What is a Paraconsistent Logic?

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively

Observation of the resonantly enhanced resolution of imaging of fluorescent nanospheres due to their coupling to the metallic nanoplasmonic arrays

International audienceVirtual imaging through dielectric microspheres is shown to possess the resolution beyond the classical diffraction limit, but the factors responsible for such resolution are debated in the literature. In this work, we experimentally demonstrated an important role of spectral overlap between the emission band of a fluorescent (FL) object and the spectral peak of localized surface plasmon resonance (LSPR) in the underlying metallic periodic nanostructure. As an object, we used green and blue FL nanospheres placed at the top of Au and Al arrays with different periods. It is shown that the maximal resolution beyond the diffraction limit can be achieved in confocal microscopy of green (blue) FL nanospheres at the top of Au(Al) arrays. Our results provide the first direct evidence for the critically important role of resonant coupling of emission of point-like objects to LSPRs in the underlying nanostructure for achieving the super-resolution

The Art of the Impossible: Sorting Dielectric Microspheres by using Light

International audienceUse of resonant light forces opens up a unique approach to high-volume sorting of microspherical resonators with 1/Q accuracy, where Q is the resonance quality factor. Based on a two-dimensional model, it is shown that the sorting can be realized by allowing spherical particles to traverse a focused beam. Under resonance with the whispering gallery modes (WGM), the particles acquire significant velocity along the laser beam which should allow sorting dielectric microspheres with almost identical positions of their WGM resonances. This is an enabling technology for developing super-low-loss coupled-cavity structures and devices

Enhancement of resolution in microspherical nanoscopy by coupling of fluorescent objects to plasmonic metasurfaces

International audienceThe resolution of microsphere-based nanoscopy is studied using fluorescently labeled nanospheres and F-actin protein filaments with the emission coupled to the localized surface plasmon resonances in the underlying Au nanodisk arrays. Virtual imaging is performed through high-index microspheres embedded in plastic coverslips placed in contact with the nanoscale objects. For 150 and 200 nm periods of nanoplasmonic arrays, the imaging has a solid immersion lens-limited resolution, whereas for shorter periods of 80 and 100 nm, the resolution was found to increase up to ∼λ/7, where λ is the emission wavelength. The results cannot be interpreted within a framework of a regular localized plasmonic structured illumination microscopy since the array period was significantly shorter than the wavelength and postimaging processing was not used. It is hypothesized that the observed super-resolution is based on coupling of the emission of nanoscale objects to strongly localized near-field maxima in the adjacent plasmonic metasurfaces followed by evanescent coupling to high-index microspheres

Microconical silicon mid-IR concentrators: spectral, angular and polarization response

It is widely discussed in the literature that a problem of reduction of thermal noise of mid-wave and long-wave infrared (MWIR and LWIR) cameras and focal plane arrays (FPAs) can be solved by using light-concentrating structures. The idea is to reduce the area and, consequently, the thermal noise of photodetectors, while still providing a good collection of photons on photodetector mesas that can help to increase the operating temperature of FPAs. It is shown that this approach can be realized using microconical Si light concentrators with (111) oriented sidewalls, which can be mass-produced by anisotropic wet etching of Si (100) wafers. The design is performed by numerical modeling in a mesoscale regime when the microcones are sufficiently large (several MWIR wavelengths) to resonantly trap photons, but still too small to apply geometrical optics or other simplified approaches. Three methods of integration Si microcone arrays with the focal plane arrays are proposed and studied: (i) inverted microcones fabricated in a Si slab, which can be heterogeneously integrated with the front illuminated FPA photodetectors made from high quantum efficiency materials to provide resonant power enhancement factors (PEF) up to 10 with angle-of-view (AOV) up to 10°; (ii) inverted microcones, which can be monolithically integrated with metal-Si Schottky barrier photodetectors to provide resonant PEFs up to 25 and AOVs up to 30° for both polarizations of incident plane waves; and iii) regular microcones, which can be monolithically integrated with near-surface photodetectors to provide a non-resonant power concentration on compact photodetectors with large AOVs. It is demonstrated that inverted microcones allow the realization of multispectral imaging with ∼100 nm bands and large AOVs for both polarizations. In contrast, the regular microcones operate similar to single-pass optical components (such as dielectric microspheres), producing sharply focused photonic nanojets.</jats:p