I'm trying find graphically the solutions of the intersection of the following functions.
d = 1;
κ = ΩH/(ΩH^2 - Ω^2);
ΩH = 1;
Ω = 1.05;
ContourPlot[
{Re[Tan[ki d] - 2 (ko ki)/(ki^2 - ko^2)] == 0, ko == (I ki)/Sqrt[1 + κ]},
{ki, -10, 10}, {ko, -10, 10},
LabelStyle ->
Directive[Black, {FontFamily -> "Latin Modern Roman", FontSize -> 20}],
FrameLabel -> {Subscript[k, i], Subscript[k, o]},
PlotLabel -> "1+κ<0",
PlotTheme -> "Scientific",
PlotPoints -> 200,
WorkingPrecision -> 100,
PerformanceGoal -> "Quality",
ImageSize -> 400,
Exclusions -> {ki == ko, ki == -ko, Cos[ki d] == 0}]
However, I don't know why there are a discontinuity of the orange function.