Background: Super-resolution optical fluctuation imaging (SOFI) achieves 3D super-resolution by computing temporal cumulants or spatio-temporal cross-cumulants of stochastically blinking fluorophores. In contrast to localization microscopy, SOFI is compatible with weakly emitting fluorophores and a wide range of blinking conditions. The main drawback of SOFI is the nonlinear response to brightness and blinking heterogeneities in the sample, which limits the use of higher cumulant orders for improving the resolution. Balanced super-resolution optical fluctuation imaging (bSOFI) analyses several cumulant orders for extracting molecular parameter maps, such as molecular state lifetimes, concentration and brightness distributions of fluorophores within biological samples. Moreover, the estimated blinking statistics are used to balance the image contrast, i.e. linearize the brightness and blinking response and to obtain a resolution improving linearly with the cumulant order. Results: Using a widefield total-internal-reflection (TIR) fluorescence microscope, we acquired image sequences of fluorescently labelled microtubules in fixed HeLa cells. We demonstrate an up to five-fold resolution improvement as compared to the diffraction-limited image, despite low single-frame signal-to-noise ratios. Due to the TIR illumination, the intensity profile in the sample decreases exponentially along the optical axis, which is reported by the estimated spatial distributions of the molecular brightness as well as the blinking on-ratio. Therefore, TIR-bSOFI also encodes depth information through these parameter maps. Conclusions: bSOFI is an extended version of SOFI that cancels the nonlinear response to brightness and blinking heterogeneities. The obtained balanced image contrast significantly enhances the visual perception of super-resolution based on higher-order cumulants and thereby facilitates the access to higher resolutions. Furthermore, bSOFI provides microenvironment-related molecular parameter maps and paves the way for functional super-resolution microscopy based on stochastic switching.
A straightforward method to achieve super-resolution consists of taking an image sequence of stochastically blinking emitters using a standard wide-field fluorescence microscope. Densely packed single molecules can be distinguished sequentially in time using high-precision localization algorithms (e.g., PALM and STORM) or by analyzing the statistics of the temporal fluctuations (SOFI). In a face-to-face comparison of the two post-processing algorithms, we show that localization-based super-resolution can deliver higher resolution enhancements but imposes significant constraints on the blinking behavior of the probes, which limits its applicability for live-cell imaging. SOFI, on the other hand, works more consistently over different photo-switching kinetics and also delivers information about the specific blinking statistics. Its suitability for low SNR acquisition reveals SOFI's potential as a high-speed super-resolution imaging technique.
We report on the characterization of long-range surface plasmon waveguide bends at telecom wavelengths ͑ = 1550 nm͒. The structures consist of a thin Au stripe embedded in a transparent polymer film. When the polymer thickness is larger than the lateral extension of the plasmon, the stripe sustains a conventional long-range mode; in the opposite case, the mode is hybrid because its field distribution is confined by total internal reflection in the dielectric cladding. This hybridization increases the damping by absorption but dramatically reduces the radiation loss that occurs for curved geometries, such as bends. Our results are supported quantitatively by full-wave finite-element simulations. DOI: 10.1103/PhysRevA.77.021804 PACS number͑s͒: 03.50.De, 41.20.Jb, 42.82.Et, 78.67.Ϫn While metals exhibit large material losses at visible wavelengths, they nevertheless have remarkable optical properties. In particular, the electron density of a metal surface can be coupled with light so as to form a surface plasmon polariton ͑SPP͒-an interface mode characterized by strong local fields and a tremendous sensitivity to its environment ͓1,2͔. The SPP modes supported by thin metal films in a homogeneous dielectric medium are of particular interest because their propagation length can reach several millimeters or more at visible and infrared wavelengths, instead of tens of microns or less as all other SPPs ͓3-5͔. The field distribution of these long-range modes has a large exponential tail extending on each side of the film. Consequently, a significant part of the energy is carried outside the metal, thus minimizing the damping by absorption. Despite their weak optical confinement, long-range SPPs are bound surface modes, so thin metal films can be utilized as efficient low-loss plasmonic waveguides. In order to guide long-range SPPs along a specific direction, the film width must be reduced until the structure becomes a thin metal stripe ͓6-14͔. A variety of components based on the stripe geometry have been designed and fabricated, including interferometers ͓9͔, couplers ͓15͔, Bragg filters ͓16͔, modulators ͓17,18͔, and an external cavity laser ͓19͔. Although the material loss in these structures is still considerably larger than in any other integrated waveguides, they might find an application as transitioning elements between purely dielectric structures and short-range SPPs with subwavelength confinement. Metal-based waveguides are also of potential interest for sensing purposes because long-range SPPs are very easily perturbed by external changes ͓12͔.In recent years, the interaction between metal stripes and dielectric structures has become the focus of several numerical studies, for example, in the context of directional couplers ͓20͔. A different type of SPP-dielectric interaction occurs for metal stripes embedded in a thin dielectric layer with a refractive index larger than that of the background host ͓15,21-23͔. When the transverse extension of the long-range SPP is larger than the thickness of the dielectri...
We perform rigorous simulations of hybrid long-range modes guided by a central metal core and a twodimensional dielectric slab. We show that these modes are subject to fewer limitations than conventional long-range plasmon modes in terms of field confinement and guiding performance. These hybrid modes may offer substantial improvements for integrated plasmonic components, as illustrated here by the consideration of 90°bends. © 2007 Optical Society of America OCIS codes: 240.6680, 130.2790, 130.3120. Surface plasmon polaritons (SPPs) are electromagnetic-electronic waves propagating at the interface between a metal and a dielectric [1]. SPPs are associated with strongly enhanced local fields that can exhibit spatial variation on a scale much smaller than the photon wavelength. This particular aspect of SPPs renders them attractive for the development of photonic components whose size is not limited by the diffraction limit of light [2]. However, SPP modes with subdiffraction confinement propagate only over distances ranging from micrometers in the visible to hundreds of micrometers in the infrared, because a substantial part of the energy is contained in the metal-an extremely absorptive medium at those frequencies [1,3,4]. To reduce the losses by absorption, the field confinement must be considerably relaxed [4]: for example, thin metal films and metal strips support long-range SPPs that propagate as far as centimeters, but the lateral extension of these modes reaches several wavelengths [5][6][7][8][9][10][11][12][13][14][15].Recently, several studies have shown that the properties of long-range SPPs propagating along infinitely wide metal films can be tailored by constraining their field in a two-dimensional dielectric waveguide [12][13][14]. Here we generalize this approach by considering the case of arbitrary curved metal strips embedded in a thin dielectric slab. We show numerically that the long-range SPPs are hybridized by total internal reflection and that, although the general trade-off between loss and propagation distance still occurs for these modes, the electromagnetic fields can be localized to significantly smaller volumes for the same propagation distance when compared with long-range SPPs.Our numerical method is based on finding the eigenmodes of the strip geometry in either an infinite-or a finite-thickness dielectric region at the wavelength = 1550 nm. To simplify the calculations, we limit our investigations to straight and uniformly bent waveguides and investigate their modes in Cartesian and cylindrical coordinates, respectively (Fig. 1). The electric field of the mode can be formally written as E = E 0 ͑x , y͒exp͑i z z͒ for the straight waveguides and E = E 0 ͑r , y͒exp͑i ͒ for the bends, where E 0 is the field distribution along the waveguide cross section and  z (in inverse meters) and  (in inverse radians) are the complex propagation constants. With the field dependence on the propagation direction assumed, the strip waveguides can be fully characterized by performing a finite-e...
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