fsolve stopped because the problem appears regular

Hi.

I want to find the value of w_s and N_s(s is subscript ) in the equations that are attached.

Please refer to the attachment.

I've written the code for it as follows

clc
clear all

c = 2.99792458e8;                    % velocity of light [cm/s]
Qt = 500;                            %total quality factor
Qi = 14300;                          %intrinsic quality factor
Qp = 10000;                          %crossport quality factor
lambda0 = 1554e-9;                   %free space wavelength
deltalambda = 0.01e-9;               %step 
lambda_start = 1540e-9;              %start wavelength
lambda_end = 1560e-9;                %end wavelength
lambda = lambda_start:deltalambda:lambda_end;
omega = 2*pi*c./lambda;
omega0 = omega(find(lambda==lambda0));      %omega0 equals 1.2121e15
gamai = omega0./2/Qi;                       %intrinsic  loss rate
gamap = omega0./2/Qp;                        %cross port  loss rate
gamat = omega0./2/Qt;                       %total loss rate
gamac = gamat-gamai-gamap;                  %cavity loss rate
gama1 = gamac./2;
gama2 = gama1;
rB = 0.2 ;
tB = sqrt(1-rB^2);
P=-1;
COS2 = 0.5*gama1./gama1.*tB^2/rB-0.5*tB^2/rB-rB;
SIN2 = P*tB./(2.*gama1*rB).*sqrt(4.*gama1.*gama1 - tB^2.*(gamac.^2));
conf = 0.5;         %confinement factor
gN =5e-20;          %differential gain
Ntr = 1e24;         %transparency carrier density
alphai = 1000;      %intrinsic factor
alpha=1;            %henry factor
sigma = 3;          %constant
L = 5e-6;           %length 
m = 25;             %constant


%rR=rB+(2*gama1*exp(COS2+1i*SIN2))/(1i*(omega0-x(2))+gamat);
F=@(x)[
%rB+(2*gama1*exp(COS2+1i*SIN2))/(1i*(omega0-x(2))+gamat);
conf*gN*(x(1)-Ntr)-alphai-(1/(2*sigma*L))*log10(1/(abs(rB+(2*gama1*exp(COS2+1i*SIN2))/(1i*(omega0-x(2))+gamat)))^2);
imag(rB+(2*gama1*exp(COS2+1i*SIN2))/(1i*(omega0-x(2))+gamat))+((2*x(2))/c)*(-c*sigma*alpha*gN*(x(1)-Ntr)/(2*x(2))./c)*L-(2*m*pi)];
x0=[1 1];
x=fsolve(F,x0);

I don't get any output.

please guide me.

[mohammad heydari]

Anybody have any idea?

Answer 1

[darova]

Try this

[X,Y] = meshgrid((-6:0)*1e34, (-10:10)*1e34);
Z1 = X*0;
Z2 = X*0;
for i = 1:size(X,1)
    for j = 1:size(X,2)
        ZZ = F([ X(i,j) Y(i,j)] );
        Z1(i,j) = ZZ(1);
        Z2(i,j) = ZZ(2);
    end
end
surf(X,Y,Z1,'facecolor','r')
hold on
surf(X,Y,Z2*1e13,'facecolor','b')
hold off

Doesn't look like solution exist

[mohammad heydari]

Thank you for your answer but I still didn't understand the concept.Please explain if possible.

[Walter Roberson]

darova is showing with a graph that the two equations are never simultaneously zero. There is a point or possibly line at which the two equations are equal, but it is not when the two are both 0.

[darova]

mohammad heydari

You have two functions, they depend on two variables

They can be represented as two surfaces (x,y variables they depend on)

You are solving equations and wants to find where surface can be zero

In this case two surfaces have zero values BUT in different places

Walter Roberson thanks bro ♥

[darova]

They should be in one place

[mohammad heydari]

Thank you darova and Walter Roberson

[darova]

Thank you for accepting answer!