What is the formula for GaussianPulse?

Date	Category
2025-09-05 17:29:25	Sources

The GaussianPulse sourcetime, if the DC component is zeroed out, has the following formula:

$(i+\frac{t}{t_w^2\omega_0})Ae^{i\phi}e^{-i\omega_0 t}e^{-\frac{(t - t_o*t_w)^2}{2t_w^2}}$

If the DC component is not zeroed out, the formula is

$iAe^{i\phi}e^{-i\omega_0 t}e^{-\frac{(t - t_o*t_w)^2}{2t_w^2}}$
where $A$ is the amplitude, $t_o$ is the time offset, $t_w=\frac{1}{2\pi f_{width}}$ is the width of the pulse in seconds, $\phi$ is the phase shift, and $\omega_0=2\pi f_0$. See the code [here](https://docs.flexcompute.com/projects/tidy3d/en/latest/_modules/tidy3d/components/source/time.html#GaussianPulse).