Author Correction: Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement.

The original version of this Article omitted the author Kuan Wang, who is from the 'College of Biomedical Engineering, Taipei Medical University, Taipei 11031, Taiwan' and 'Nanyang Environment & Water Research Institute, Nanyang Technological University, Singapore 637141, Singapore.'Also, the author S.H. Lim was incorrectly given as L.S. Hoi and A. Larsson was incorrectly given as A. Larson.The "Author contributions" was amended to reflect the authorship changes. It previously read 'Y.Z.S., C.-W.Q., and A.Q.L. jointly conceived the idea. Y.Z.S., S.X., Y.Z., J.B.Z., W.S., J.H.W., T.N.C., Z.C.Y., Y.L.H., B.L., P.H.Y., D.P.T., and C.-W.Q. performed the numerical simulations and theoretical analysis. Y.Z.S., S.X., and L.K.C. did the fabrication and experiments of particle hopping, biomolecule binding and flow cytometry. A.L. and L.S.H. did the SPR experiments. S.X., Y.Z.S., Y.Z., C.-W.Q., Y.-Y.C., L.K.C., T.H.Z., and A.Q.L. prepared the manuscript. S.X., Y.Z., C.-W.Q., and A.Q.L. supervised and coordinated all the work. All authors commented on the manuscript.' The correct version states 'B.L., K. W., P.H.Y.' instead of 'B.L., P.H.Y.' and 'S.H.L.' in place of 'L.S.H.'This has been corrected in both the PDF and HTML versions of the Article.

Thermal meta-device in analogue of zero-index photonics.

Inspired by the developments in photonic metamaterials, the concept of thermal metamaterials has promised new avenues for manipulating the flow of heat. In photonics, the existence of natural materials with both positive and negative permittivities has enabled the creation of metamaterials with a very wide range of effective parameters. In contrast, in conductive heat transfer, the available range of thermal conductivities in natural materials is far narrower, strongly restricting the effective parameters of thermal metamaterials and limiting possible applications in extreme environments. Here, we identify a rigorous correspondence between zero index in Maxwell's equations and infinite thermal conductivity in Fourier's law. We also propose a conductive system with an integrated convective element that creates an extreme effective thermal conductivity, and hence by correspondence a thermal analogue of photonic near-zero-index metamaterials, a class of metamaterials with crucial importance in controlling light. Synergizing the general properties of zero-index metamaterials and the specific diffusive nature of thermal conduction, we theoretically and experimentally demonstrate a thermal zero-index cloak. In contrast with conventional thermal cloaks, this meta-device can operate in a highly conductive background and the cloaked object preserves great sensitivity to external temperature changes. Our work demonstrates a thermal metamaterial which greatly enhances the capability for molding the flow of heat.

Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement.

Particle trapping and binding in optical potential wells provide a versatile platform for various biomedical applications. However, implementation systems to study multi-particle contact interactions in an optical lattice remain rare. By configuring an optofluidic lattice, we demonstrate the precise control of particle interactions and functions such as controlling aggregation and multi-hopping. The mean residence time of a single particle is found considerably reduced from 7 s, as predicted by Kramer's theory, to 0.6 s, owing to the mechanical interactions among aggregated particles. The optofluidic lattice also enables single-bacteria-level screening of biological binding agents such as antibodies through particle-enabled bacteria hopping. The binding efficiency of antibodies could be determined directly, selectively, quantitatively and efficiently. This work enriches the fundamental mechanisms of particle kinetics and offers new possibilities for probing and utilising unprecedented biomolecule interactions at single-bacteria level.

Analysis of mid-infrared lasing in active random media.

Lasing behaviour of 2-dimensional active random structures, designed to work in the Mid-IR region, has been investigated at different input powers by varying the amount of scattering intensity. A Monte Carlo based simulation tool has been developed including a model to manage the optical amplification. The analysis of photon travel distance has been considered to show the random lasing behaviour with particular attention on lasing threshold at different scattering intensity. The simulated results are in agreement with experiments.

Controlling light scattering and polarization by spherical particles with radial anisotropy.

Based on full-wave electromagnetic theory, we derive the zero-forward and zero-backward scattering conditions for radially anisotropic spheres within the quasi-static limit. We find that the near-field intensity can be tuned dramatically through the adjustment of the radial anisotropy, while the far-field light scattering diagrams are similar under the zero-forward or zero-backward scattering conditions. Generalized "Brewster's angle" for anisotropic spheres is also derived, at which the scattering light is totally polarized. In addition, the high-quality polarized scattering wave and the tunable polarization conversion can be achieved for the radially anisotropic spheres.

Non-Rayleigh scattering behavior for anisotropic Rayleigh particles.

Derived from the light scattering by a radially anisotropic sphere, unusual scattering behavior is exhibited, which breaks the Rayleigh law (scattering efficiency Q(sca)~q(4) as q→0, where q is the size parameter). Under certain conditions, we demonstrate an asymptotical relation between Q(sca) and q, i.e., Q(sca)=Fq(8), which is not realizable for isotropic particles in Rayleigh regime. Moreover, suitable adjustment of the anisotropic parameters can further suppress the coefficient F, resulting in enhanced transparency of the anisotropic particle.

Isotropic non-ideal cloaks providing improved invisibility by adaptive segmentation and optimal refractive index profile from ordering isotropic materials.

Mimicking the ideal cloak, which is anisotropic and inhomogeneous, can be achieved by alternating homogeneous isotropic materials, whose permittivity and permeability of each isotropic coating can be determined from effective medium theory. An improved two-fold method is proposed by optimally discretizing the cloak and re-ordering the combination of the effective parameters of each layer to form a smooth step-index profile. The roles of impedance matching and index matching are investigated for cloaking effects. Smoothing the index profile leads to better invisibility than that obtained by smoothing the impedance profile, since the forward scattering can be further diminished. Nonlinear-transformationbased spherical ideal cloaks are studied, and improved design method is explored together with different segmentation schemes. Significant improvement in invisibility is always observed for the optimal segmentation in virtual space with the proposed two-fold design method no matter how nonlinear the coordinate transformation is.

Electromagnetic transparency by coated spheres with radial anisotropy.

We establish an account of electromagnetic scattering by coated spheres with radial dielectric and magnetic anisotropy. Within full-wave scattering theory, we show that the total scattering cross section Qs is strongly dependent on both the dielectric anisotropy and magnetic anisotropy. As a consequence, by a suitable adjustment of the radius ratio, one may make the anisotropic coated particle nearly transparent or invisible. In the quasistatic case, we take one step forward to derive the effective permittivity and permeability for the coated particle, and the near-zero scattering radius ratio can be well described within effective medium theory. To one's interest, the introduction of radial anisotropy is helpful to achieve better transparency quality such as a much smaller Qs and wider range of near-zero scattering ratio. Moreover, when the coated particle is anisotropic, the position of the near-zero scattering radius ratio can be tunable, resulting in a tunable electromagnetic cloaking.

Shifted resonances in coated metamaterial cylinders: enhanced backscattering and near-field effects.

Electromagnetic wave properties in the presence of a thin or thick coating on a cylinder are investigated. The theoretical treatment starts from the formulation of electromagnetic fields in all regions where the coating and the core are allowed to rotate. The angular velocities of the core and coating can be different and even antidirectional. The present general approach can be applied to a wide range of specific cases such as rotating and stationary and left-handed and right-handed core-coating combinations. In particular, the optical resonances due to the surface plolaritons and morphology-dependent resonances are examined. Because of the rotation, the resonances are found to shift, and the effects of velocity on such phenomena are investigated. The backscattering can thus be controlled to achieve suppression or enhancement by using proper metamaterial coatings. Physical insights as well as the numerical results are presented.

Expression and significance of PTEN and VEGF in canine mammary gland tumours.

To investigate the relationship between the expression of the PTEN (phosphatase and tensin homolog deleted on chromosometen) and VEGF (vascular endothelial growth factor) and the clinicopathological features in canine mammary gland tumours, the expression levels of PTEN and VEGF protein were assessed in 50 cases of canine mammary gland tumours tissues and 4 cases of normal mammary gland tissues with using immunohistochemical method. The over-expression rate of PTEN protein was 100% in normal and well-differentiated mammary gland tissues and 67% in breast cancer cases respectively with a significant difference between the two groups (P<0.01). Expression of PTEN was not related to age and tumour size, but closely correlated to lymph node metastasis (P<0.01). The over-expression rate of VEGF protein was 33.3% in normal mammary gland tissues, and 78% in canine mammary gland tumours with a significant difference between the two groups (P<0.01). Expression of VEGF was not related to age or tumour size, but closely correlated with lymph node metastasis and clinical stage (P<0.05). Therefore the combination detection of PTEN and VEGF could serve as an important index to estimate the biological behavior and prognosis of canine mammary gland tumours. Reduced expression of PTEN might be involved in carcinogenesis and progression of canine breast cancer by up-regulating the VEGF expression to enhance angiogenesis.