A laser produces light of wavelength 625 nm in an ultrashort pulse. What is the minimum duration

A laser produces light of wavelength 625 nm in an ultrashort...

Key Concepts

Time-Energy Uncertainty Principle

This principle, a manifestation of the more general Heisenberg uncertainty principle, states that the more precisely one determines the energy of a system, the less precisely one can know the time interval over which that energy is defined (and vice versa). In contexts such as ultrashort laser pulses, this trade-off sets a fundamental lower bound on the pulse duration based on the uncertainty in the photon energy.

Photon Energy and Wavelength Relationship

In quantum mechanics, the energy of a photon is directly related to its frequency by the relation E = h?, where h is Planck's constant and ? is the frequency. Since frequency and wavelength are inversely related via ? = c/?, understanding this relationship is crucial to converting between the wavelength of light and the energy or frequency domain, especially when calculating energy uncertainties.

Time-Bandwidth Product in Pulse Physics

This concept highlights the intrinsic link between the duration of a pulse and its spectral bandwidth (or energy uncertainty). In ultrashort pulse applications, the finite bandwidth of the pulse implies that there is a minimum possible duration — mathematically expressed through the time-bandwidth product — constraining how short the pulse can be for a given spectral spread.

Transcript

00:01 Hello everybody.

00:02 So we're going to work on this problem where we're given a laser that presuses the light of 625 nanometers, right? and an ultristern pulse.

00:16 Based on the minimum, what is the minimum duration of this pulse if the uncertainty of the energy of the photon is approximately 1%.

00:29 So this, with all the uncertainties, it's screaming, i use the uncertainty principle.

00:35 And since they give you the wavelength and they're asking about time, you just simply want to use the energy time uncertainty principle.

00:42 So that gives you your uncertainty in e times your uncertainty in time.

00:48 It's going to be greater than our h bar over 2, right? so what they're trying to, since we're looking at this, is they're asking the minimum uncertainty, the minimum duration based on the minimum uncertainty.

01:04 So if we just solve for t or delta t, it's greater than h bar over 2, right? so as long as t has to be greater, so this would give us our minimum based on our delta e right here, right? we also know that our e is equal to hc over landa, right? and then our uncertainty, which is for delta e, it would just simply be hc over landa times that 1%, right? it would be 0 .01.

01:44 So if we were to plug that back into our equation over here, delta t is h -bar landa over t over t.

01:59 2hc times our 0 .01, right? that 1%.

02:03 But, so you could just plug in numbers here at this point, but i like to, i don't like working with h or h bar.

02:10 They're very, very small, minus 35 numbers.

02:13 So it might as well just convert our age to an h bar and cross them out, right? so in that relation, age equals 2 pi h bar...

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