Coupled-mode theory of field enhancement in complex metal nanostructures

Abstract

We describe a simple yet rigorous theoretical model capable of analytical estimation of plasmonic field enhancement in complex metal structures. We show that one can treat the complex structures as coupled multi-pole modes with highest enhancements obtained due to superposition of high order modes in small particles. The model allows one to optimize the structures for the largest possible field enhancements, which depends on the quality factor of the metal and can be as high as for two spherical particles. The "hot spot"can occur either in the nano-gaps between the particles or near the smaller particles. We trace the optimum field enhancement mechanism to the fact that the extended dipole modes of larger particles act as the efficient antennas while the modes in the gaps or near the smaller particles act as the compact sub-wavelength cavities. We also show how easily our approach can be extended to incorporate large numbers of particles in intricate arrangements.

Analytical Model of Raman Enhancement by Metal Nanoparticles

“…To facilitate our calculation, we shall first establish the SP modes of a single metal nanosphere and their associated properties [20]. Under the electro-static approximation, a single metal nanosphere with a radius being placed in a dielectric media with the dielectric constant , supports infinite number of SP modes, each characterized by an associated Legendre polynomial of index ranging from 1 to with resonant frequency defined by where is the metal dielectric function.…”

“…The goal of this paper is to provide this simple explanation as well as to outline the ways for optimizing enhancement of PL and Raman in sensing applications. This work is based on a recently developed comprehensive model of optical properties enhancement by single and coupled metal nanoparticles [12][13][14][15][16][17][18][19][20], using which we have previously treated PL enhancement [15] by combining analytical models for light absorption [14] and emission [12,13] in the presence of isolated metal nanoparticles. The salient feature of our approach, often overlooked before, is inclusion of all the competing radiative and non-radiative processes leading to the conclusion that the attainable enhancement is above all dependent on the original efficiency of the given optical process.…”

Taking cascaded plasmonic field enhancement to the ultimate limit in silver nanoparticle dimers

“…In a recent study, Sun et al used a fully analytical coupled-mode model to investigate the optical properties of plasmonic metal dimers 11,12 . The optical field enhancement inside the small nanoparticle and in the gap between two nanoparticles was studied taking into account dipolar and multipolar plasmon resonances.…”

Explaining the Giant Difference in Surface Plasmon Enhancement of Fluorescence, Resonance and Non-Resonance Raman Scattering

“…In fact, both fluorescence and resonance Raman measurements are subject to quenching when the molecule is placed too close to the metal surface, such an effect, however, is completely absent from the normal nonresonant Raman process. In this work, we present an analytical model that reveals the physics behind the strikingly different orders of magnitude in enhancement that have been observed, provide a fundamental explanation for the quenching effect observed in fluorescence and resonance Raman but not in normal Raman, establish limits for attainable enhancement, and outline the path to optimization of all three processes.We extend a recently developed comprehensive model of enhancement of optical properties by metal nanoparticles [4,5] to include the effect of high order SP modes [6] and apply it to fluorescence, resonance and normal (non-resonance) Raman to demonstrate that emission into non-radiative higher order modes does quench fluorescence and to a lesser extent may quench resonance Raman scattering, while it has no measurable effect on non-resonance Raman. In fact, one can think of Raman process as fluorescence with extremely low efficiency.…”

“…We extend a recently developed comprehensive model of enhancement of optical properties by metal nanoparticles [4,5] to include the effect of high order SP modes [6] and apply it to fluorescence, resonance and normal (non-resonance) Raman to demonstrate that emission into non-radiative higher order modes does quench fluorescence and to a lesser extent may quench resonance Raman scattering, while it has no measurable effect on non-resonance Raman. In fact, one can think of Raman process as fluorescence with extremely low efficiency.…”