If you have the curve as computed points, see
doc interp1
Switch the normal X,Y meanings to interpolate with Y as the independent variable instead of X in this case. Also, NB: You'll need to do this in two separate calls, one with the values to the left and another with those to the right of the maximum as interp1 must have unique values for the interpolating function.
This will solve for the precise location; not necessarily integer. If you want the nearest index, then either a) round the above results or b) use
[~,ix]=min(abs(y-sqrt(2)/2*ymax));
Again you'll have to do the above piecewise accounting for the length of the subvectors in the returned indices as there's no guarantee the locations will be symmetric or the same on both sides except under very particular circumstances.
