Plasmon coupling using eigenmode expansion and its sensing applications (2023)


The collective oscillations of surface electron in the metal nanoparticles are of immense interest for the researchers in every scientific background. This oscillation when with resonance with the incident source is known as localized surface plasmon resonance (LSPR). This LSPR can further be modified and used depending upon the need of any particular applications like optical antenna[1], [2], nano lenses[3], energy devices[4], biomedical applications[5], etc. These applications for a given metal nanoparticles are defined by the surface charge distribution, huge near field enhancement and focusing the light to the nanoscale[6], [7]. The morphology and the dielectric constant of the surrounding medium of the metal nanostructures is readily used for tunning the LSPR[8].

Further the interaction between these nanostructures is studied in detailed manner but still it’s difficult to clearly visualize all the coupling or hybrid plasmonic modes. Usually, the polarization angle of the incident electromagnetic wave defines the number and nature of plasmonic modes [9], [10] and for a well-defined perspective of these polarization dependent resonance scattering, the nature of plasmonic modes is very much essential for the interacting system. These plasmonic hybrid modes are additionally controlled by the interparticle distance between the nanostructure which dies off after precise nanometric distance. Hence, to regulate the coupling between any nanostructure the interparticle gap is manipulated depending upon certain scaling rules defined by P.K. Jain et. al[11]. Also, when nanostructures interact, an extended plasmonic nature appears due to excitation of the entire lattice typically determined by the eigenmodes and these additional plasmonic modes relates this system to the properties of metamaterials[12].

In this study, we presented the optical response of various gold nanostructure with different shape and sizes as shown in Fig. 1a and c. For interaction study, a generalized Au-Au dimer is considered with 10nm particle dimension. The interparticle gap variation calculation via scattering spectra of these particles helps to find out the universal coupling decay scaling rule. Different polarization effects were studied using surface charge distribution for various angle of incidence of the EM waves and to justify the various plasmonic coupling modes for this system, the eigenmode expansion method is used which provides the optical and degenerated modes. At last, the refractive index (RI) sensing for the interacting nanostructures were calculated and studied by sensitivity factor and Figure of Merit (FoM).

Section snippets

Theoretical simulation

Herein our study we have used Boundary Element Method (BEM) based MATLAB toolbox MNPBEM17[13], [14]. In this method the surface of a metal nanoparticle is discretized into the boundary element and on these boundary interfaces between system and surrounding the Maxwell equations are solved (using boundary condition). As only the surface takes part in discretization so the time and space required for any kind of simulation is very less compared with other methods like FDTD (Fourier difference

Plasmonic response of gold nanostructures

The interaction of plane wave with single spherical metal nanoparticles produces localized surface plasmons resonance (LSPR) at particular wavelength depending upon their size and environment. Fig. 1(a, c) represent the different morphologies of Au nanostructures utilized for calculating their respective scattering cross-section spectra, as displayed in Fig. 1b, d. The shape of Au nanostructures considered here are sphere, disc, cube and triangle (all having dimensions 10nm) to study the


Herein our presented studies we simulated the optical response of Au - Au dimer. The scattering spectra calculated for the dimer with various interparticle gap provides the universal scaling rule for the plasmonic coupling decay up to an interparticle gap of 0.2 times the particle dimensions. The electric field direction depended spectra further stretches the angle of incidence effect on the surface charge distribution and more comparable results to the experiment data (as experimental spectra

Author contributions

All authors together design the problem. AD with help of GJ and ST simulated all the results using MATLAB. AD wrote and revised the manuscript with an editorial contribution from PSK.

CRediT authorship contribution statement

Annu Dahiya: Conceptualization, Methodology, Software, Writing – original draft. Gaurav Jalendra: Data curation. Suraj Tamta: Visualization. Pandian Senthil Kumar: Supervision, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


AD, GJ and ST acknowledges the Council of Scientific & Industrial Research (CSIR), Govt. of India for NET-SRF and NET-JRF fellowships. The authors are thankful to the University of Delhi for the infrastructure to carry out the research work. The authors are grateful to IoE, DU for-research funding (IoE/2021/12/FRP).

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