Laser pulse: spectral width vs time

[SchroedingersLion]

Hi guys,

I am learning for an optics examination and found a picture that is supposed to show the duration of a light pulse with respect to the spectral bandwidth (appended).

At this point in the lecture, we have not gone through modelocking yet, so I assume one should understand the picture without it.
Why does the sun's light not consist of laser pulses when it covers such a large spectrum?

 

[Simon Bridge]

Why does the sun's light not consist of laser pulses when it covers such a large spectrum?

You are asking why the Sun's light does not consist of laser pulses? Um ... because it is not made by lasers?
Maybe you are asking why the Suns lihght is not well modeled as a sum over carefully selected laser pulses?
What makes you think it cannot?

What does the width of the spectrum have to do with whether or not the Sun's light consists of laser pulses?

Perhaps you mean "consistent"... ie how come the suns light has the duration is does considering the bandwidth?
Could that have something to do with not being a pulse? For instance, what is the duration of a continuous laser beam?
I have a feeling this may be more what you are asking about... but correct me if I am wrong.

Your attached picture illustrates how this happens: see how none of the samples waves in sunlight (or other continuous examples) ever "line up" completely like with the laser example?

Maybe you are asking how it is that the waves never line up ... well that is how geometry works: it is possible to arrange the output of a light source so that the waves periodically have the same phase at some stage and not at others. This makes a pulse. However, this is generally not the case ... normally you make a pulse by switching the source on then off again.

Usually a randomly selection of more than 3 or 4 (iirc) wavelengths all at random initial phases and amplitudes will rarely have a situation where they all match tidily. What you get instead is an irratic assortment of peaks and troughs as some waves match up and then not.
This is ignoring the sun not being a point source.

I am being a bit pedantic above because you are advanced enough to start to think about how you ask questions.
Most of physics is about forming the right question... it's something of an artform though.

Did I manage to cover your concern?

 

[SchroedingersLion]

Why does the sun's light not consist of laser pulses when it covers such a large spectrum?

You are asking why the Sun's light does not consist of laser pulses? Um ... because it is not made by lasers?
Maybe you are asking why the Suns lihght is not well modeled as a sum over carefully selected laser pulses?
What makes you think it cannot?

What does the width of the spectrum have to do with whether or not the Sun's light consists of laser pulses?

Perhaps you mean "consistent"... ie how come the suns light has the duration is does considering the bandwidth?
Could that have something to do with not being a pulse? For instance, what is the duration of a continuous laser beam?
I have a feeling this may be more what you are asking about... but correct me if I am wrong.

Your attached picture illustrates how this happens: see how none of the samples waves in sunlight (or other continuous examples) ever "line up" completely like with the laser example?

Maybe you are asking how it is that the waves never line up ... well that is how geometry works: it is possible to arrange the output of a light source so that the waves periodically have the same phase at some stage and not at others. This makes a pulse. However, this is generally not the case ... normally you make a pulse by switching the source on then off again.

Usually a randomly selection of more than 3 or 4 (iirc) wavelengths all at random initial phases and amplitudes will rarely have a situation where they all match tidily. What you get instead is an irratic assortment of peaks and troughs as some waves match up and then not.
This is ignoring the sun not being a point source.

I am being a bit pedantic above because you are advanced enough to start to think about how you ask questions.
Most of physics is about forming the right question... it's something of an artform though.

Did I manage to cover your concern?

The bold part is exactly my question. You are right about my question being too vague, I apologize, I am just a bit in a hurry at the moment.
So if I have a large number of frequencies, I have to experimentally make sure that they all interfere constructively at some point (and thus periodically). However, with the sun, this is not a given. And only if all the waves of different frequencies interfere constructively, I will get a pulse whose duration decreases with increasing bandwidth?

 

[vanhees71]

Well to a good approximation the sun is radiating black-body (i.e., thermal) radiation with the spectrum given by the Planck spectrum. It's as incoherent as anything can get!

 

[Cthugha]

So if I have a large number of frequencies, I have to experimentally make sure that they all interfere constructively at some point (and thus periodically). However, with the sun, this is not a given. And only if all the waves of different frequencies interfere constructively, I will get a pulse whose duration decreases with increasing bandwidth?

This is a tricky question. Actually it is a common myth, that the temporal duration of a light pulse forms a Fourier pair with its spectrum (or more exactly its power spectral density). In fact, it is not the temporal duration of the light field, but the autocorrelation of the light field that forms the Fourier pair with the power spectral density via the Wiener-Khinchin theorem. Or to put it simply: A broad spectrum means a short coherence time (as this is given by the decay of the autocorrelation function) and vice versa.

Now, for ultrashort pulses, the minimum duration of the pulse that can be achieved is indeed proportional to the coherence time: If all modes present are in phase at some point in time, the coherence time also defines the timescale on which the phases will become very different again, which defines the pulse duration. Now you might wonder, why multiple pulses are coherent with respect to each other, although the coherence time is so short. If you have a really close look at the spectrum, you will find that it is not really continuous, but consists of lots of closely spaced modes, almost like a frequency comb. The envelope of that spectrum will give you the short-time features, while the periodic discrete peaks will give you "revivals" that occur with the pulse repetition rate.

Now, returning to the question, why sunlight does not consist of short pulses: It does - in a sense. The coherence time defines the time scale of phase fluctuations and as such also the time scale of photon number fluctuations. If you have a look at the Bose-Einstein photon number distribution of thermal light, you will find that the fluctuations are huge and that 0 is the most probable photon number. This can be understood quite easily. A good model for thermal light is given by just taking 100 harmonic oscillators with the same amplitude and completely random phase and giving them a phase kick at random at certain time steps, which represent the coherence time. Most of the time all the fields will cancel out (thus, 0 is the most probable photon number), but at some rare times many of the oscillators will align by chance and provide large residual field and high photon numbers for a very short time. This is what sunlight actually looks like: A train of random short bursts of high intensity and long periods of darkness. However as the duration of the bright and dark periods are given by the coherence time and this is in the hundreds of femtosecond range for sunlight, your eyes (and almost all detectors) just see an averaged constant intensity. Sunlight consists of plenty of short pulses. They just come totally at random.

 

[SchroedingersLion]

Cthugha, thanks for the explanation!