Extra solutions using fimplicit

Question has three parts

1) For a slab waveguide, I have been trying to obtain Dispersion plot like this:

2) So, I wrote a code using fimplicit and some well-chosen parameters:

function main
fimplicit (@(x,y)f(x,y),[0 10])
end
function fun = f(x,y)
nc=1.45;    %cladding
nf=1.5;
ns=1.4;    %substrate
   h=5;  %width of waveguide
   beta=sqrt(x^2*nf^2-y.^2);
   gammas=sqrt(beta.^2-x^2*ns^2);
   gammac=sqrt(beta.^2-x^2*nc^2);
   z=sin(h*y);
   %TE mode
fun=z-cos(h*y)*(gammac+gammas)./(y-gammas.*gammac./y);
   %TM mode
   %b=(nf^2*gammas/ns^2+nf^2*gammac/nc^2)./(kappa-gammas.*gammac./kappa*nf^4/nc^2/ns^2);
%fun = ((3*I2).^(n/2)).* (an1 + an2 + an3) - (2*(189.32)^8);
end

It produced:

3) Now to verify the correctness of this plot, I took an example from a book for x=according to which (,0.55), (,1.2),(,1.65),(,2.15)should be data points in dispersion curve. In plot above, corresponding to x=, there are 5 values with the zig-zag line being unwanted one, why is this zig-zag spoiling the diagram ?