Theory of Multiple Scattering Enhanced Single Particle Plasmonic Sensing

Abstract

Methods to increase the light scattered from small particles can help improve the sensitivity of many sensing techniques. Here, we investigate the role multiple scattering plays in perturbing the scattered signal when a particle is added to a random scattering environment. Three enhancement factors, parametrizing the effect of different classes of multiple scattering trajectories on the field perturbation, are introduced and their mean amplitudes explored numerically in the context of surface plasmon polariton scattering. We demonstrate that there exists an optimum scatterer density at which the sensitivity enhancement is maximized, with factors on the order of 102 achievable. Dependence of the enhancement factors on scatterer properties are also studied.

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

“…The statistics of this quantity are explored in more detail in Ref. [48], but here we note that in the low loss case, |γ 1,3 | are very different from | γ 1,3 |, by up to two orders of magnitude, whereas in the high loss case, the quantities are similar in value. Importantly, the low loss case allows for mean total amplitude enhancements |γ 1 γ 2 γ 3 | > 1, implying that multiple scattering increases the sensitivity, quite significantly, for a wide range of densities, whereas in the high loss case, multiple scattering only acts to decrease sensitivity on average.…”

“…For the low loss case, long range scattering paths play a significant role as is discussed further in Ref. [48].…”

“…For example, correlations present in the speckle patterns have been used for refractive index sensing, spectrometry and imaging [39][40][41][42]. Speckle patterns generated by disordered multiple scattering environments have also been shown to depend on the properties of individual scatterers [43,44], such as their position, effective charge or orientation [45][46][47], whilst also providing enhanced sensitivity as compared to single scattering environments [48]. Approaches to extract the position of a single scatterer accounting for multiple scattering effects have thus been developed, for example based on diffusive models of light propagation [49] or extension of single scattering holography localization techniques [50,51].…”

“…To address this question, in Sections II A and II B we first derive three enhancement factors, arising from three distinct categories of multiple scattering paths, which describe the effect of multiple scattering on the electric field perturbation caused by the presence of an additional analyte particle. We recently studied the amplitude of these enhancement factors in the context of multiple scattering of SPPs [48] by randomly distributed scatterers on a metal surface, however here we study the full probability distribution of the enhancements on the complex plane, including phase effects. Approximate analytic results for the mean enhancement factors are derived in Section II C, before numerical results are given in Section III.…”

“…The other significant difference between the low and high loss cases is in the mean of the absolute value of the enhancement factors (Fig.3(d)). The statistics of this quantity are explored in more detail in Ref [48],. but here we note that in the low loss case, |γ 1,3 | are very different from | γ 1,3 |, by up to two orders of magnitude, whereas in the high loss case, the quantities are similar in value.…”