begin{tikzpicture}
begin{axis}[
width=0.75textwidth,
height=0.5textwidth,
xmin=0, xmax=29000,
ymin=-10,ymax=10,
xlabel={$k$},
xlabel near ticks,
ylabel near ticks,
restrict y to domain=-11:11,
restrict x to domain=0:24000,
samples=1000,
axis x line=center,
axis y line=left,
scaled ticks=false, tick label style={/pgf/number format/fixed,
      /pgf/number format/1000 sep = thinspace }
]

defnf{1.50}
defns{1.45}
defnc{1.40}
defd{0.0005}
deflamda{0.0001}
defk{2*pi/lamda}

addplot[name path global=Aymm] gnuplot [domain=1:25000]{
 ((sqrt((sqrt(((2*pi/lamda)^(2)*nf^(2))-x^(2)))^(2)-((2*pi/lamda)^(2)*ns^(2))))+(sqrt((sqrt(((2*pi/lamda)^(2)*nf^(2))-x^(2)))^(2)-((2*pi/lamda)^(2)*nc^(2)))))/((x-(sqrt((sqrt(((2*pi/lamda)^(2)*nf^(2))-x^(2)))^(2)-((2*pi/lamda)^(2)*ns^(2)))*(sqrt((sqrt(((2*pi/lamda)^(2)*nf^(2))-x^(2)))^(2)-((2*pi/lamda)^(2)*nc^(2))))/x)))
     };

addplot[magenta, name path global=Symm] gnuplot [domain=1:25000]{ tan(d*x)};

draw[name intersections={of=Aymm and Symm,total=t,name=j}]
    foreach s in {1,...,t}{(j-s) node[circ](as){s}};
end{axis}
end{tikzpicture}

pgfextra{
    pgfextractx{len}{pgfpointdiff{pgfplotspointaxisxy{0}{0}}{pgfpointanchor{j-s}{center}}}
    pgfextractx{plotwidth}{pgfpointdiff{pgfplotspointaxisxy{getvalue{xmin}}{0}}%
    {pgfplotspointaxisxy{getvalue{xmax}}{0}}}%
    pgfmathparse{len*(getvalue{xmax}-getvalue{xmin})/plotwidth}
    globalletmacroxpgfmathresult%
    xdefintsectX{pgfmathresult}%
}