Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures

摘要

Plasmonic structures are utilized in many applications ranging from bio-medicineudto solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods.udOne of these quantum effects is the tunneling, which is observed when two structuresudare located within a sub-nanometer distance of each other. At these small distancesudelectrons “jump" from one structure to another and introduce a path for electric currentudto flow. Classical equations of electrodynamics and the schemes used for solvingudthem do not account for this additional current path. This limitation can be liftedudby introducing an auxiliary tunnel with material properties obtained using quantumudmodels and applying a classical solver to the structures connected by this auxiliaryudtunnel. Early work on this topic focused on quantum models that are generated usinguda simple one-dimensional wave function to find the tunneling probability and assumeuda simple Drude model for the permittivity of the tunnel. These tunnel models areudthen used together with a classical frequency domain solver.udIn this thesis, a time domain surface integral equation solver for quantum correctedudanalysis of transient plasmonic interactions is proposed. This solver has severaludadvantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differentialudequation solvers, it only discretizes surfaces (reducing number of unknowns), enforcesudthe radiation condition implicitly (increasing the accuracy), and allows for time stepudselection independent of spatial discretization (increasing efficiency). The quantumudmodel of the tunnel is obtained using density functional theory (DFT) computations,udwhich account for the atomic structure of materials. Accuracy and applicability ofudthis (quantum corrected) time domain surface integral equation solver will be shownudby numerical examples.