No legends in parametric plot

plotting some descibing functions, I wondered why I don’t get any legends in my plot.

The describing functions (and options):

N1[a_] := (4 d)/(π a)
N2[a_] := (4 d)/π 1/(I ϵ + Sqrt[a^2 – ϵ^2])
N3[a_] := (4 d)/(π a) Sqrt[1 – (ϵ/a)^2] – I (4 d ϵ)/(π a^2)
N4[a_] := (4 d)/(π a) E^(-I ArcSin[ϵ/a])

opt = {d -> 1, ϵ -> 5}

and the ParametricPlot

ParametricPlot[{
(*{Re@N1[a],Im@N1[a]},*)
{Re[N2[a]], Im[N2[a]]},
{Re@N3[a], Im@N3[a]},
{Re@N4[a], Im@N4[a]}
} /. opt, {a, .001, 1000},
PlotRange -> All,
PlotPoints -> 1000,
MaxRecursion -> 15,
PlotLegends -> “Expressions”]

(The first function is out commented, because it has wired behavior. Bonus for the one who can explain it 😉 )

What I get is this:

Why are there no legends? Is it because of the userdefined functions?

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2

see parametricplot-and-plotlegends-dont-seem-to-cooperate
– Nasser
Jan 28 ’15 at 9:34

Thanks for the Accept.
– Mr.Wizard♦
Jan 29 ’15 at 8:00

– Phab
Jan 29 ’15 at 8:04

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1

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This is a variation of Plot draws list of curves in same color when not using Evaluate. By using /. the head of the first argument is ReplaceAll rather than a List, and the styling subroutine of ParametricPlot does not know what to do with it.

Make the substitutions part of the definitions and you get this:

N1[a_] := (4 d)/(π a) /. opt
N2[a_] := (4 d)/π 1/(I ϵ + Sqrt[a^2 – ϵ^2]) /. opt
N3[a_] := (4 d)/(π a) Sqrt[1 – (ϵ/a)^2] – I (4 d ϵ)/(π a^2) /. opt
N4[a_] := (4 d)/(π a) E^(-I ArcSin[ϵ/a]) /. opt

opt = {d -> 1, ϵ -> 5}

ParametricPlot[
{{Re@N2[a], Im@N2[a]},
{Re@N3[a], Im@N3[a]},
{Re@N4[a], Im@N4[a]}}, {a, .001, 1000}, PlotRange -> All, PlotPoints -> 1000,
MaxRecursion -> 15, PlotLegends -> “Expressions”]

+1 for the link to the topic with an explanation why it doesn’t work.
– Phab
Jan 29 ’15 at 8:02