Wave Propagation in Linear Media | re-examined

8.2 Outline of the program structure
Driver modules are named according to the scheme kPhijfNULL, Inc, Ref, Trans,
Evangk, depending on whether the function depends on the region and the propagation
direction or not.
Two options, Shape and PPoints, are provided to control the execution of the user accessible
modules. The allowed values of the latter depend on the waveform.
Shape 2fRect, Tria, Gaussg de nes the shape of the wave packet under consideration.
The default value is Tria.
PPoints 2 fApproximate, Zeros, Truncateg selects the way the integrals are evaluated.
Which one is applicable depends on the waveform. For triangular and rectangular
waves inside the tunnel, where the exponential functions have no polynomial arguments,
the partition points can be determined either using a polynomial approximation or by
computing the zeros of the integrand numerically. Outside the tunnel, the partition
points are exactly the zeros, anyhow, and this option is irrelevant.
For the Gaussian wave packet, on the contrary, it is possible not to use extrapolation
but to compute the integrals directly by truncating them at reasonably large abscissa
values. This is possible both inside and outside the tunnel and also for the evanescent
part of the wave. For the other shapes, the option is ignored for the evaluation of the
de nite integrals. The default value of this option is Approximate.
Beside these two options all other options of the quadrature function OscInt can be used.
They take, however, no in uence on the evaluation of the modules in the package but are
simply passed to the quadrature routine.
The list of arguments that have to be passed to the driver module comprises the spatial and
time coordinate X and T , the ratio between cut-o frequency and the signal frequency
and the number of wavelengths k that the initial wave packet spans. For Gaussian waves,
the geometry parameter n is needed, otherwise an error message will be generated. For all
other shapes, this additional parameter is not necessary and will be ignored. Following these
arguments, options may be given, like in the examples below.
Phi[x,t,w,k,Shape->Rect]
PhiInc[x,t,w,k,n,Shape->Gauss,PPoints->Truncate]
PhiRef[x,t,w,k,Shape->Tria,NSumTerms->30]
PhiEvan[x,t,w,k,Shape->Rect,WorkingPrecision->25]
PhiTrans[x,t,w,k,Shape->Tria,PPoints->Zeros]
PhiGrad[x,t,w,k,n,Shape->Gauss]
PhiGradTrans[x,t,w,k,Shape->Tria]
PhiGradEvan[x,t,w,k,Shape->Tria]
These examples are a comprehensive list of all available functions of the package.
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