A Power spectral density of a laser's frequency noise

[Malamala]

Hello! I am a bit confused about what power spectral density (PSD) is in the context of a laser. In particular, I came across this paper. In Fig. 1 they show PSD vs frequency. As far as I understand, PSD is just the square of the FT spectrum of a laser frequency/phase as a function of time. Later in the paper (Fig. 2), they mention that a way to get a plot as in Fig. 1 is to make a self-heterodyne measurement. However, in other papers (and this was my understanding so far, too), doing a self heterodyne would give you a spectrum with a Lorentzian/Gaussian lineshape, from which you can directly get the linewidth of the laser (e.g. this paper, Fig. 2). My confusion is in the fact that the 2 plots appear to be obtained the same way (self-heterodyne method), they both show PSD vs frequency, yet they look so vastly different. The first one shows a 1/f noise followed by white noise at high frequencies, while the second one has a Lorentzian shape or some other weirder shape depending on the length difference between the 2 optical fibers.

Is the length difference the only difference between them, or am I missing something else? In the first paper they use 20 m difference, while in the second paper the fibers difference is on the order of 1 km. And if that is the case, I have a second question. It seems like the plot in the first paper gives you more information than the second one. The second one basically gives you just the laser linewidth, but the first one can be used to get the laser linewidth (e.g. using the beta-line method described there), but you can get further insight, too (e.g. what bandwidth would you need for a servo to suppress the 1/f noise). If that is the case, why are many people using a large fiber difference between the 2 arms for getting the laser linewidth (I know from experience, as everyone I talked to mentioned the second method, of using fibers of 1-10 km difference for linewidth measurements). What advantage does the second method gives, as in my naive understanding the first method is better from all points of view (more info provided about the laser and cheaper, shorter optical fibers). Thank you!

 

[Baluncore]

I guess, the longer fibre, gives a longer time delay between samples, so the frequency resolution will be improved. That should better resolve phase noise that varies more slowly, that is, closer to the centre frequency of the laser. Very long fibres should give the Gaussian profile of the line.

 

[Malamala]

I guess, the longer fibre, gives a longer time delay between samples, so the frequency resolution will be improved. That should better resolve phase noise that varies more slowly, that is, closer to the centre frequency of the laser. Very long fibres should give the Gaussian profile of the line.

But I guess my main question is: does the different shape come only from the longer delay? And if I make the fiber longer, would that beta-line method still work at all, given that the spectrum shape would be completely different?

What exactly do you mean by "phase noise that varies more slowly, that is, closer to the centre frequency of the laser"? Isn't slowly varying phase noise close to f = 0 (i.e. to the very left of x-axis)?

 

[Baluncore]

But I guess my main question is: does the different shape come only from the longer delay? And if I make the fiber longer, would that beta-line method still work at all, given that the spectrum shape would be completely different?

The longer line makes more information available, so the PSD becomes more realistic.

What exactly do you mean by "phase noise that varies more slowly, that is, closer to the centre frequency of the laser"? Isn't slowly varying phase noise close to f = 0 (i.e. to the very left of x-axis)?

"A self-heterodyne measurement" beats the signal against a delayed version of the signal. That is sensitive to phase noise and down-converts it to zero frequency. But the self-heterodyne has also down-converted the line to zero frequency, which tends to saturate that channel, and to jump around since low frequencies are present. To eliminate that instability, the light was first modulated with 100 MHz, so there is also a component that falls into the spectrum analyser centred on 100 MHz. The more stable spectrum analysed near 100 MHz is digitised by the SA, and scaled to convert it to the PSD.

 

[Malamala]

The longer line makes more information available, so the PSD becomes more realistic.


"A self-heterodyne measurement" beats the signal against a delayed version of the signal. That is sensitive to phase noise and down-converts it to zero frequency. But the self-heterodyne has also down-converted the line to zero frequency, which tends to saturate that channel, and to jump around since low frequencies are present. To eliminate that instability, the light was first modulated with 100 MHz, so there is also a component that falls into the spectrum analyser centred on 100 MHz. The more stable spectrum analysed near 100 MHz is digitised by the SA, and scaled to convert it to the PSD.

Uhh... I am still confused... if i measure the PSD experimentally using the self-heterodyne method, what would I see? Would I see 1/f + white noise, as in the first paper, or the Lorentzian shape as in the second paper?

Also, it's still not clear to me how the length of the line matters i.e. what do you mean by more information? The first paper mentions that the length matters only in going to higher frequencies. For 20 m, they can get the PSD only up 10 MHz. However, going higher than that is usually not needed, as at these frequency the lasers have white noise at a known level. Also, based on the first paper, TOPTICA uses that method (of 20 m difference) to define the linewidth of their lasers. However, TOPTICA is one of the best laser companies in the world, so if using a longer fiber would give a much better linewidth measurement, why are they using this one (buying few km of fiber is a few thousand dollars, which is definitely not an issue for TOPTICA)? There has to be a reason for using this method over the other one (involving a bigger difference in fiber lengths).

 

[Cthugha]

Uhh... I am still confused... if i measure the PSD experimentally using the self-heterodyne method, what would I see? Would I see 1/f + white noise, as in the first paper, or the Lorentzian shape as in the second paper?

Your question confuses me because both show essentially the same data. Baluncore already explained it well, but just to add a simplified summary:
You use the self-heterodyning to get the noise you are interested in to a frequency range where little other noise sources are. So (oversimplifying - the details are slightly more complicated) by modulating at 100 MHz you will find the noise component for 1 kHz shifted to a signal frequency of 100.001 MHz, the noise component for 10 kHz shifted to a signal frequency of 100.01 MHz and the noise component for 1 MHz shifted to 101 Mhz.

When you take figure 2, shift the x-axis by 100 MHz and plot everything on a log axis, you will end up with something similar to figure 1.

The good thing is that only noise that is actually originating from the laser is shifted to higher frequencies, while, e.g., mechanical noise originating from vibrations of the table is not.

 

[Andy Resnick]

Hello! I am a bit confused about what power spectral density (PSD) is in the context of a laser. In particular, I came across this paper. In Fig. 1 they show PSD vs frequency. As far as I understand, PSD is just the square of the FT spectrum of a laser frequency/phase as a function of time. Later in the paper (Fig. 2), they mention that a way to get a plot as in Fig. 1 is to make a self-heterodyne measurement. However, in other papers (and this was my understanding so far, too), doing a self heterodyne would give you a spectrum with a Lorentzian/Gaussian lineshape, from which you can directly get the linewidth of the laser (e.g. this paper, Fig. 2). My confusion is in the fact that the 2 plots appear to be obtained the same way (self-heterodyne method), they both show PSD vs frequency, yet they look so vastly different. The first one shows a 1/f noise followed by white noise at high frequencies, while the second one has a Lorentzian shape or some other weirder shape depending on the length difference between the 2 optical fibers.

I wonder if some of your confusion is caused by the vastly different scales in the two plots, for both the x- and y-axes.