File:Bragg mirror vs number of layers.gif

c = 3 10^8; (*speed of light*)

M[n_, k_, d_] := {{Cos[n k d], I c/n Sin[n k d]}, {I n/c Sin[n k d], Cos[n k d]}}; (*transfer matrix*)

Mi[n_, k_, d_] := {{Cos[d k n], -((I c Sin[d k n])/n)}, {-((I n Sin[d k n])/c), Cos[d k n]}}; (*Inverse of a transfer matrix*)

t[m_, n0_, n2_] := (2 n0/c)/(n2/c m[[1, 1]] - (n0 n2)/c^2 m[[1, 2]] - m[[2, 1]] + n0/c m[[2, 2]]); (*transmission coefficient*)

d = 0.4 10^-6; (*layer thickness in m*)
nstep = 1500;
\[Omega]min = 405. 10^12;
\[Omega]max = 790. 10^12;
dimmax = 45; (*number of layers in the Bragg mirror*)

p0 = Reap[For[nlayers = 0, nlayers <= 35, nlayers++,
      s = Join[Table[1., 10], Table[If[EvenQ[j], 1.5, 2.5], {j, 1, nlayers}], Table[1., dimmax - nlayers - 10]];(*Reflective indices of each layer (including some space to show the pulse arrive*)
      dim = Dimensions[s][[1]];
      trasm = Reap[For[\[Omega] = \[Omega]min, \[Omega] <= \[Omega]max, \[Omega] = \[Omega] + (\[Omega]max - \[Omega]min)/nstep,           
           tm = Apply[Dot, Table[M[s[[j]], \[Omega]/c, d], {j, 1, dim}]];
           Sow[N[t[tm, 1, 1]] ];
           ];][[2, 1]];
      field = trasm; (*Field at the last interface*)
      sexpand = 5; (*increase spatial resolution*)
      s2 = Flatten@Table[Table[s[[j]], sexpand], {j, 1, dim}];
      freq = Table[j, {j, \[Omega]min, \[Omega]max, (\[Omega]max - \[Omega]min)/nstep}];
      fn = Transpose[{field, field/c}];
      tmp0 = fn;
      ssm = Reap[For[i = dim*sexpand, i > 0, i--,
           tmp = Table[((Mi[s2[[i]], freq/c, d/sexpand])[[All, All, j]].tmp0[[j]]), {j, 1, nstep}];
           Sow[tmp[[All, 1]]];
           tmp0 = tmp;
           ];][[2, 1]];
      Sow@Grid[{
         {ListPlot[Abs[trasm]^2, Joined -> True, 
           DataRange -> {\[Omega]min, \[Omega]max}, 
           AspectRatio -> 1/2, ImagePadding -> {{40, 10}, {5, 0}}, 
           ImageSize -> {250, UpTo[250]}, PlotStyle -> {Thick, Black},
            Axes -> False, Frame -> True, 
           FrameTicks -> {{{0, 0.5, 1}, None}, {None, None}}, 
           FrameStyle -> {Directive[Thick, Gray]}, 
           FrameLabel -> {None, "T"}, Ticks -> {None, Automatic}, 
           LabelStyle -> {Black, Bold}, PlotRange -> {0, 1.05}]
          , ""
          }, {
           ArrayPlot[Abs[ssm]/1.5, AspectRatio -> 1, 
           ColorFunction -> "SunsetColors", 
           ColorFunctionScaling -> False, Frame -> True, 
           FrameTicks -> {{None, None}, {Automatic, None}}, 
           DataRange -> {{\[Omega]min, \[Omega]max}, {0, 
              d*Dimensions[s][[1]]}}, 
           ImagePadding -> {{40, 10}, {35, 0}}, ImageSize -> 250, 
           FrameLabel -> {None, "\[Omega]"}, 
           LabelStyle -> {Black, Bold}]
          ,
           BarLegend[{"SunsetColors", {0, 1}}, 
           LegendLabel -> Placed["|E|", Right], LegendMargins -> 0, 
           Ticks -> None, LabelStyle -> Directive[Bold]]
          }
         }, Alignment -> Top]
      ];][[2, 1]];
ListAnimate[p0]

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