How to plot transcendental equation?

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Vaswati Biswas
Vaswati Biswas 2021-11-5
评论： Vaswati Biswas 2021-11-7
I want to plot neff vs lambda graph following a analytical expression. But when I run my code it doesnot show me any error but also no graphical image is shown.Here I want to calculate the values of neff by varying the lambda following the expression given below.
My code is given below:
clc
clear all
close all
nf= 1.3;
ns=1.5;
nc=1;
rho=1;
hf=1.5;
lambda = 100:1:350;
m=1;
syms func(lambda,neff)
phi_c = - atand((nf/nc)^(2*rho)*sqrt ((neff^2-nc^2)/(nf^2-neff^2)));
phi_s = -atand((nf/ns)^(2*rho)*sqrt ((neff^2-ns^2)/(nf^2-neff^2)));
func(lambda,neff) = @(lambda,neff)(((2*pi/lambda)*(sqrt(nf^2-neff^2)*hf))+ phi_c + phi_s -(m*pi))==0;
ezplot(func)
Myouput is
How can I resolve the Problem? Kindly help.
  1 个评论
Paul
Paul 2021-11-5
Are you sure that phi_c/s should be using atand() and not atan() ?
Are there any values of neff for which phi_c and phi_s are both real? It looks like phi_c is real for nc < abs(neff) < nf (1 < abs(neff) < 1.3) but those values of neff result in neff^2 - ns^2 < 0.

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采纳的回答

Sulaymon Eshkabilov
Here is how it can be solved and plotted:
clc
clearvars
close all
nf= 1.3;
ns=1.5;
nc=1;
rho=1;
hf=1.5;
lambda = 100:350;
m=1;
syms neff
phi_c = - atand((nf/nc)^(2*rho)*sqrt ((neff^2-nc^2)/(nf^2-neff^2)));
phi_s = -atand((nf/ns)^(2*rho)*sqrt ((neff^2-ns^2)/(nf^2-neff^2)));
NEFF = zeros(size(lambda));
for ii=1:numel(lambda)
Eqn = (((2*pi./lambda(ii))*(sqrt(nf^2-neff^2)*hf))+ phi_c + phi_s -(m*pi))==0;
NEFF(ii)=double(vpasolve(Eqn));
end
%%
plot(lambda, real(NEFF), 'r-o', 'DisplayName', 'neff: real part'), hold on
plot(lambda, imag(NEFF), 'b-d', 'DisplayName', 'neff: imag part'), hold on
legend; grid on
  5 个评论
显示 3更早的评论
Sulaymon Eshkabilov
Sulaymon Eshkabilov 2021-11-7
Note that you're calling a different variable name NEFF1(ii)=double(vpasolve(Eqn)). That should be NEFF(ii)=double(vpasolve(Eqn))
The code does not have any problem with nf=2 and runs ok. It produces solutions correctly.
Vaswati Biswas
Vaswati Biswas 2021-11-7
I am sorry sir but even if I am calling NEFF(ii)=double(vpasolve(Eqn)) still the same error is coming when I put nf = 2. I feel as tan inverse is involved in the equation therefore it is not taking all the values. I even tried to run the code by putting -pi +0.0001 still I am getting the same error.
"Unable to perform assignment because the left and right sides have a different number of elements."
Error in (line 17)
NEFF(ii)=double(vpasolve(Eqn));

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更多回答（1 个）

Sulaymon Eshkabilov
Ran in:
clc
clearvars
close all
nf= 1.3;
ns=1.5;
nc=1;
rho=1;
hf=2;
lambda = 100:350;
m=1;
syms neff
phi_c = - atand((nf/nc)^(2*rho)*sqrt ((neff^2-nc^2)/(nf^2-neff^2)));
phi_s = -atand((nf/ns)^(2*rho)*sqrt ((neff^2-ns^2)/(nf^2-neff^2)));
NEFF = zeros(size(lambda));
for ii=1:numel(lambda)
Eqn = (((2*pi./lambda(ii))*(sqrt(nf^2-neff^2)*hf))+ phi_c + phi_s -(m*pi))==0;
NEFF(ii)=double(vpasolve(Eqn));
end
%%
plot(lambda, real(NEFF), 'r-o', 'DisplayName', 'neff: real part'), hold on
plot(lambda, imag(NEFF), 'b-d', 'DisplayName', 'neff: imag part'), hold on
legend; grid on
  2 个评论
Sulaymon Eshkabilov
Sulaymon Eshkabilov 2021-11-7
You are doing something wrong while typing the script contents
Vaswati Biswas
Vaswati Biswas 2021-11-7
Sir I was talking about 'nf' that is involved in tan inverse equation. hf isn't involved in that equation.

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