To represent a gaussian pulse having energy given as 100 milli joule and ,FWHM of pulse as 120 femto sec.
from the equation of Gaussain pulse
A(t)= A0(1+ic/2)exp(t/t0)^2
A0 =sqrt (Po)
where Po=input power
t0= input pulse duration
t=fwhm of input pulse( 120 Fs in my case)
but if i have to represent the gaussain field envelop in terms of Energy variable then what modification do i need to make in above equation
Also for the pulse having 100 milli joule energy , what could be the approximated power.
I think the precise pulse energy is not important here. The value of A0 will be dependent on the measuring instrument (alignment, focus). The value should be guessed from the raw data. The important parameter here is FWHM which is independent of A0.
You can find some help on the Fourier transformation here
https://math.stackexchange.com/questions/453062/fourier-transform-of-short-pulse
https://link.springer.com/chapter/10.1007%2F978-3-662-03682-2_2
I am not sure what is your ultimate goal it but measuring the spectrum is more straight forward than the mathematics. Also for an transform limited pulse (Gaussian) the spectral width and temporal width is equal to 0.44.
https://www.rp-photonics.com/gaussian_pulses.html
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