Why is the pulse in picture 20130320182307.png positively chirped?

[einstein1921]

why the pulse is positively chirped pulse in picture 20130320182307.png ? thank you!
I also confused by another picture(20130320183049.png ).Does a femtosecond laser pulse contain a lot of wavelength?if so, a pulse should contains photons which have different energy. why we always say Ti:sappire laser is 800nm?thank you!

 

[DrClaude]

In a positive chirped pulse, the frequency increases as a function of time, such that a high frequency should lag behind a low, which seems to be contrary to what is plotted.

A pulse must contain many frequencies (only a continuous wave can be strictly monochromatic). And the shorter the pulse, the wider the frequency range, which can be seen by taking the Fourier transform. By the way, pulses where the frequency range is the narrowest possible are called "transform limited", but unless special care is taken in producing the pulses, the frequency range will be wider than the minimum.

When a specific wavelength is quote, it usually refers to the central frequency of the laser pulse.

 

[einstein1921]

In a positive chirped pulse, the frequency increases as a function of time, such that a high frequency should lag behind a low, which seems to be contrary to what is plotted.

A pulse must contain many frequencies (only a continuous wave can be strictly monochromatic). And the shorter the pulse, the wider the frequency range, which can be seen by taking the Fourier transform. By the way, pulses where the frequency range is the narrowest possible are called "transform limited", but unless special care is taken in producing the pulses, the frequency range will be wider than the minimum.

When a specific wavelength is quote, it usually refers to the central frequency of the laser pulse.

thank you for your answers! 1.why when a pulse is positive chirped, the high frequency should lag behind a low!
2.how to get the central frequency of a laser pulse?
thank you!

 

[DrClaude]

1.why when a pulse is positive chirped, the high frequency should lag behind a low!

Writing the laser as a classical electromagnetic wave, a chirped pulse behaves as
$$\propto \cos(\omega(t) t)$$
A positive chirp would be defined as
$$\frac{d \omega}{dt} > 0$$
Therefore, highier frequencies appear later.

2.how to get the central frequency of a laser pulse?

Do you mean how to measure it? I will leave that to more knowledgeable people (I'm not an experimentalist).

 

[einstein1921]

Writing the laser as a classical electromagnetic wave, a chirped pulse behaves as
$$\propto \cos(\omega(t) t)$$
A positive chirp would be defined as
$$\frac{d \omega}{dt} > 0$$
Therefore, highier frequencies appear later.


Do you mean how to measure it? I will leave that to more knowledgeable people (I'm not an experimentalist).

thank you,sir! the formule you typed display as \propto \cos(\omega(t) t) , so I can't read them correctly!Can you type them again!

 

[DrClaude]

thank you,sir! the formule you typed display as \propto \cos(\omega(t) t) , so I can't read them correctly!Can you type them again!

Funny, comes out fine on my screen.

proportional to cos(ω(t) t)

 

[einstein1921]

Funny, comes out fine on my screen.

proportional to cos(ω(t) t)

we often represent the field of pulse:E(t)=Af(t)cos(wt),where f(t) is envelope.so it seems that there is only one frequency w. I know this is wrong, but I can't understand where are other frequencies. in picture 2 ,there are many frequency ,which one is central frequency? thank you!

 

[DrClaude]

we often represent the field of pulse:E(t)=Af(t)cos(wt),where f(t) is envelope.so it seems that there is only one frequency w. I know this is wrong, but I can't understand where are other frequencies. in picture 2 ,there are many frequency ,which one is central frequency? thank you!

The other frequencies appear because the amplitude of the field is time dependent. Here, ω is the central frequency. But if you Fourier transform f(t) cos(ω t), you will find that the frequency spectrum is broaden by the presence of the envelope. In other words, if you had E(t) = A cos(ω t), the frequency spectrum would be a single line (delta function) at frequency ω. With the presence of f(t), this line is broaden into a wider peak, centered on ω (hence the name central frequency). The narrower the time domain of f(t), the wider the frequency range.

Hope this helps.

 

[dmriser]

It is an interesting exercise to open some graphing software like MATLAB and plot a sine wave. Then add another sine wave with slightly different frequency and plot again. Continue to add more waves and observe what happens to the signal. You'll see that the more frequencies you add, the narrower the pulse becomes.