how can I solve transcendental equation?

Question

Rizwan 2013-11-4

0
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https://ww2.mathworks.cn/matlabcentral/answers/104838-how-can-i-solve-transcendental-equation

回答： Walter Roberson 2013-11-4

I want to solve the given equation in matlab to find the value of beta but getting error. I am posting the code and error below.

Thanks in advance.

n1=1.77;
n2=1.45;
d=1e-6;
lambda = 1e-6;
ko = 2*pi/lambda;
A=(ko*n1)^2;
B=(ko*n2)^2;
syms beta;
s = 'sqrt(A-beta^2)*(d/2)*tan(sqrt(A-beta^2)*d/2)=sqrt(beta^2-B)*(d/2)';
solve (s);

Error:

Error using solve>processString (line 337) ' sqrt(A-beta^2)*(d/2)*tan(sqrt(A-beta^2)*d/2)=sqrt(beta^2-B)*(d/2) ' is not a valid expression or equation.

Error in solve>getEqns (line 267) eqns = processString(eqns, v, vc);

Error in solve (line 150) [eqns,vars,options] = getEqns(varargin{:});

Error in transcendetal (line 9) solve (s);