I want to take a plot from this equation α(ω)/α(νi) Vs ω-νi. Can someone help me

[ANKUR KUMAR]

Come up with some trail codes.

[SriMiGSS]

%%PARAMETERS
D = 1*10^6;     %FWHM of free runing laser
b = 0.01;       % value depends on the injection ratio
vi = 10^6;      % frequency of teh injected signal
r = 10^4;       % FWHM after injection locking

%%RANGE
w = linspace(0.9*10^6,1.1*10^6,211);

%%EQUATION
syms m n;
Y1 = (((D/(4.*b))^m)*((2*m.*b)+(r/2)))./(factorial(m)*(((2*m.*b)+(r/2))^2+(w-vi).^2));
Y = symsum(Y1, m, 0, 100);
X1 = (((D/(4*b))^n)*((2*n*b)+(r/2)))/(factorial(n)*(((2*n*b)+(r/2))^2));
X = symsum(X1, n, 0, 100);
PowerDensity = Y./X;

%%PLOT
figure;
plot(w-vi,PowerDensity);
xlabel('Frequency Detuning (Hz)');
ylabel ('Relative Power Density');

[ANKUR KUMAR]

So, what is your problem now?

[SriMiGSS]

this code don't work. it do not give correct plot. Can someone help me

[Birdman]

What does the plot that you want look like?

[SriMiGSS]

[David Goodmanson]

Hi Sri,

Your code gives a curve of width 10 kHz and the constant r, which is filling the role of gamma, is 10 kHz. On the face of it that looks all right,better than the Fig 2 plot. But there appear to be issues with the equation. Is b intended to be a dimensionless quantity? Given its role in the equation, unitwise it has to equal .01 Hz.

The quantity (D/(4*b)) equals 2.5e7, which means that the terms in the sum keep getting larger, not peaking out until m = 2.5e7. Something must be incorrect. Also, not that it couldn't be right, but to me (2*m*b + gamma/2) seems less likely than (2*m*b + i*gamma/2). It would help if you could post what eqn. 11 looks like.

[SriMiGSS]

[SriMiGSS]

This is the equation.

[David Goodmanson]

Thanks for providing it. For both of the alpha expressions (numerator and denominator), the largest term in the sum occurs at m = 2.5e7, so you won't get there by adding terms.