How do I use the solve function to solve the following equation

Question

Poonam 2013-3-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/67568-how-do-i-use-the-solve-function-to-solve-the-following-equation

Here is my code. My aim is to solve for value beta using the following equations. I have used the solve function. But I get the following error The probem is that the equation fir beta is not being solved

Error using plot
Conversion to double from sym is not possible.
Error in proj (line 23)
plot(neff, lambda); 
clc;
clear all;
close all;
    lambda=1500;
    nm=1e-9;
  lambda=lambda*nm;
  c=3e8;
  w=c./lambda;
  width=20: 20:100;
  width=width.*nm
  ev=1240*nm;
  einf=3.7;
  wp=9.7*ev;
  gamma=.018*ev;
  emw=einf-(wp.*wp)./(w.*(w+gamma.*i))
    nd=1.46;
  ed=nd*nd;
  k0=2*pi./lambda;
    syms beta
  solve(emw.*sqrt(beta*beta-ed.*k0.*k0).*tanh(width.*sqrt(beta*beta-ed.*k0.*k0)./2)+ed.*sqrt(beta*beta-emw.*k0.*k0)==0)
  neff = beta./ k0;
  plot(w, real(neff));

I cant really figure out what I'm doing wrong. Thank you for the help.

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Answer 1

Walter Roberson 2013-3-18

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/67568-how-do-i-use-the-solve-function-to-solve-the-following-equation#answer_79011

在 MATLAB Online 中打开

You solve() but you do not assign the result to anything. Try

Beta = solve(emw.*sqrt(beta*beta-ed.*k0.*k0).*tanh(w.*sqrt(beta*beta-ed.*k0.*k0)./2)+ed.*sqrt(beta*beta-emw.*k0.*k0)==0, beta);
neff = Beta ./ k0;

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Poonam 2013-3-22

Beta = [ empty sym ]

Poonam 2013-3-22

在 MATLAB Online 中打开

but when I plot the eqn emw.*sqrt(beta*beta-ed.*k0.*k0).*tanh(w.*sqrt(beta*beta-ed.*k0.*k0)./2 and -ed.*sqrt(beta*beta-emw.*k0.*k0) they intersect. So I do not know what I'm doing wrong with the solve

width=linspace(20,100,100);
length(width)
width=width.*nm;
beta= linspace(5e5,5e7,100);
for i1= 1:100
  for i2= 1:100
      a1(i1,i2)= -ed.*sqrt(beta(i2).*beta(i2)-emw.*k0.*k0);
     a2(i1,i2)=emw.*sqrt(beta(i2).*beta(i2)-ed.*k0.*k0).*tanh(width(i1).*sqrt(beta(i2).*beta(i2)-ed.*k0.*k0)./2);
  end
end
 mesh(beta,width,real(a1));   
hold on;
 mesh(beta,width,real(a2));   
 xlabel('beta');
 ylabel('w');
 zlabel('eqn');