Apply Group Velocity Dispersion to a Pulse

Hi, I've created a gaussian pulse and want to apply the group velocity dispersion to it. I'm looking for it to be similar to he image attached, where the top is the original pulse, the middle is positive dispersion and the bottom is negative dispersion, as I'm trying to understand how they did this.

So far my pulse code:

if true
  clear all ; close all ; clc
f=374.7e12;%Thz
fs=f*10; %sampling frequency
T=1/fs;
L=1000;
sigma=5e-15;
t=(0:L-1)*T; %time base
x =(exp(-(t-50e-15).^2/(2*sigma)^2)).*exp(1i*2*pi*f*t);
x = x.*5e-11
plot(t,real(x),'b');
title(['Gaussian Pulse \sigma=', num2str(sigma),'s']);
xlabel('Time(s)');
ylabel('Amplitude');
ylim([-1 1]) 
xlim([10e-15 90e-15])

end
The formula for the group velocity dispersion

$$GVD = \frac{dv_g}{dk} = -\frac{w}{n}\frac{d^2 n}{d\lambda^2}$$

Or the formula for the temporal spreading due to the group velocity dispersion:

$$\Delta\tau = -\frac{L}{c}(\lambda^2\frac{d^2 n}{d\lambda^2})\frac{d\lambda}{lambda}$$

Thanks!