PyFocus a Python package for vectorial calculations of focused optical fields under realistic conditions. Application to toroidal foci

Focused optical fields are key to a multitude of applications involving light-matter interactions, such as optical microscopy, single-molecule spectroscopy, optical tweezers, lithography, or quantum coherent control. A detailed vectorial characterization of the focused optical fields that includes a description beyond the paraxial approximation is key to optimize technological performance as well as for the design of meaningful experiments and interpret properly their results. Here, we present PyFocus, an open-source Python software package to perform fully vectorial calculations of focused electromagnetic fields after modulation by an arbitrary phase mask and in the presence of a multilayer system. We provide a graphical user interface and high-level functions to easily integrate PyFocus into custom scripts. Furthermore, to demonstrate the potential of PyFocus, we apply it to extensively characterize the generation of toroidal foci with a high numerical aperture objective, as it is commonly done in super-resolution fluorescence microscopy methods such as STED or MINFLUX. We provide examples of the effects of different experimental factors such as polarization, aberrations, and misalignments of key optical elements. Finally, we present calculations of toroidal foci through an interface of different mediums, and, to our knowledge, the first calculations of toroidal foci generated in total internal reflection conditions

Media 1: Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna

Originally published in Optics Express on 07 July 2008 (oe-16-14-10858

A common framework for single-molecule localization using sequential structured illumination

Localization of single fluorescent molecules is key for physicochemical and biophysical measurements such as single-molecule tracking and super-resolution imaging by single-molecule localization microscopy (SMLM). Recently a series of methods have been developed in which the localization precision is enhanced by interrogating the molecular position with a sequence of spatially modulated patterns of light. Among them, the MINFLUX technique outstands for achieving a ~10-fold improvement compared to wide-field camera-based single-molecule localization, reaching ~1-2 nm localization precision at moderate photon counts. Here, we present a common mathematical framework for this type of measurement that allows a fair comparison between reported methods and facilitates the design and evaluation of new methods. With it, we benchmark all reported methods for single-molecule localization using sequential structured illumination, including long-established methods such as orbital tracking, along with two new proposed methods: orbital tracking and raster scanning with a minimum of intensity

Optical Nanorod Antennas Modeled as Cavities for Dipolar Emitters: Evolution of Sub- and Super-Radiant Modes

Optical antennas link objects to light. Here we derive an analytical model for the interaction of dipolar transitions with radiation through nanorod antenna modes, by modeling nanorods as cavities. The model includes radiation damping, accurately describes the complete emission process, and is summarized in a phase-matching equation. We analytically discuss the quantitative evolution of antenna modes, in particular the gradual emergence of subradiant, super-radiant, and dark modes, as antennas become increasingly more bound, i.e., plasmonic. Our description is valid for the interaction of nanorods with light in general and is thus widely applicable

Immobilization of Gold Nanoparticles on Living Cell Membranes upon Controlled Lipid Binding

We present a versatile and controlled route to immobilize gold nanoparticles (NPs) on the surface of living cells, while preserving the sensing and optothermal capabilities of the original colloid. Our approach is based on the controlled and selective binding of Au NPs to phospholipids prior to cell incubation. We show that in the presence of the cells the lipid-bound Au NPs are delivered to the cellular membrane and that their diffusion is rather slow and spatially limited, as a result of lipid binding. Avoiding nonspecific membrane labeling, this approach is of general application to several types of colloids and cells and thereby provides a platform for controlled plasmonic and optothermal investigations of living cell membranes

One-Pot Preparation of Dendrimer−Gold Nanoparticle Hybrids in a Dipolar Aprotic Solvent

We present a simple one-pot, one-step method to obtain stable and nearly monodisperse gold nanoparticles in dipolar aprotic solvents. Novel thiomethyl-functionalized polyphenylene dendrimers are used to control the growth and stabilize the nanoparticles in suspension. The dendrimer functionalized gold nanoparticles have an average size of roughly 10 nm and are stable in suspension for several weeks. The stability in dipolar aprotic solvents and the great functionalization flexibility offered by the dendrimers make these metal/dendrimer hybrid systems promising for applications such as nanophotonics, molecular electronics, and sensing

Super-resolved FRET imaging by confocal fluorescence-lifetime single-molecule localization microscopy

FRET-based approaches are a unique tool for sensing the immediate surroundings and interactions of (bio)molecules. FRET imaging and FLIM (Fluorescence Lifetime Imaging Microscopy) enable the visualization of the spatial distribution of molecular interactions and functional states. However, conventional FLIM and FRET imaging provide average information over an ensemble of molecules within a diffraction-limited volume, which limits the spatial information, accuracy, and dynamic range of the observed signals. Here, we demonstrate an approach to obtain super-resolved FRET imaging based on single-molecule localization microscopy using an early prototype of a commercial time-resolved confocal microscope. DNA Points Accumulation for Imaging in Nanoscale Topography (DNA-PAINT) with fluorogenic probes provides a suitable combination of background reduction and blinking kinetics compatible with the scanning speed of usual confocal microscopes. A single laser is used to excite the donor, a broad detection band is employed to retrieve both donor and acceptor emission, and FRET events are detected from lifetime information

Exciton Diffusion, Antenna Effect, and Quenching Defects in Superficially Dye-Doped Conjugated Polymer Nanoparticles

Energy transfer (ET) in conjugated polymer nanoparticles (CPNs) is a critical process that affects the performance of these materials in diverse applications such as biological–chemical–physical sensing, imaging, photovoltaics, and phototherapy. Herein, we performed an in-depth study of ET in the CPNs of poly­(9,9-dioctylfluorene-altbenzothiadiazole) (F8BT) superficially doped with well-controlled amounts of rhodamine B (RhB) dye using a combined experimental and theoretical approach. In these particles, the conjugated polymer acts as the excitation energy donor, whereas adsorbed dye molecules and non-emissive quenching defect sites (Q) act as energy acceptors. Fitting of simulated polymer emission to experimental data provided the intrinsic exciton diffusion length (Ld = 8.6 nm) of the polymer and the mean number of quenching defects per particle (ρQ̅=1.56×10−2defects/nm2). Importantly, results provide for the first time sound evidence indicating that quenching defect centers are superficially, rather than volumetrically, distributed in these CPNs. The so-called antenna effect (AE), a parameter frequently used to characterize the ET process in donor–acceptor multichromophoric systems, was also calculated. The AE in these CPNs takes a maximum value of ∼40, which compares well with the values reported for similar systems. The developed model (and associated computational Python code) represents a significant improvement over previous models/codes by correcting inconsistencies and successfully simulating ET processes in dye-doped CPNs taking into account: exciton diffusion, ET to non-emissive quenching defect centers, ET to dye dopants, spatial distribution of dyes and defects within CPNs, and individual particle excitation probability among other parameters. The model calculates the ensemble-averaged, time-resolved, and time-averaged emission intensity of CPNs and dye dopants for specific CPN size distributions, allowing for direct comparison with experimental bulk measurements. We envisage that the presented improvements in both the theoretical model and the experimental strategy will prove useful in the study and design of new dye-doped CPNs for practical applications

Controlled Reduction of Photobleaching in DNA Origami–Gold Nanoparticle Hybrids

The amount of information obtainable from a fluorescence-based measurement is limited by photobleaching: Irreversible photochemical reactions either render the molecules nonfluorescent or shift their absorption and/or emission spectra outside the working range. Photobleaching is evidenced as a decrease of fluorescence intensity with time, or in the case of single molecule measurements, as an abrupt, single-step interruption of the fluorescence emission that determines the end of the experiment. Reducing photobleaching is central for improving fluorescence (functional) imaging, single molecule tracking, and fluorescence-based biosensors and assays. In this single molecule study, we use DNA self-assembly to produce hybrid nanostructures containing individual fluorophores and gold nanoparticles at a controlled separation distance of 8.5 nm. By changing the nanoparticles’ size we are able to systematically increase the mean number of photons emitted by the fluorophores before photobleaching

DNA-Templated Ultracompact Optical Antennas for Unidirectional Single-Molecule Emission

Optical antennas are nanostructures designed to manipulate light–matter interactions by interfacing propagating light with localized optical fields. In recent years, numerous devices have been realized to efficiently tailor the absorption and/or emission rates of fluorophores. By contrast, modifying the spatial characteristics of their radiation fields remains challenging. Successful phased array nanoantenna designs have required the organization of several elements over a footprint comparable to the operating wavelength. Here, we report unidirectional emission of a single fluorophore using an ultracompact optical antenna. The design consists of two side-by-side gold nanorods self-assembled via DNA origami, which also controls the positioning of the single-fluorophore. Our results show that when a single fluorescent molecule is positioned at the tip of one nanorod and emits at a frequency capable of driving the antenna in the antiphase mode, unidirectional emission with a forward to backward ratio of up to 9.9 dB can be achieved