# Time signal for dipole source

Hello,

On the Lumerical website, it gives an equation for the time signal of standard source, but says “Note: There are some small difference between the pulse generated by this code and the actual time signal generated by the ‘standard’ source pulse setting.” I wonder what the differences are.

Also, for the broadband source, it says “Note: The ‘broadband’ option is generated with a more complex function. The precise function is not provide.” I wonder if this information definitely cannot be revealed to the users.

I understand that we can do custom time signal, but I haven’t had much success with it. And even if I did have success, I would like to compare with Lumerical’s time signal. So I would really want to know the exact equations of the time signal set by Lumerical.

Thank you very much.

Dear @wendu.ding

Sorry for the long wait.

I have discussed your question with our R&D scientist, @jniegemann, and he will get back to you hopefully soon.

Dear @wendu.ding,
my apologies for the delay. As you mentioned, you can find some information on the source pulses on our Knowledge Base: https://kb.lumerical.com/en/ref_sim_obj_sources_plane_waves_and_beam.html

All the default pulses use a Gaussian envelope and the different options influence the width of the pulse and the type of carrier modulation used. Specifically, if you choose the “broadband source” we apply a chirped carrier, i.e. there is an additional phase term which depends on time.

A simplified expression of our chirped pulse reads

pulse = sin( phi(t) ) * exp( -(t-offset)^2/2/delta_t^2 );

where the phase used takes the form

phi(t) = a + bt + csin(d*t).

Here, a,b,c,d are constants chosen such that the phase changes smoothly from f_mint to f_maxt across the pulse.

The exact expressions used for the constants are lengthy and depend on many internal parameters (e.g. if the simulation uses complex or real-valued fields). We generally don’t recommend to rely on the details of a specific pulse shape as we might change the expressions (slightly) between releases. If you need to know the exact shape of a source pulse, we recommend to use the custom pulse, which gives you full control over the shape. If you have problems using this feature, please let us know and we will assist you in setting this up.

I hope this helps and please let me know if you need additional details.

2 Likes

Dear @jniegemann

Thank you very much for the detailed reply, and now I understand more about the broadband source I was using. As you and the knowledge base suggested, I will try to use custom pulses for my project.