How I can solve the equation :
$$R -\tan^{-1}[(m1/m3)*(k3/k1)] - \tan^{-1}[(m1/m2)*(k2/k1)]=0$$
I tried on it using findroot as following :
$$
F = 0.56;
w0 = 4*10^9*3.14;
wp = 10*10^9*3.14;
gama = 0.03*wp;
T = 0.03*w0;
e1 = -3.7;
m1 = -1;
e2 = 1;
m2 = 1;
e3 = -9.5;
m3 = 1;
w = 4.6*10^9*3.14;
c = 3*10^8;
k0 = w/c;
k1 = Sqrt[(k0^2*e1*m1) - b^2];
k2 = Sqrt[b^2 - (k0^2*e2*m2)];
k3 = Sqrt[b^2 - (k0^2*e3*m3)];
R = 3.45;
bbValue =
FindRoot[R - ArcTan[(m1/m3)*(k3/k1)] - ArcTan[(m1/m2)*(k2/k1)] , {b,0.5}]$$
But it give me an error :
The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.
Regards
b -> 2.34938*10^-13 - 3.75897 I}
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