# How to predict the time domain of pulse from an amplitude mask in frequency domain?

I am studying ultrafast spectroscopy (pump-probe) and I know that ultrashort laser pulses are used for the pump and probe. These pulses often contain multiple frequencies (i.e. polychromatic pulse) that are generated by pulse broadening. Broadening in the frequency domain also means broadening in the time domain, so usually pulse shaping techniques are used to compress the pulse to the Fourier limit (i.e. uncertainty principle).

If I understand correctly, the time domain and frequency domains can be interconverted with Fourier transform. Now, usually pulse shaping involves applying a "mask" on the input light pulse. In my lectures, the professor showed us several examples of amplitude masks and phase masks. For example-

In this case the amplitude of specific wavelengths are being reduced in an input pulse containing a range of wavelengths. And that changes the shape of the pulse in the time domain.

An example of a phase mask-

Here the phases are being changed for different wavelengths (i.e. frequency domain) and the shape of the pulse changes in the time domain.

My problem is that I have no idea how to get to the shape of the output pulse by looking at the shape of the mask (which is what we are supposed to learn from the lecture). I did not find any books on this topic, but I did find some research papers, which did not help me.

I want to know what is the intuitive way to predict the output pulse shape from the shape of the phase or amplitude mask. Any help is appreciated. Also recommend any book or paper you know that is at the undergraduate reading level on this topic.

• Hint: how can you go from a signal in the time domain to one in the frequency domain? How do you go back? May 25, 2022 at 21:35
• @JonCuster Fourier transform and inverse Fourier transform? But how does that help? I know that already, I just need to figure out how to intuitively predict the shape after Fourier transform. I can't do that in my head. May 26, 2022 at 9:10
• Well, do a half dozen or so different shapes and see what you think. That is how you build intuition. It doesn’t magically just happen (sadly). May 26, 2022 at 12:11
• There is no intuitive way. No one can make fourier transforms in their heads. With experience you memorize a few rules/transforms and you can start making educated guesses about the output, mostly about widths, but there is no way other than using a computer and making the fourier transform of the filter. May 29, 2022 at 13:57