Plasmonic structures are utilized in many applications ranging from biomedicine
to 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.
One of these quantum effects is the tunneling, which is observed when two structures
are located within a subnanometer distance of each other. At these small distances
electrons “jump" from one structure to another and introduce a path for electric current
to flow. Classical equations of electrodynamics and the schemes used for solving
them do not account for this additional current path. This limitation can be lifted
by introducing an auxiliary tunnel with material properties obtained using quantum
models and applying a classical solver to the structures connected by this auxiliary
tunnel. Early work on this topic focused on quantum models that are generated using
a simple onedimensional wave function to find the tunneling probability and assume
a simple Drude model for the permittivity of the tunnel. These tunnel models are
then used together with a classical frequency domain solver.
In this thesis, a time domain surface integral equation solver for quantum corrected
analysis of transient plasmonic interactions is proposed. This solver has several
advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential
equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces
the radiation condition implicitly (increasing the accuracy), and allows for time step
selection independent of spatial discretization (increasing efficiency). The quantum
model of the tunnel is obtained using density functional theory (DFT) computations,
which account for the atomic structure of materials. Accuracy and applicability of
this (quantum corrected) time domain surface integral equation solver will be shown
by numerical examples.
Date of Award  Oct 2016 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Hakan Bagci (Supervisor) 

 Plasmonics
 Timedomain
 Quantumtunneling
 Integralequation