Theoretical Studies of Plasmonic Effects in Organic Solar Cells - Organic Solar Cells: Materials and Device Physics - page 179

methods. For noble metals with plasmonic effects in the visible light range, such as
silver and gold, the complex refractive index has to be described by a large number of
summation terms in the Lorentz-Drude model [ 51 ] leading to longer calculation
time. However, for frequency-domain methods, one can directly employ an exper-
imentally tabulated refractive index of the dispersive materials. Another difficulty in
time-domain methods is to treat the periodic boundary condition particularly for the
oblique incidence caused by the anticausal property of the Floquet theorem. In most
places, unless a solar panel is mounted on an expensive tracking system, most of the
time, light is incident on the array obliquely. Hence, the ability of frequency-domain
methods to handle the case of oblique incidence is clearly an important advantage
over time-domain methods [ 52 ]. Moreover, time-domain methods suffer from
numerical dispersion and stability problems in contrast to frequency-domain
methods [ 53 , 54 ]. This drawback becomes more serious if a 3-dimensional large-
scale SC structure is investigated. A significant merit associated with time-domain
method is a broadband simulation in the solar spectrum of interest. The frequency-
domain method can employ the parallel computing technique to circumvent the
problem.
Integral equation methods versus differential equation methods. Differen-
tial equation methods involving finite-difference and finite-element algorithms
[ 54 , 55 ] can treat a variety of inhomogeneous boundary conditions conveniently.
The methods have a powerful ability to model the complex device structure of
OSCs incorporating the metallic gratings or nanoparticles. The produced matrix by
the differential equation methods is sparse due to the ''local'' differential operators
of Maxwell's equations or wave equations. The method consumes memory cost of
O ð N Þ and complexity of O ð N Þ per matrix-vector multiplication in Krylov subspace
iteration algorithm [ 55 , 56 ]. Moreover, multifrontal or multigrid methods [ 57 , 58 ]
can speed up the solution process of the differential equations. To simulate the
interaction between light and OSCs, an efficient absorption boundary condition, as
well as additional volume grids enclosing the OSC device, has to be adopted.
In comparison with differential equation methods, integral equation methods
[ 56 , 59 ] connect field components to equivalent currents by using ''global'' inte-
gral operators represented with the dyadic Green's functions. As a result, integral
equation methods always guarantee higher accuracy but lead to full dense matrix.
Fortunately, matrix-free fast algorithms [ 60 ], such as fast Fourier transform (FFT)
[ 61 , 62 ] and fast multipole methods [ 63 , 64 ], can significantly reduce the computer
resources occupied by the dense matrix. Thanks to the Green's tensor, the integral
equation methods automatically satisfy the radiation boundary condition but need
singularity treatments. In particular, the surface integral equation method having a
unique feature of surface triangulation produces much smaller unknowns. However,
the method can only be employed to analyze a homogenous or piecewise-
homogenous structure. For an arbitrary inhomogeneity or complex environment
encountered in plasmonic nanodevices, the near-field calculation by the SIE
method is hard to implement.
Mode-matching methods. Mode-matching method [ 59 , 65 ] is a commonly
used technique for the formulation of optical problems, especially for structures