Wave Propagation in Linear Media | re-examined

8.2 Outline of the program structure
8.2 Outline of the program structure
Since we have to cope with a large variety of similar functions, we must adopt a modular
approach for the individual subroutines. This means that the integrands are combined from
several function modules following the aforementioned structure, which is the only possibility
to ensure consistency within the package and to provide comparatively easy extendability. A
reasonable implementation strategy involves three distinct hierarchical levels.
Driver modules provide the basic interface to the user. The most user-friendly of
them expects nothing more than the parameters required to compute the wave function
and an option de ning the shape of the initial waveform. Depending on the spatial
coordinate it then returns either the wave function inside the tunnel or the sum of the
incident and re ected parts on the outside. These partial solutions are computed in
turn by other driver modules that can also be accessed directly. All modules must take
into account that di erent waveforms may need di erent numbers of parameters (such
as the Gaussian wave packet, which requires an additional geometry parameter for the
variance of the distribution).
Quadrature modules are distinct for all waveforms. The reason for this is that the
number of exponential functions in the sum of equation (8.15) as well as the respective
coe cients as;i are di erent for each possible waveform. Furthermore, some of
the in nite integrals can be computed in di erent ways. So these modules are typically
implemented as waveform-dependent templates that need the more general part
ss( ) cr( ) of the integrand as input parameter. The they add the speci c functions
P m
i=1 as;i e j(gs;i( )+pr( )) and call the actual quadrature routine with the appropriate
options.
The only exception to this scheme is the computation of the evanescent part of the
integrals. As this involves only a single de nite integral, there is no point in dividing the
integrands like we do for the in nite integrals in order to meet the formal requirements
of our quadrature strategy. Hence there is only one template for this task, and the
whole integrand function is passed to this routine from the calling module. Because all
these routines are highly specialised, they are not made available to the user.
Function modules are the actual building blocks of the integrands. There are atomic
functions describing the shape- and region-dependent coe cients ss( ), cr( )aswell as
the constants Cs. These elements are then combined to form the integrands for the two
inde nite transmissive parts and the evanescent section of the integration range. These
functions, too, are internal to the package and cannot be accessed by the user.
For the triangular and Gaussian wave packet, the gradient of the wave function inside the
tunnel is also of interest for the computation of the energy density and nally the energy
velocity. These functions have not been included in the general framework, in that they
cannot be accessed from the same driver routine as the wave functions themselves. Although
the gradient functions share the quadrature modules of the plain wave computation, they use
separate driver and, of course, function modules.
197