Effective Optical Properties of Inhomogeneously Distributed Nanoobjects in Strong Field Gradients of Nanoplasmonic Sensors

Abstract

Accurate and efficient modeling of discontinuous, randomly distributed entities is a computationally challenging task, especially in the presence of large and inhomogeneous electric near-fields of plasmons. Simultaneously, the anisotropy of sensed entities and their overlap with inhomogeneous fields means that typical effective medium approaches may fail at describing their optical properties. Here, we extend the Maxwell Garnett mixing formula to overcome this limitation by introducing a gradient within the effective medium description of inhomogeneous nanoparticle layers. The effective medium layer is divided into slices with a varying volume fraction of the inclusions and, consequently, a spatially varying effective permittivity. This preserves the interplay between an anisotropic particle distribution and an inhomogeneous electric field and enables more accurate predictions than with a single effective layer. We demonstrate the usefulness of the gradient effective medium in FDTD modeling of indirect plasmonic sensing of nanoparticle sintering. First of all, it yields accurate results significantly faster than with explicitly modeled nanoparticles. Moreover, by employing the gradient effective medium approach, we prove that the detected signal is proportional to not only the nanoparticle size but also its size dispersion and potentially shape. This implies that the simple volume fraction parameter is insufficient to properly homogenize these types of nanoparticle layers and that in order to quantify optically the state of the layer more than one independent measurement should be carried out. These findings extend beyond nanoparticle sintering and could be useful in analysis of average signals in both plasmonic and dielectric systems to unveil dynamic changes in exosomes or polymer brushes, phase changes of nanoparticles, or quantifying light absorption in plasmon assisted catalysis.

Simultaneous Monitoring of Molecular Thin Film Morphology and Crystal Structure by X-ray Scattering

“…More rigorously speaking, the molecular islands with unequal volumes should be described by a spatially varying effective permittivity, i.e., index of refraction. However, such a complicated environment can be simplified by introducing a gradient effective medium approach (originating from the Maxwell Garett formula; see ref for more details). In this model, the randomly distributed DIP islands are substituted by several closed DIP layers with spatially varying effective refractive index, n eff DIP , in the direction normal to the substrate.…”

Quantitative Determination of the Surface Distribution of Supported Metal Nanoparticles: A Laser Ablation–ICP–MS Based Approach

“…Most of the above-mentioned strategies ideally lead to the homogeneous deposition of metal NPs [21], but physical sputtering and laser-induced direct deposition can generate non-homogeneous NP distributions [22,23], especially over large-sized supports. Variations in NPs' spatial loading are often intentionally induced, as they can positively affect optical and electronic properties of the composite material and, consequently, its performances for electrochemical and catalytic applications [23][24][25]. Analytical tools to quantitatively determine the spatial distribution of NPs over a given substrate are accordingly highly desirable.…”

Отражение Света От Плазмонных Пленок Золота И Серебра: Сравнение Эксперимента И Теории

“…Напыленные в вакууме ПМП (особенно после их термического отжига) можно представить в виде ансамбля наночастиц, самоорганизованных поверх сплошной металлической поверхности [13]. Ранее было показано [14][15][16][17][18][19][20], что расширенная теория Максвелла-Гарнетта вполне приемлема для соотнесения эффективной диэлектрической функции с подобной морфологией поверхности. Таким образом, анализ возможностей и ограничений разных моделей приводит к выбору расширенной теории Маквелла-Гарнета для моделирования процессов отражения света плазмонными металлическими пленками.…”