Wave Propagation in Linear Media | re-examined

8 Application of the quadrature routine
OscInt[fneg[a, 0,-c,0,w,k],
QuadZero[a, -c,0,o12],1,FunctionType->ZeroList,opts]) +
(OscInt[fpos[a, b, c,d,w,k],
QuadZero[a, b +c,d,o21],1,FunctionType->ZeroList,opts] +
OscInt[fneg[a,-b,-c,d,w,k],
QuadZero[a,-b -c,d,o22],1,FunctionType->ZeroList,opts])
) RectConst[w,k]
];
The second possibility to compute this integral is not to use the approximate partitioning
strategy but employ the exact zeros for this purpose. Since we do not need this module for
any other function than the one inside the tunnel, we need not write it as a template. So we
pass only the parameters of the wave to the module but keep the names of the integrands
xed. This time we call the quadrature routine without a value for the option FunctionType
because it defaults to Argument which is exactly what we want in order to compute the zeros
numerically. The rest of the module is the same as the previously discussed version.
RectTransExact[x_, t_, w_, k_, opts___Rule] :=
Module[fa,b,c,d,
wp = WorkingPrecision/.foptsg/.Options[OscInt]g,
a = -t;
b = N[2 Pi k/Sqrt[w],wp+2];
c = x;
d = N[-2 Pi k,wp+2];
(-(OscInt[RectTransPos[a, 0, c,0,w,k],
PhiArg[a, 0, c,0],1,opts] +
OscInt[RectTransNeg[a, 0,-c,0,w,k],
PhiArg[a, 0,-c,0],1,opts]) +
(OscInt[RectTransPos[a, b, c,d,w,k],
PhiArg[a, b, c,d],1,opts] +
OscInt[RectTransNeg[a,-b,-c,d,w,k],
PhiArg[a,-b,-c,d],1,opts])
) RectConst[w,k]
];
The template for the calculation of the evanescent part of the wave is di erent. First, we
do not split the integrand and thus have only one call of the integration routine. Second,
as we use the built-in Mathematica function NIntegrate, we must set a number of options
according to the values given by the user. As method for the evaluation of this de nite integral
we choose again DoubleExponential. A third di erence is that this module can be used for
all waveforms and therefore the waveform-dependent constant must be passed to the module
as an argument.
EvanTemp[f_, const_, opts___Rule] :=
Module[fwp = WorkingPrecision/.foptsg/.Options[OscInt],
ag = AccuracyGoal/. foptsg/.Options[OscInt],
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