how i can simulate it on MATLAB

I wanne simulate joint spectral amplitude that is based on pump envelope and phase matching. lamdaP value is 1550nm and i write code but my alpha value is 0, and i dont know why!

I wanne a picture like that I attach.

clear;

close all;

%...................parameters...............

lambdaP = 1.55e-6; % pump wavelength

nelithiumP = 2.142; % refractive index lithium niobate for pump lambda

lambdaS = 0.775e-6 ; % signal wavelength

nelithiumS = 2.186; % refractive index lithium niobate for signal lambda

lambdaI = 0.775e-6 ; % idler wavelength

nelithiumI = 2.186; % refractive index lithium niobate for idler lambda

kP = 2*pi*(nelithiumP/lambdaP);

kS = 2*pi*(nelithiumS/lambdaS);

kI = 2*pi*(nelithiumI/lambdaI);

capital_lambda = 17.6e-6;

Deltak =(kP-kS-kI-(2*pi/capital_lambda));

%Deltak = linspace(a-1e7,a+1e7,100); % phase matching condition

L = 2e-2;

sigmaP=10e-9;

%deltat=50e-12;

sigmaP = deltat/(2*sqrt(log(2))); % pulse width

c = 3e8; % speed of light in vacuum

fS = c/lambdaS; fP = c/lambdaP; fI = c/lambdaI;

wS = 2*pi*fS; wP = 2*pi*fP; wI = 2*pi*fI; % angel frequncy

%alpha=exp(-(2*(pi^2)*(sigmaP^2))*((wP-(wS+wI))^2));

%b=wS+wI-wP;

alphaa = exp(-((wS+wI-wP)/sigmaP)); % pump envelope function

phi = (sinc(Deltak.*L./2)).*exp(1i.*Deltak.*L./2); % phase matching function

f = alphaa*phi; % joint spectral amplitude

joint_spectral_intensity = abs((f).^2); % joint spectral intensity

Answer 1

[SOUMNATH PAUL]

Hi @asma,

I see you have commented out the definition of "deltat" and have an incorrect computation for "sigmap" that follows.

Assuming you define "deltat" the corrected portion of your code will be :

% Assuming deltat is defined, I have taken an arbitrary value for mock computation:
deltat = 50e-12; % pulse width in seconds

% Correct calculation of sigmaP for a Gaussian pulse in the frequency domain
sigmaP = 1 / (deltat * sqrt(2 * log(2)));

% Corrected alpha calculation using the Gaussian envelope formula
alpha = exp(-((wP - (wS + wI))^2) / (2 * sigmaP^2));

% Continue with phi and f as before
phi = (sinc(Deltak * L / 2)) .* exp(1i * Deltak * L / 2); % phase matching function
f = alpha * phi; % joint spectral amplitude
joint_spectral_intensity = abs((f).^2); % joint spectral intensity

Hope this Helps!

Soumnath