Wave Propagation in Linear Media | re-examined

RectRefPos[a_,b_,c_,d_,w_,k_][xi_] :=
RefCoeff[xi] * RectShapePos[w,xi] * OutOsc[a,b,c,d,xi];
RectRefNeg[a_,b_,c_,d_,w_,k_][xi_] :=
RefCoeff[xi] * RectShapeNeg[w,xi] * OutOsc[a,b,c,d,xi];
RectRefEvan[a_,b_,c_,d_,w_,k_][xi_] :=
RectRefPos[a,b,c,d,w,k][xi] *
(-1 + Exp[I 2 (Pi k/Sqrt[w] xi - Pi k)]);
RectIncPos[a_,b_,c_,d_,w_,k_][xi_] :=
RectShapePos[w,xi] * OutOsc[a,b,c,d,xi];
RectIncNeg[a_,b_,c_,d_,w_,k_][xi_] :=
RectShapeNeg[w,xi] * OutOsc[a,b,c,d,xi];
RectIncEvan[a_,b_,c_,d_,w_,k_][xi_] :=
RectIncPos[a,b,c,d,w,k][xi] *
(-1 + Exp[I 2 (Pi k/Sqrt[w] xi - Pi k)]);
(*-- Exponential Shape inside the tunnel --*)
GaussConst[w_,k_,n_] := k Sqrt[2 Pi / (w n Sqrt[2 Pi])];
GaussShapePos[w_,k_,n_,xi_] := Exp[-(Pi k (xi/Sqrt[w] - 1)/n)^2];
GaussShapeNeg[w_,k_,n_,xi_] := Exp[-(Pi k (-xi/Sqrt[w] - 1)/n)^2];
GaussTransPos[a_,b_,c_,d_,w_,k_,n_][xi_] :=
TunCoeff[xi] * GaussShapePos[w,k,n,xi] * TunOsc[a,b,c,d,xi];
GaussTransNeg[a_,b_,c_,d_,w_,k_,n_][xi_] :=
TunCoeff[xi] * GaussShapeNeg[w,k,n,xi] * TunOsc[a,b,c,d,xi];
GaussGradTransPos[a_,b_,c_,d_,w_,k_,n_][xi_] :=
TunCoeff[xi] * GaussShapePos[w,k,n,xi] * TunOsc[a,b,c,d,xi] *
I Sqrt[xi^2 - 1];
GaussGradTransNeg[a_,b_,c_,d_,w_,k_,n_][xi_] :=
TunCoeff[xi] * GaussShapeNeg[w,k,n,xi] * TunOsc[a,b,c,d,xi] *
(-I Sqrt[xi^2 - 1]);
GaussEvan[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussTransPos[a,b,c,d,w,k,n][xi];
GaussGradEvan[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussGradTransPos[a,b,c,d,w,k,n][xi];
(*-- Exponential Shape outside the tunnel --*)
GaussRefPos[a_,b_,c_,d_,w_,k_,n_][xi_] :=
RefCoeff[xi] * GaussShapePos[w,k,n,xi] * OutOsc[a,b,c,d,xi];
GaussRefNeg[a_,b_,c_,d_,w_,k_,n_][xi_] :=
RefCoeff[xi] * GaussShapeNeg[w,k,n,xi] * OutOsc[a,b,c,d,xi];
GaussRefEvan[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussRefPos[a,b,c,d,w,k,n][xi];
GaussIncPos[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussShapePos[w,k,n,xi] * OutOsc[a,b,c,d,xi];
GaussIncNeg[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussShapeNeg[w,k,n,xi] * OutOsc[a,b,c,d,xi];
GaussIncEvan[a_,b_,c_,d_,w_,k_,n_][xi_] :=
GaussIncPos[a,b,c,d,w,k,n][xi];
(*-- Templates for wave computations depending on the shape --*)
TriaTransTemp[fpos_, fneg_, x_, t_, w_, k_, opts___Rule] :=
Module[{a,b,c,d,o11,o12,o21,o22,o31,o32,
wp = WorkingPrecision/.{opts}/.Options[OscInt]},
a = -t;
b = N[Pi k/Sqrt[w],wp+2];
c = x;
d = N[-Pi k,wp+2];
o11 = QuadOffset[a, c,0];
o12 = QuadOffset[a,-c,0];
o21 = QuadOffset[a, b+c,d];
o22 = QuadOffset[a,-b-c,d];
o31 = QuadOffset[a, 2 b + c,2 d];
o32 = QuadOffset[a,-2 b - c,2 d];
(-(OscInt[fpos[a, 0, c,0,w,k],
QuadZero[a, c,0,o11],1,FunctionType->ZeroList,opts] +
224
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