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Renaud Marty

Publications and source records attributed to Renaud Marty.

7 recordsLinked to original sources
arXiv2021

A full discretization of the rough fractional linear heat equation

We study a full discretization scheme for the stochastic linear heat equation \begin{equation*}\begin{cases}\partial_t \langleΨ\rangle = Δ\langleΨ\rangle +\dot{B}\, , \quad t\in [0,1], \ x\in \mathbb{R},\\ \langleΨ\rangle_0=0\, ,\end{cases}\end{equation*} when $\dot{B}$ is a very \emph{rough space-time fractional noise}. The discretization procedure is divised into three steps: $(i)$ regularization of the noise through a mollifying-type approach; $(ii)$ discretization of the (smoothened) noise as a finite sum of Gaussian variables over rectangles in $[0,1]\times \mathbb{R}$; $(iii)$ discretization of the heat operator on the (non-compact) domain $[0,1]\times \mathbb{R}$, along the principles of Galerkin finite elements method. We establish the convergence of the resulting approximation to $\langleΨ\rangle$, which, in such a specific rough framework, can only hold in a space of distributions. We also provide some partial simulations of the algorithm.

math.PR↗
arXiv2015

Coupling of individual quantum emitters to channel plasmons

Efficient light-matter interaction lies at the heart of many emerging technologies that seek on-chip integration of solid-state photonic systems. Plasmonic waveguides, which guide the radiation in the form of strongly confined surface plasmon-polariton modes, represent a promising solution to manipulate single photons in coplanar architectures with unprecedented small footprints. Here we demonstrate coupling of the emission from a single quantum emitter to the channel plasmon polaritons supported by a V-groove plasmonic waveguide. Extensive theoretical simulations enable us to determine the position and orientation of the quantum emitter for optimum coupling. Concomitantly with these predictions, we demonstrate experimentally that 42% of a single nitrogen vacancy centre emission efficiently couples into the supported modes of the V-groove. This work paves the way towards practical realization of efficient and long distance transfer of energy for integrated solid-state quantum systems.

physics.optics↗
arXiv2014

Fast optical modulation of the fluorescence from a single NV centre

The much sought after optical transistor --the photonic counterpart of the electronic transistor-- is poised to become a central ingredient in the development of optical signal processing. The motivation for using photons rather than electrons not only comes from their faster dynamics but also from their lower crosstalk and minor environmental decoherence, which enable a high degree of integration and the realization of quantum operations. A single-molecule transistor has been recently demonstrated at cryogenic temperatures. Here, we demonstrate that a single NV centre at room temperature can operate as an optical switch under non-resonant CW illumination. We show optical modulation of more than 80% and time response faster than 100 ns in the green-laser-driven fluorescence signal, which we control through an independent near-infrared (NIR) gating laser. Our study indicates that the NIR laser triggers a fast-decay channel of the NV mediated by promotion of the excited state to a dark band. This simple concept opens a new approach towards the implementation of nanoscale optical switching devices.

physics.optics↗
arXiv2012

Plasmonic Nanoparticle Networks for Light and Heat Concentration

Self-assembled Plasmonic Nanoparticle Networks (PNN) composed of chains of 12-nm diameter crystalline gold nanoparticles exhibit a longitudinally coupled plasmon mode cen- tered at 700 nm. We have exploited this longitudinal absorption band to efficiently confine light fields and concentrate heat sources in the close vicinity of these plasmonic chain net- works. The mapping of the two phenomena on the same superstructures was performed by combining two-photon luminescence (TPL) and fluorescence polarization anisotropy (FPA) imaging techniques. Besides the light and heat concentration, we show experimentally that the planar spatial distribution of optical field intensity can be simply modulated by controlling the linear polarization of the incident optical excitation. On the contrary, the heat production, which is obtained here by exciting the structures within the optically transparent window of biological tissues, is evenly spread over the entire PNN. This contrasts with the usual case of localized heating in continuous nanowires, thus opening opportunities for these networks in light-induced hyperthermia applications. Furthermore, we propose a unified theoretical framework to account for both the non-linear optical and thermal near-fields around PNN. The associated numerical simulations, based on a Green s function formalism, are in excellent agreement with the experimental images. This formalism therefore provides a versatile tool for the accurate engineering of optical and thermodynamical properties of complex plasmonic colloidal architectures.

physics.optics↗
arXiv2010

A general framework for waves in random media with long-range correlations

We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this paper, we prove in particular that the asymptotic time-shift can be described in terms of non-Gaussian and/or multifractal processes.

math.PR↗
arXiv2008

Invariance principle, multifractional Gaussian processes and long-range dependence

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.

math.PR↗