How to plot transcendental equation?

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.

[Paul]

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.

Answer 1

[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

[Vaswati Biswas]

Thank you so much

[Sulaymon Eshkabilov]

Most welcome!

[Vaswati Biswas]

Hello Sulaymon Eshkabilov Sir, whenever I am changing the parameters let's say if I put nf = 2 I am getting an error "Unable to perform assignment because the indices on the left side are not compatible with the size of the right side:

Error in (line 17)

NEFF1(ii)=double(vpasolve(Eqn));

This error is coming because double(vpasolve(Eqn)) is empty. It seems that this code is specific for some particular values . But I want to plot this equation where nf > nc and ns but it doesn't give me any plot in this senerio. Kindly help.

[Sulaymon Eshkabilov]

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]

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));

Answer 2

[Sulaymon Eshkabilov]

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

[Sulaymon Eshkabilov]

You are doing something wrong while typing the script contents

[Vaswati Biswas]

Sir I was talking about 'nf' that is involved in tan inverse equation. hf isn't involved in that equation.