Nanoscale optical energy concentration and focusing is crucial for many high-throughput nanomanufacturing applications, such as material processing, imaging and lithography. The use of surface plasmons has resulted in the rapid development of nanofocusing devices and techniques at spatial confinements as good as a few nanometers associated with strong nonlocal plasmonic response. However, operations of these plasmonic nanofocusing structures usually require extremely high optical energy density at nanoscale, which leads to intense structure heating and causes unreliable device functions and short device lifetimes. In many plasmonic applications, optical heating has become a very important issue, which has not been investigated intensively yet. In these structures, the ballistic transport and interface scattering of the energy carriers both become significant because the characteristic lengths of the devices are comparable to or smaller than the mean free paths of the carriers. A comprehensive model is desired to understand the heat generation and transport inside the plasmonic nanofocusing structures.

This work studied the electromagnetic and optothermal responses of plasmonic nanofocusing nanostructures. At the nanometer length scale, the local optical response and diffusive thermal model are no longer sufficient to describe the device optothermal response because of the strong interactions between energy carriers and the ballistic nature of carriers. Here, we used the hydrodynamic Drude model to consider the nonlocality of plasmonic response and calculate the heat generation inside the metallic nanostructures. Starting from Boltzmann transport equation, we derived the energy transport equations for both electron and phonon systems under the relaxation-time approximations. The obtained multi-carrier ballistic-diffusive model was used to study the non-equilibrium heat transports inside the structures. We assume that the ballistic electrons originate from boundaries and the electron-photon couplings inside the structure, experiencing out-scattering only in the material. The optically-generated “hot” electrons are considered as ballistic and are treated separately from the “ordinary” electrons which are in local thermal equilibrium and have significantly lower energies. Meanwhile, the electron-phonon couplings are considered under the non-equilibrium conditions between the electron and phonon systems. Using our model, we further investigated the transient optothermal responses of a one-dimensional (1D) plasmonic nanofocusing structure. In comparison to the diffusive transport description, our multi-carrier ballistic-diffusive model can more accurately describe the optothermal responses of the plasmonic nanofocusing structures which are crucial for predicting the performance and the lifetime of the plasmonic nanofocusing devices.

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