ListDensityPlot and DensityPlot do not give the same results?

Question

I am plotting the same function using ListDensityPlot and DensityPlot but the output is different!
There are some points where the function is complex or pure imaginary where DensityPlotshow this region as White. However, ListDensityPlot show coloring in the same region.

mod = ParallelTable[
   With[{κ = 0.23}, {ky, ϵ, 
     Sqrt[-ky^2 + ϵ^2 + κ^2 - 
      Sqrt[ϵ^2 - 4 ky^2 κ^2 + 
       4 ϵ^2 κ^2]]}], {ky, -0.35, 0.35, 
    0.001}, {ϵ, 0, 0.2, 0.001}];
ListDensityPlot[Flatten[mod, 1]]  

With[{κ = 0.23}, 
 DensityPlot[
  Sqrt[-ky^2 + ϵ^2 + κ^2 - 
   Sqrt[ϵ^2 - 4 ky^2 κ^2 + 
    4 ϵ^2 κ^2]], {ky, -0.35, 0.35}, {ϵ, 
   0, .2}, PlotRange -> Full, Exclusions -> None, PlotPoints -> 50]]

Answer 1

The problem is that ListDensityPlot discards all of the complex valued entries, and then interpolates the remaining data. One possible workaround is to replace all the complex valued entries with some number, and then adjust the plot range so that the number is out of range. For instance:

With[{trunc = Replace[Flatten[mod, 1], _Complex -> -20., {2}]},
    ListDensityPlot[trunc, PlotRange -> {0, 1}]
]