the domain of solid state electronics. Amongst the most prominent of such mesoscopic effects are those of universal conductance fluctuations [1] and Anderson localization [2]. The case of localization, in which transport is completely halted due to interference effects in the presence of sufficiently strong disorder, has been of considerable interest over the years. Indeed it was one of the two pieces of work for which Anderson was jointly awarded a Nobel prize in 1977, and its complexity has prompted many to quote Anderson’s Nobel lecture: “Very few believed it at the time…among those who failed to fully understand it at first was certainly its author.” [3]

Past 2Physics articles by Erik Bakkers:
May 20, 2012: "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices" by Vincent Mourik, Kun Zuo, Sergey Frolov, Sébastien Plissard, Erik Bakkers, Leo Kouwenhoven.

Due to the strong analogy between electron and wave transport, such phenomena should also occur for wave transport in random media. However this presents a significant challenge, as mesoscopic effects occur when the probability of a diffusion scattering back to the same point and interfering with itself becomes significant. Intuitively this break down of the traditional ‘random walk’ description requires scattering mean free paths significantly lower than the wavelength. As a consequence, demonstrations of Anderson localization of light in three dimensions have proved difficult, with most observations being for other systems such as microwaves in a waveguide [4], acoustic waves [5] and even cold atoms [6]. A couple of pioneering studies have reported localization of light in three dimensional media [7,8], however the interpretation of their results is complicated by absorption and fluorescence, which can mimic certain localization effects.

Figure 1: (left) The process of Vapour-liquid-solid growth starting from a gold nanoparticle catalyst is used to grow nanowires on a substrate. A lateral growth step increases the diameter of the wires, without affecting their length. (right) A typical high-density nanowire mat used in our experiments.

In our recent work published in Nature Photonics [9], we presented experimental results obtained using densely packed disordered mats of semiconductor nanowires. We demonstred strong mesoscopic effects using visible light in these layers. The nanowire mats were fabricated at the University of Eindhoven using the method of metallo-organic vapour phase epitaxy (MOVPE), see Fig. 1. By using a recipy of alternating cycles of vapour-liquid-solid (VLS) nanowire growth, followed by lateral growth to increase the wire diameter, precise control could be achieved over the length and diameters of the wire. A very high nanowire density of up to 50% area percentage was necessary to achieve the strong scattering strength required for observing the mesoscopic effects. These nanowire mats are remarkable as they have optical mean free paths as low as 0.2 micrometres, which along with their low intrinsic absorption make them ideal candidates for exploring Anderson localization.

Figure 2 [click on image to see higher resolution]: (left) typical intensity images of light transmitted through a nanowire mat, for a tight laser focus ('in focus') and for a laser illumination out of focus. Total image size ~20 μm. (middle) Intensity distribution normalized to ensemble average, showing the speckle fluctuations in space at the exit plane of the nanowire mat. (right) the total intensity fluctuations are enhanced for a tigthly focused laser, see Ref. [9].

By examining the intensity statistics of the transmitted light we found that it exhibited the large intensity fluctuations and long range correlations (both spatial and spectral) typical of mesoscopic interference (Fig. 2). Fitting these fluctuations with predictions from theory, we found an average of only 4 independent transmission channels through our sample, which is several orders of magnitude lower than previously reported values. These measurements unambiguously show for the first time that strong mesoscopic interference corrections can be achieved in three-dimensional nanomaterials and at optical wavelengths.

Mesoscopic transport corrections are a precursor of the strong or Anderson localization transition, where transport of light is halted by self-interference of many light paths returning to the same position in the medium. We are now in the exciting position where we can probe in detail the mesoscopic physics of light, as well as tuning our nanowire growth parameters further in a bid to observe localization itself. For practical applications, semiconductor nanowires have great potential in solar cell and light generation. A deep understanding of light transport in such materials is of great importance for further optimizing these applications. Ultimately, it may be possible for mesoscopic effects to be harnessed and turned into a new design tool for maximizing performance of real-world devices.

References:
[1] P.A. Lee and A. Douglas Stone, “Universal Conductance Fluctuations in Metals”, Physical Review Letters, 55, 1622-1625 (1985). Abstract.
[2] P.W. Anderson, “Absence of diffusion in certain random lattices”, Physical Review, 109, 1492-1505 (1958). Abstract.
[3] Philip W. Anderson, Nobel lecture (1977).
[4] A.A. Chabanov, M. Stoytchev, A.Z. Genack, “Statistical Signatures of Photon Localization”, Nature 404, 850-853 (2000). Abstract.
[5] Hefei Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, B. A. van Tiggelen, “Localization of Ultrasound in a Three-Dimensional Elastic Network”, Nature Physics, 4, 945-948 (2008). Abstract.
[6] Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Clément, Laurent Sanchez-Palencia, Philippe Bouyer, Alain Aspect, “Direct Observation of Anderson localization of matter waves in a controlled disorder”, Nature, 453, 891-894 (2008). Abstract. 2Physics Article.
[7] Diederik S. Wiersma, Paolo Bartolini, Ad Lagendijk, Roberto Righini, “Localization of light in a disordered medium”, Nature 390, 671-673 (1997). Abstract.
[8] Martin Störzer, Peter Gross, Christof M. Aegerter, and Georg Maret, “Observation of the Critical Regime Near Anderson Localization of Light”, Physical Review Letters, 96, 063904 (2006). Abstract.
[9] Tom Strudley, Tilman Zehender, Claire Blejean, Erik P. A. M. Bakkers, Otto L. Muskens, “Mesoscopic Light Transport by Very Strong Collective Multiple Scattering in Nanowire Mats”, Nature Photonics, 7, 413-418 (2013). Abstract.