Wave Propagation in Linear Media | re-examined

];
PhiGradEvan[x_, t_, w_, k_, opts___Rule] :=
If[(Shape/.{opts}/.Options[Phi]) === Gauss,
Message[Phi::missingval],
PhiGradEvan[x,t,w,k,1,opts]];
(*-- outside the tunnel --*)
(* Note that in this case the spatial coordinate is inverted in the function calls
because of the reverse motion of the reflected wave. *)
PhiRef[x_, t_, w_, k_, n_?Positive, opts___Rule] :=
Module[{sh = Shape/. {opts}/.Options[Phi],
pt = PPoints/.{opts}/.Options[Phi]},
Switch[sh,
Rect,
RectTransTemp[RectRefPos,RectRefNeg,-x,t,w,k,opts] +
EvanTemp[RectRefEvan[-t,0,-x,0,w,k],RectConst[w,k],opts],
Tria,
TriaTransTemp[TriaRefPos,TriaRefNeg,-x,t,w,k,opts] +
EvanTemp[TriaRefEvan[-t,0,-x,0,w,k],TriaConst[w,k],opts],
Gauss,
Switch[pt,
Approximate, GaussTransTemp[GaussRefPos,GaussRefNeg,-x,t,w,k,n,opts] +
EvanTemp[GaussRefEvan[-t,Pi k/Sqrt[w],-x,-Pi k,w,k,n],
GaussConst[w,k,n],opts],
Truncate, GaussTransTruncTemp[GaussRefPos,GaussRefNeg,-x,t,w,k,n,opts] +
GaussEvanTruncTemp[GaussRefEvan[-t,Pi k/Sqrt[w],-x,-Pi k,w,k,n],
w,k,n,opts],
_, Message[Phi::invalidpart,pt]],
_,
Message[Phi::invalidshape,sh]
]
];
PhiRef[x_, t_, w_, k_, opts___Rule] :=
If[(Shape/.{opts}/.Options[Phi]) === Gauss,
Message[Phi::missingval],
PhiRef[x,t,w,k,1,opts]];
PhiInc[x_, t_, w_, k_, n_?Positive, opts___Rule] :=
Module[{sh = Shape/. {opts}/.Options[Phi],
pt = PPoints/.{opts}/.Options[Phi]},
Switch[sh,
Rect,
RectTransTemp[RectIncPos,RectIncNeg,x,t,w,k,opts] +
EvanTemp[RectIncEvan[-t,0,x,0,w,k],RectConst[w,k],opts],
Tria,
TriaTransTemp[TriaIncPos,TriaIncNeg,x,t,w,k,opts] +
EvanTemp[TriaIncEvan[-t,0,x,0,w,k],TriaConst[w,k],opts],
Gauss,
Switch[pt,
Approximate, GaussTransTemp[GaussIncPos,GaussIncNeg,x,t,w,k,n,opts] +
EvanTemp[GaussIncEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n],
GaussConst[w,k,n],opts],
Truncate, GaussTransTruncTemp[GaussIncPos,GaussIncNeg,x,t,w,k,n,opts] +
GaussEvanTruncTemp[GaussIncEvan[-t,Pi k/Sqrt[w],x,-Pi k,w,k,n],
w,k,n,opts],
_, Message[Phi::invalidpart,pt]],
_,
Message[Phi::invalidshape,sh]
]
];
PhiInc[x_, t_, w_, k_, opts___Rule] :=
If[(Shape/.{opts}/.Options[Phi]) === Gauss,
Message[Phi::missingval],
PhiInc[x,t,w,k,1,opts]];
Phi[x_, t_, w_, k_, n_?Positive, opts___Rule] :=
Which[t == 0 && x == 0 && (Shape/.{opts}/.Options[Phi]) === Rect, 0.5,
t < 0, 0,
x >= 0, PhiEvan[x,t,w,k,n,opts] + PhiTrans[x,t,w,k,n,opts],
x < 0, PhiInc[x,t,w,k,n,opts] + PhiRef[x,t,w,k,n,opts]];
Phi[x_, t_, w_, k_, opts___Rule] :=
If[(Shape/.{opts}/.Options[Phi]) === Gauss,
Message[Phi::missingval],
Phi[x,t,w,k,1,opts]];
PhiGrad[x_, t_, w_, k_, n_?Positive,opts___Rule] :=
If[x < 0 || t < 0 || x == 0 && t == 0, 0,
PhiGradEvan[x,t,w,k,n,opts] + PhiGradTrans[x,t,w,k,n,opts]];
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