. We demonstrate below that singular-phase behaviour can be achieved by using plasmonic nanostructures (see Fig. 1 ) we solve the problem of inherent losses and create the complete darkness yielding to phase singularities. By using graphene hydrogenation, we estimate the detection limit of our nanomaterials at a level of 0.1fg/mm 2 , which is 4 orders of magnitude better than reported in literature for SPR. We also show that suggested nanomaterials can be applied for biosensing and provide an unprecedented sensitivity in the absence of labels. Topologically protected darkness and phase sensitivity of coupled LPR. Consider a light reflection from a thin film placed on a dielectric substrate. In the visible range, there exists a set of n, k (here n n ik   is the refractive index of the film) for which the reflection is exactly zero.This set is shown by the solid brown curve in Fig. 1(c), where for concreteness the film thickness d is chosen to be 170nm, angle of incidence =60 and the substrate is made of glass. In principle, it is possible to achieve these values of n, k by using a dielectric film near the Brewster angle. Although the enhanced phase sensitivity near the Brewster angle is used in Brewster angle microscopy 20 (and ellipsometry, in general), it is not widely used in biophysics since local electric fields for dielectric substrates are small. On the other hand, metal films can generate much stronger local fields due to plasmons and, therefore, provide a better phase sensitivity.Unfortunately, it is quite difficult to achieve phase singularity using a continuous metal film. For example, dispersion relations n(), k() for gold yield the curve shown at the top of the image and result in non-zero reflection for gold films across the entire visible spectrum (measured ellipsometric reflection from a 170nm gold film is shown in the top panel of Fig. 1(c)). 5The situation is different for a nanomaterial with DCLP. Using such plasmonic nanomaterials, one can manipulate effective n eff (), k eff () and make them to intersect the zero reflection line in Fig. 1(c). The middle panel in this figure shows the effective dispersion curve and the measured reflection from the gold nanostripe structure schematically shown in Fig. 1(a) 27. One can see a narrow plasmon resonance with the half-width of 12nm and quality of about Q~200. The detailed analysis shows that the light intensity reaches zero at certain wavelength and angle of incidence, which results in a singular behaviour of phase in the Fourier space.Indeed, the zero reflection line (the brown curve) separates two different regions in the (n, k) plane due to a nature of Fresnel reflection coefficients. Because the dispersion curve for the nanostructured gold starts in one of these regions and finishes in the other, it implies that it will always intersect the line of zero reflection curve due to the Jordan theorem 28 (which states that the line connecting two different regions separated by a boundary always intersects the boundary), see Fig 1(c). Relativ...

Anticounterfeiting labels based on physical unclonable functions (PUFs), as one of the powerful tools against counterfeiting, are easy to generate but difficult to duplicate due to inherent randomness. Gap-enhanced Raman tags (GERTs) with embedded Raman reporters show strong intensity enhancement and ultra-high photostability suitable for fast and repeated readout of PUF labels. Herein, we demonstrate a PUF label fabricated by drop-casting aqueous GERTs, high-speed read using a confocal Raman system, digitized through coarsegrained coding methods, and authenticated via pixel-by-pixel comparison. A threedimensional encoding capacity of over 3 × 10 15051 can be achieved for the labels composed of ten types of GERTs with a mapping resolution of 2500 pixels and quaternary encoding of Raman intensity levels at each pixel. Authentication experiments have ensured the robustness and security of the PUF system, and the practical viability is demonstrated. Such PUF labels could provide a potential platform to realize unbreakable anticounterfeiting.

Surface-enhanced Raman spectroscopy (SERS) is advantageous over fluorescence for bioimaging due to ultra-narrow linewidth of the fingerprint spectrum and weak photo-bleaching effect. However, the existing SERS imaging speed lags far behind practical needs, mainly limited by Raman signals of SERS nanoprobes. In this work, we report ultrabright gap-enhanced Raman tags (GERTs) with strong electromagnetic hot spots from interior sub-nanometer gaps and external petal-like shell structures, larger immobilization surface area, and Raman cross section of reporter molecules. These GERTs reach a Raman enhancement factor beyond 5 × 10 9 and a detection sensitivity down to a single-nanoparticle level. We use a 370 μW laser to realize high-resolution cell imaging within 6 s and high-contrast (a signal-to-background ratio of 80) wide-area (3.2 × 2.8 cm 2 ) sentinel lymph node imaging within 52 s. These nanoprobes offer a potential solution to overcome the current bottleneck in the field of SERS-based bioimaging.