MATLAB: Fsolve stopped because the problem appears regular

error

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.

Best Answer

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

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MATLAB: Unable to perform assignment because the left and right sides have a different number of elements in the ode45

Your function rate_eq_program_1 uses a number of variables defined in the main program, but without importing them. You need to add a "function" statement at the very top of your code, and add an "end" statement at the end of your code, in order to make rate_eq_program_1 into a nested function that can access the variables.

Now, in the main part of your program you have

lambda = lambda_start:deltalambda:lambda_end;

so lambda is a vector

omega = 2*pi*c./lambda;

so omega is a vector because it is built from the vector lambda

omega0 = omega(find(lambda==lambda0));

As mentioned before due to floating point round-off the == might not find any matches. It will find either 0 or 1 match, so omega0 will end up either empty or a scalar.

E = hbar_eV.*omega;

E is constructed from the vector omega, so E is a vector. Did you want to construct E from omega0 ?

Now, inside rate_eq_program_1 you have

ys(1) = I./(E.*Vp)-(z(1)./tc)-GN.*(z(1)-Ntr).*sigmas.*((abs(z(3)).^2)./Vc);

As noted above, E is a vector, so the right hand side of the assignment is a vector, but the left hand side only has room for a scalar.

Now look a little further and it turns out that sigmas is a vector as well:

deltac=omega0+deltawc-omega;

You use all of the vector omega, so deltac will be a vector.

rR=(-P.*gamac)./(1i*(deltac)+gamat-(1/2*(1-1i)*confinec*vg*gN).*(z(2)-Ntr));
rRS=-P.*gamac./(1i.*(deltac)+gamat);

Those use the vector deltac so they will both be vectors.

    g=alphai+(1/(2*L)).*log(1./(abs(rRS)).^2);

Uses the vector rRS so g is a vector

    A=(2*epsilon0*n*ng)./(hbar.*omega0);

Use the undefined variable n . If we assume that n is a scalar, then A will be a scalar.

    B=(1+(abs(rRS))).*(1-(abs(rRS)));

Uses the vector rRS so B will be a vector

    D=((g)-alphai);

g is a vector so D will be a vector.

    H=c./(omega0.*n);

Use the undefined variable n. If we assume that n is a scalar, then H will be a scalar.

    F=imag(rRS)./abs(rRS);

Uses the vector rRS so F will be a vector.

    sigmas=A.*((B./D)+(H.*F));

Uses the vector B, the vector D, the vector F, so sigmas will be a vector.

ys(1) = I./(E.*Vp)-(z(1)./tc)-GN.*(z(1)-Ntr).*sigmas.*((abs(z(3)).^2)./Vc);

Uses the vector sigmas, so even if E was a scalar instead of being a vector, the right hand side will be a vector.

Now, if E were a scalar instead of a vector, and if you could make deltac a scalar instead of a vector, then the other variables involved would become scalars and the assignment could work.

ys(2) = (-z(2)./tc)-GLA.*(z(2)-Ntr).*(abs(z(4)).^2)./Vnc;

GLA is a vector constructed in the main routine based on E, so if E were a scalar then GLA would be a scalar.

ys(3) = 1/2*(1-1i)*GN.*(z(1)-Nss).*z(3)+(1/tin.*((z(4)./rR)-z(3)));

Uses the undefined variable Nss. Uses rR which as explained above is a vector because it is built from the vector deltac so if deltac were made into a scalar somehow, then rR would become a scalar and the right hand side would be a scalar (assuming that the undefined Nss is a scalar.)

ys(4) =((-1i.*deltawc-gamat).*z(4))-(P.*gamac.*z(3))+(1/2*(1-1i).*confinec*vg*gN.*(z(2)-Ntr).*z(4));

This used the vectors gamat and gammac from the main routine.

gamai = omega./2/Qi;
gamap = omega./2/Qp;
gamat = omega./2/Qt;

Those use all of the vector omega, so all three are vectors.

gamac = gamat-gamai-gamap;

The right hand side are all vectors, so gamac is a vector.

So ys(4) is a vector.

Beyond defining the undefined n, Nss, and param_rate_eq_fano, there are two approaches you could use:

Loop the whole ode45 call over individual values implied by omega, such as by passing in an index and indexing with that were appropriate so that you get 4 x 1 output from the function; Or
Reconstruct the ode45 not as a 4 x 1 system but instead as a (4*2001) x 1 system, running all of those 2001 odes at the same time.

MATLAB: Differential equations of time with two parameters given as functions of time.

First of all: remember about array/vector operators (vectorization)

Can't you just put Omega_C and Omega_F inside the function?

Best Answer

Related Solutions

MATLAB: Unable to perform assignment because the left and right sides have a different number of elements in the ode45

MATLAB: Differential equations of time with two parameters given as functions of time.

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