How to integral function and plot it

Hi, Could you help me how to integral function "fun" and get the q, then plot dL vs q. The code as below. Thanks a lot.

clear all; close all; clc

Gamma = 1; 
kappa = 0.75*Gamma; 

Dp = 0*Gamma; 
Dc = 0*Gamma; 

Finese = 350; 
OD0 = 0.025;
OD = (Finese/pi)*OD0; 
G = OD; 
Oc = 2*Gamma; 
Op = 0.00001*Gamma; 
T0 = 1;
rR = 0*Gamma;

dL = linspace(-6*Gamma,6*Gamma,2000); 

kappat = -i*kappa/2+Dp-dL-df;
Gammat = -i*Gamma/2-dL-df; 
gammat = -i*rR/2+Dc-dL-df; 
Gammaf = 0.00001*Gamma;
A = -4*gammat.*Gammat;

T = T0*(kappa/2)^2.*...
    abs((A+Oc^2)./((G^2*gammat)+(kappat.*(A+Oc^2)))).^2;

fun = @(df) (exp(-(df^2/Gammaf^2))/(sqrt(pi)*Gammaf))*T;
q = integral(fun,-Inf,Inf)

figure(1)
plot(dL, q)
xlabel ('dL')
ylabel('Transmission signal')

[Sergey Kasyanov]

Are kappat, Gammat, gammat functions of df?

What is dL? Why is it array?

[Tina Hsiao]

Yes! kappat, Gammat, gammat are functions of df. The dL is an array once I get the q result. I would like to put all the value (eg. Gamma = 1; kappa = 0.75*Gamma; Dp = 0*Gamma; Dc = 0*Gamma; ...etc into q and with different dL. And plot dL vs q.

Answer 1

[Star Strider]

‘kappat, Gammat, gammat are functions of df.’

I created them (as well as ‘A’, ‘T’, and ‘fun’) as anonymous functions of ‘df’ to define them as such.

Check this to be certain it prooduces the desired result, otherwise make necessary corrections (since I do not understand what this code does) —

Gamma = 1; 
kappa = 0.75*Gamma; 

Dp = 0*Gamma; 
Dc = 0*Gamma; 

Finese = 350; 
OD0 = 0.025;
OD = (Finese/pi)*OD0; 
G = OD; 
Oc = 2*Gamma; 
Op = 0.00001*Gamma; 
T0 = 1;
rR = 0*Gamma;

dL = linspace(-6*Gamma,6*Gamma,2000); 

kappat = @(df) -i*kappa./2+Dp-dL-df;
Gammat = @(df) -i*Gamma./2-dL-df; 
gammat = @(df) -i*rR./2+Dc-dL-df; 
Gammaf = 0.00001*Gamma;
A = @(df) -4*gammat(df).*Gammat(df);

T = @(df) T0*(kappa/2)^2.*...
    abs((A(df)+Oc^2)./((G^2*gammat(df))+(kappat(df).*(A(df)+Oc^2)))).^2;

fun = @(df) (exp(-(df.^2./Gammaf^2))./(sqrt(pi)*Gammaf)).*T(df);

q1 = integral(fun,-Inf,0, 'ArrayValued',1);
q2 = integral(fun,0,Inf, 'ArrayValued',1);
q = q1 + q2;

figure(1)
plot(dL, q)
xlabel ('dL')
ylabel('Transmission signal')

Since ‘q’ as originally defined is uniformly 0, I broke it into two regions and added them.

.

[Tina Hsiao]

Prima! Thanks a lot...I like this solution.

[Star Strider]

As always, my pleasure!

Thank you!