arXiv subjects

Eric C. Le Ru

Publications and source records attributed to Eric C. Le Ru.

15 recordsLinked to original sources

arXiv2026

T-matrix representation of optical scattering response: Suggestion for a data format

The transition matrix, frequently abbreviated as T-matrix, contains the complete information in a linear approximation of how a spatially localized object scatters an incident field. The T-matrix is used to study the scattering response of an isolated object and describes the optical response of complex photonic materials made from ensembles of individual objects. T-matrices of certain common structures, potentially, have been repeatedly calculated all over the world again and again. This is not necessary and constitutes a major challenge for various reasons. First, the resources spent on their computation represent an unsustainable financial and ecological burden. Second, with the onset of machine learning, data is the gold of our era, and it should be freely available to everybody to address novel scientific challenges. Finally, the possibility of reproducing simulations could tremendously improve if the considered T-matrices could be shared. To address these challenges, we found it important to agree on a common data format for T-matrices and to enable their collection from different sources and distribution. This document aims to develop the specifications for storing T-matrices and associated metadata. The specifications should allow maximum freedom to accommodate as many use cases as possible without introducing any ambiguity in the stored data. The common format will assist in setting up a public database of T-matrices.

physics.optics↗

arXiv2023

Generalised coupled-dipole model for core-satellite nanostructures

Plasmonic core-satellite nanostructures have recently attracted interest in photocatalytic applications. The core plasmonic nanoparticle acts like an antenna, funnelling incident light into the near-field region, where it excites the smaller satellite nanoparticles with resonantly enhanced absorption. Computer simulations of the optical absorption by such structures can prove challenging, even with state-of-the-art numerical methods, due to the large difference in size between core and satellite particles. We present a generalised coupled-dipole model that enables efficient computations of light absorption in such nanostructures, including those with many satellites. The method accurately predicts the local absorption in each satellite despite being two orders of magnitude weaker than the absorption in the core particle. We assess the range of applicability of this model by comparing the results against the superposition $T$-matrix method, a rigorous solution of Maxwell's equations that is much more resource-intensive and becomes impractical as the number of satellite particles increases.

physics.optics↗

arXiv2021

Multiple scattering of light in nanoparticle assemblies: user guide for the TERMS program

We introduce TERMS, an open-source Fortran program to simulate near-field and far-field optical properties of clusters of particles. The program solves rigorously the Maxwell equations via the superposition T-matrix method, where incident and scattered fields are decomposed into series of vector spherical waves. TERMS implements several algorithms to solve the coupled system of multiple scattering equations that describes the electromagnetic interaction between neighbouring scatterers. From this formal solution, the program can compute a number of physically-relevant optical properties, such as far-field cross-sections for extinction, absorption, scattering and their corresponding circular dichroism, as well as local field intensities and degree of optical chirality. By describing the incident and scattered fields in a basis of spherical waves the T-matrix framework lends itself to analytical formulas for orientation-averaged quantities, corresponding to systems of particles in random orientation; TERMS offers such computations for both far-field and near-field quantities of interest. This user guide introduces the program, summarises the relevant theory, and is supplemented by a comprehensive suite of stand-alone examples in the website accompanying the code.

physics.comp-ph↗

arXiv2021

Mean path length inside non-scattering refractive objects

It has recently been argued that the geometric-optics mean path length of rays inside a refractive object under Lambertian illumination is independent of the scattering strength of the medium [Savo et al., Science 358, 765 (2017)]. We here show that it is in fact different in the case of zero-scattering. We uncover and explain the role of trapped ray trajectories in creating this unexpected discontinuity from zero- to low-scattering. This allows us to derive new analytic results for the zero-scattering mean path length of simple refractive shapes. This work provides a fresh perspective on the study of path length inside refractive objects, with possible applications in for example the study of scattering by large particles or the design of optical systems.

physics.optics↗

arXiv2021

Definition and properties of logopoles of all degrees and orders

Logopoles are a recently proposed class of solutions to Laplace's equation with intriguing links to both solid spheroidal and solid spherical harmonics. They share the same finite line singularity with the former and provide a generalization of the latter as multipoles of negative order. In [Phys. Rev. Res. 1, 033213 (2019)], we introduced and discussed the properties and applications of these new functions in the special case of axi-symmetric problems (with azimuthal index $m=0$). This allowed us to focus on the physical properties without the added mathematical complications. Here we expand these concepts to the general case $m\neq 0$. The chosen definitions are motivated to conserve some of the most interesting properties of the $m=0$ case. This requires the inclusion of Legendre functions of the second kind with degree $-m\leq n<m$ (in addition to the usual $n\geq |m|$) and we show that these are also related to the exterior spheroidal harmonics. We show that Logopoles can also be defined for $n\le m$, and discuss in particular logopoles of degree $n=-m$, which correspond to the potential of line segments of uniform polarization density.

math-ph↗

arXiv2019

Relationships between solid spherical and toroidal harmonics

We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity about the plane of the torus. The expansion coefficients are given in terms of a recurrence relation. As an example application we apply one of the expansions to express the potential of a charged conducting torus on a basis of spherical harmonics.

math-ph↗

arXiv2019

A new class of solutions to Laplace equation: Regularized multipoles of negative orders

We introduce a new class of solutions to Laplace equation, dubbed logopoles, and use them to derive a new relation between solutions in prolate spheroidal and spherical coordinates. The main novelty is that it involves spherical harmonics of the second kind, which have rarely been considered in physical problems because they are singular on the entire z axis. Logopoles, in contrast, have a finite line singularity like solid spheroidal harmonics, but are also closely related to solid spherical harmonics and can be viewed as an extension of the standard multipole ladder toward the negative multipolar orders. These new solutions may prove a fruitful alternative to either spherical or spheroidal harmonics in physical problems.

math-ph↗

arXiv2019

Laplace's equation for a point source near a sphere: improved internal solution using spheroidal harmonics

As shown recently [Phys. Rev. E 95, 033307 (2017)], spheroidal harmonics expansions are well suited for the external solution of Laplace's equation for a point source outside a spherical object. Their intrinsic singularity matches the line singularity of the analytic continuation of the solution and the series solution converges much faster than the standard spherical harmonic solution. Here we extend this approach to internal potentials using the Kelvin transformation, i.e. radial inversion, of the spheroidal coordinate system. This transform converts the standard series solution involving regular solid spherical harmonics into a series of irregular spherical harmonics. We then substitute the expansion of irregular spherical harmonics in terms of transformed irregular spheroidal harmonics into the potential. The spheroidal harmonic solution fits the image line singularity of the solution exactly and converges much faster. We also discuss why a solution in terms of regular solid spheroidal harmonics cannot work, even though these functions are finite everywhere in the sphere. We also present the analogous solution for an internal point source, and two new relationships between the solid spherical and spheroidal harmonics.

math-ph↗

arXiv2018

Quasistatic limit of the electric-magnetic coupling blocks of the $T$-matrix for spheroids

The $T$-matrix formally describes the solution of any electromagnetic scattering problem by a given particle in a given medium at a given wavelength. As such it is commonly used in a number of contexts, for example to predict the orientation-averaged optical properties of non-spherical particles. The $T$-matrix for electromagnetic scattering can be divided into four blocks corresponding physically to coupling between either magnetic or electric multipolar fields. Analytic expressions were recently derived for the electrostatic limit of the electric-electric $T$-matrix block $\mathbf T^{22}$, of prolate spheroids. In such an electrostatic approximation, all the other blocks were zero. We here analyse the long-wavelength limit for the other blocks ($\mathbf T^{21}$, $\mathbf T^{12}$, $\mathbf T^{11}$) corresponding to electric-magnetic, magnetic-electric, and magnetic-magnetic coupling respectively. Analytic expressions (finite sums) are obtained in the case of spheroidal particles by expressing the fields with solutions to Laplace's equation, expanding the fields in terms of spheroidal harmonics and applying the boundary conditions. Similar expressions are also presented for the auxiliary matrices in the extended boundary condition method, often used in conjunction with the $T$-matrix formalism.

physics.class-ph↗

arXiv2018

Approximate T-matrix and optical properties of spheroidal particles to third order in size parameter

We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P- and Q-matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e. dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X^3) and equivalent to the quasi-static limit or Rayleigh approximation. Expressions to order O(X^5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X^6). Orientation-averaged extinction, scattering, and absorption cross-sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally-friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly-used Rayleigh approximation.

physics.optics↗

arXiv2017

Electrostatic limit of the $T$-matrix for electromagnetic scattering: Exact results for spheroidal particles

The $T$-matrix, often obtained with Waterman's extended boundary condition method (EBCM), is a widely-used tool for fast calculations of electromagnetic scattering by particles. Here we investigate the quasistatic or long-wavelength limit of this approach, where it reduces to an electrostatics problem. We first present a fully electrostatic version of the EBCM/T-matrix method (dubbed ES-EBCM). Explicit expressions are then given to quantitatively express the long-wavelength limit of the EBCM matrix elements in terms of those of the ES-EBCM formalism. From this connection we deduce a number of symmetry properties of the ES-EBCM matrices. We then investigate the matrix elements of the ES-EBCM formalism in the special case of prolate spheroids. Using the general electrostatic solution in spheroidal coordinates, we derive fully analytic expressions (in the form of finite sums) for all matrix elements. Those can be used for example for studies of the convergence of the $T$-matrix formalism. We illustrate this by discussing the validity of the Rayleigh hypothesis, where analytical expressions highlight clearly the link with analytical continuation of series.

physics.class-ph↗

arXiv2016

Spheroidal harmonic expansions for the solution of Laplace's equation for a point source near a sphere

We propose a powerful approach to solve Laplace's equation for point sources near a spherical object. The central new idea is to use prolate spheroidal solid harmonics, which are separable solutions of Laplace's equation in spheroidal coordinates, instead of the more natural spherical solid harmonics. We motivate this choice and show that the resulting series expansions converge much faster. This improvement is discussed in terms of the singularity of the solution and its analytic continuation. The benefits of this approach are illustrated for a specific example: the calculation of modified decay rates of light emitters close to nanostructures in the long-wavelength approximation. We expect the general approach to be applicable with similar benefits to a variety of other contexts, from other geometries to other equations of mathematical physics.

physics.class-ph↗

arXiv2015

Modified optical absorption of molecules on metallic nanoparticles at sub-monolayer coverage

Enhanced optical absorption of molecules in the vicinity of metallic nanostructures is key to a number of surface-enhanced spectroscopies and of great general interest to the fields of plasmonics and nano-optics. Yet, experimental access to this absorbance has long proven elusive. We here present direct measurements of the intrinsic absorbance of dye-molecules adsorbed onto silver nanospheres, and crucially, at sub-monolayer concentrations where dye--dye interactions become negligible. With a large detuning from the plasmon resonance, distinct shifts and broadening of the molecular resonances reveal the intrinsic properties of the dye in contact with the metal colloid, in contrast to the often studied strong-coupling regime where the optical properties of the dye-molecules cannot be isolated. The observation of these shifts together with the ability to routinely measure them has broad implications in the interpretation of experiments involving resonant molecules on metallic surfaces, such as surface-enhanced spectroscopies and many aspects of molecular plasmonics.

physics.optics↗

arXiv2012

Radiative correction in approximate treatments of electromagnetic scattering by point and body scatterers

The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the scattering matrix ($S$-matrix) used in quantum mechanics and quantum field theory. Focusing on electromagnetic scattering, we highlight an alternative formulation of the $T$-matrix approach, based on the use of the reactance matrix or $K$-matrix, which is more suited to formal studies of energy conservation constraints (such as the optical theorem). We show in particular that electrostatics or quasi-static approximations can be corrected within this framework to satisfy the energy conservation constraints associated with radiation. A general formula for such a radiative correction is explicitly obtained, and empirical expressions proposed in earlier studies are shown to be special cases of this general formula. This work therefore provides a justification of the empirical radiative correction to the dipolar polarizability and a generalization of this correction to any types of point or body scatterers of arbitrary shapes, including higher multipolar orders.

physics.optics↗

arXiv2008

Guiding molecules with electrostatic forces in Surface Enhanced Raman Spectroscopy (SERS)

In Surface Enhanced Raman Scattering (SERS) the problem of drawing molecules to the places where surface plasmon resonance enhancements will produce signals is one of the most basic ones, and the initial obstacle to every application of the effect. We explore the possibility of using electrostatic forces as a means to "guide" charged molecules in solution toward SERS active substrates. We also show explicitly the possibility of selectively enhancing different types of dyes according to their charge, and we discuss briefly possible extensions for other applications where "electrostatic guiding" could be an option.

physics.chem-ph↗