I made a ContourPlot of a fuction at the points where its value is zero. So my command is written as follows:

ContourPlot[(TE[n, k0, \[Beta]] //. {\[Beta] -> k0*neff, n -> 0}) == 0, {k0, 2 \[Pi]/3, 2 \[Pi]/0.5}, {neff, n2*(1 + \[Delta]),n1*(1 - \[Delta])}, PlotPoints -> 100]

And so I have a 2D plot of several lines, given the condition I set. The code and plot look like this: contour lines of TE function where it equals zero

I want to extract the first line of this plot to use it in another plot. I don't need its coordinates and I don't want any region between lines, I just want to restrict the quantity of lines in this plot to only one, specifically, the first one, since my interest lies in the first set of values for which my function is zero. I've tried using the "Contour" option but it seems to work only for contour plots with no restrictions. In my case, it worked when I plotted the contours of the function with no conditions, but given the condition that it should equals zero, the Contour option makes no difference at all in this case.

Thanks in advance for any help!

Edit: for clarity's sake here goes the definition of my function and all the parameters involved in it:

definition of TE function and the parameters used

  • 2
    $\begingroup$ what are TE, n1 and n2? $\endgroup$
    – kglr
    Nov 16, 2018 at 20:18
  • $\begingroup$ TE is called the dispersion relation, which is the characteristic function for the eletromagnetic waves in a optical fiber. A eletromagnectic wave is guided in the optical fiber when k0 and beta are so that TE equals zero. The variable "n" of the function indicates the order of the Bessel functions involved. So for each "n" there is a set of k0 and beta for which TE is zero and therefore we have a "physical solution" of the problem. n1 and n2 are the refractive indexes previously defined as n1=1.45 and n2=1. $\endgroup$ Nov 16, 2018 at 22:28
  • $\begingroup$ If you provide the mathematica code(!) @kglr asked for your chance of getting a helpful answer would increase dramatically! $\endgroup$ Nov 17, 2018 at 13:34
  • $\begingroup$ oh ok, sorry, i'm new here. didn't know how to add the code in the comment section. i'll edit my question. $\endgroup$ Nov 17, 2018 at 15:31

1 Answer 1


As an example (because OP doesn't provide all info...) here is a picture with three diffeerent lines:

pic = ContourPlot[{(y == 1/x ) , (y - 1/2 == 1/(x - 1/2)), (y - 1 == 1/(x - 1))  }, {x, 0, 4}, {y, 0, 4}]

enter image description here

Now let's try to get the first line of the plot

points = pic[[1, 1]]; (* all points*)
lines = Level[Cases[pic, _Line, Infinity], {-2}] (* all lines *)

plot of first line lines[[1]]

Show[pic,Graphics[{Red, Opacity[.2], Thickness[.025],Line[points[[lines[[1]]]]]}]]

enter image description here

  • $\begingroup$ it was very helpful! seting the opacity to 1 and the colour of the line to white, i could "remove" all of the lines i don't want in the plot. but i didn't quite understand what's happening on "lines" command, if you could comment on that i would be very grateful. but my problem is solved, anyways. thanks :) $\endgroup$ Nov 17, 2018 at 16:14
  • $\begingroup$ If you look into the picture (??pic) you see a GraphicsComplex. pic[[1,1]] gives you all the plotted points. In the listed GraphicsComplex you find several (in the example 3) commands beginning with Line[...]` My code lines=...just extracts the pointnumbers of these Lines. $\endgroup$ Nov 17, 2018 at 16:21

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