What is the bandwidth (in eV) of a transform limited pulse with a (100 as) pulse duration?
The law that rules the transform limited pulse is similar to the uncertity principle in quantum mechanics which state that
(sigmax . sigmay)>= h/(4.pi)
The one that limites the pulse duration is:
(Bandwidth . PulseDuration) >= C
where C is 0.315 for a sech2 profile pulse, and 0.44 for a gaussian pulse. If I'm right the pulse duration in this formula is the 1/e.
You can take a look here: https://www.rp-photonics.com/transform_limit.html
Expressed in eV, it doesn't depend on the wavelength. The formula is pretty simple: dE=h*K/dt where K is the constant given above (0.315 for sech2) and h is the plank constant. So a 100as pulse will have a bandwidth of about 13eV.
Dear Eyad Abdur-Rahman,
it depends on how you define the widths (in the time and the energy domains) and what shape the pulses have. If the widths are considered at the half maximum and your pulse has a Gaussian shape, you will need about 18 eV. The central frequency is not important.
Regards,
AT
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