PHYSICAL REVIEW B 102, 064209 (2020) Multipolar scattering of subwavelength interacting particles: Extraction of effective properties between transverse and longitudinal optical modes Cédric Blanchard, 1 , * Jean-Paul Hugonin, 2 Alima Nzie, 1 and Domingos De Sousa Meneses 1 1 CNRS, CEMHTI UPR3079, Univ. Orléans, F-45071 Orléans, France 2 Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau, France (Received 1 April 2020; revised 20 June 2020; accepted 4 August 2020; published 18 August 2020) The general concern of this investigation is the extraction of the effective electromagnetic properties of agglomerates of randomly located particles, which are small compared to the wavelength. The focus is on the spectral window ranging from the transverse phonon to the longitudinal phonon frequencies, in which resonances may be excited. In this frequency domain, it is shown that limiting the problem to bare dipole-dipole interactions leads to inaccurate calculations of the electromagnetic fields, resulting in a doubtful extraction of the effective properties. We perform the complete electromagnetic calculation by taking into account the higher multipole orders that are activated when the agglomerates are illuminated. Several results, which are not usually observed outside the frequency range highlighted here, are revealed by means of extensive numerical simulations. In particular, we evidence large deviations compared to the predictions provided by the effective medium theories, while we find that the volume of the microstructures (each one with a different internal geometry) that are used to average the fields must be unusually large to avoid a bias in the determination of the effective properties. Furthermore, the evolution of the incoherent component of the fields between the two optical phonon modes is investigated. DOI: 10.1103/PhysRevB.102.064209 I. INTRODUCTION The conceptual and fundamental issue of determining the effective refractive index of inhomogeneous media has at- tracted the attention of the scientific community for long; early quantitative discussions on this topic turn out to date back to the first part of the 19th century [1]. From a practical viewpoint, the knowledge of the effective refractive index n eff provides useful information, for example in the realm of heat transfer or in the propagation of light in random media, where its imaginary part is directly related to the absorption coefficient appearing in the radiative transfer equation or in the Beer-Lambert law. There is a wide range of applications lying in the determination of n eff , e.g., characterization of industrial nanopowders [2] or colloids [3], thermoradiative properties of foams for solar absorbers [4], etc. Several predicting models with different level of sophisti- cation exist. Let us mention the well-known Maxwell-Garnett (MG) [5] and Bruggeman [6] models, which are two formulas expressing the effective permittivity (ǫ eff = n 2 eff ) of a mixture in terms of the relative permittivities and volume fractions of the bare components. However, these last two quantities are in general insufficient to correctly describe the effective proper- ties of a mixture. Accordingly, other approximation methods that take into account further inputs, such as microstructural information [7], were developed. Another approach lies in the computation of the electromagnetic fields and in the obtention of the effective parameters by means of different techniques: * Corresponding author: cedric.blanchard@cnrs-orleans.fr e.g., (i) using the formula ǫ eff =〈D〉/〈E〉 where E and D are the electric and displacement fields, averaged over a volume that is representative of the inhomogeneous medium under study [8], (ii) averaging the electromagnetic field scattered by many spherical agglomerates (in all the realizations, the volume fraction is maintained constant while the position of the particles is varied) and comparing with the response of a homogeneous sphere for which the scattered field is provided by Mie’s theory [9], or (iii) calculating the reflection and transmission coefficients of an inhomogeneous slab consisting of a distribution of particles and comparing with the analytical coefficients that hold for a homogeneous slab [10]. The diffraction of an electromagnetic radiation by a single particle is a classic problem. So long as the size of the particle remains small compared to the wavelength, the diffracted field reduces to the first-order component of the expansion in terms of the vector spherical wave functions. In this case and if the host media is free space, it should be noted that the formula giving the oscillation amplitude exhibits a pole when the permittivity of the particle takes the value ǫ p =−2[11]. The particle experiences surface plasmon polariton resonances and the frequency at which this occurs is called the Fröhlich frequency ω F [12], accordingly given by ǫ p (ω F ) =−2. The case where two particles are involved provides an in- teresting simplified frame to understand the collective effects that may arise. This problem was largely investigated in the past, many contributions [13–15] are based on a T -matrix kind approach, which lies in a multipole expansion of the field around the scatterers and in the addition theorem that allows us to express the spherical harmonics about one origin in terms of those at other origins. 2469-9950/2020/102(6)/064209(12) 064209-1 ©2020 American Physical Society