Modeling the synchronization of plasmonic nanoparticles

In optical instrumentation, plasmonic nanoparticles, consisting of a metallic medium, have long been of interest due to their unique properties, including surface plasmon resonance. Under light, the electrons of these nanoparticles will excite and oscillate at consistent frequency. Though dielectric nanoparticles have no intrinsic rhythm themselves, this behavior can be transmitted to and synchronized with neighboring nanoparticles. Cubillos et al. modeled this synchronization using a Kuramoto-Sakaguchi model.

While the traditional Kuramoto model describes synchronization under symmetrical interactions between oscillators, this modified version considers asymmetric interactions under an additional phase-lag parameter.

“This analogy offered a way to interpret the dynamics in metal nanoparticle colloids and potentially explain the spectral amplification observed when carbon nanostructures are added,” author Fabián Cubillos said.

The authors developed a graph-based model in which each node corresponded to a metallic nanoparticle, and interactions between them depended on the propagation of their oscillations.

“This approach allowed us to identify the pathways of optical energy transport through the system,” Cubillos said.

Their network, amplification, frequency tuning, and laser driving were all interchangeable routes toward coherence. They found adding carbon nanoparticles could push the assembly across the synchronization threshold.

Unlike most other models, in which coupling and disorder are freely chosen, their model determined each parameter from measured optical properties. This allowed the model to be tested against an experimental spectrum.

“Unexpectedly, the absorbance band intensified as the carbon content increased, while its spectral position remained unchanged,” Cubillos said. “From a sensing perspective, this behavior is useful for quantifying molecular-level changes.”

Their findings ultimately indicate that graph theory, which remains underutilized in nanomaterials modeling, can provide us with a better understanding of collective optical phenomena in terms of a system’s parameters.

Source: “Tunable synchronization and energy transport networks in plasmonic-dielectric nanoparticle assemblies,” by Fabián C. Cubillos, J. Alejandro Menchaca-Rivera, Manuel Quijano, Henry Riascos, and Johan Duque, Journal of Applied Physics (2026). The article can be accessed at https://doi.org/10.1063/5.0350129 .