Gaussian Time-Bandwidth

Hi all

this is an idea that I have for my thesis

I have Gaussian pulse and i am deciding to divide it to wavelength slots like this :

the slots are defined like that-> each slot will have the same energy -> so the each interval will be different in wavelengths.
i(receiver) have to know the duration of each slot. thought of two ways to calculate it:

1. the basic formula

and from that

2. or to calculate the inverse Fourier transform for every slot but how then i can know the duration of the slot ?

thx in advance