Correlation properties of quasi-thermal light

[kvantarina]

Hello!

I'm measuring the second order correlation function g(2) of quasi-thermal light, generated by focusing a 633 nm laser onto a rotating sandpaper-like surface at 45 deg. Part of the dispersed light is collected into a fiber and split with a fiber beam splitter. A simple HBT setup.

g(2) is supposed to be equal to 2 for thermal light at zero delay. However, I'm getting a higher value, somewhere around 2.7. I'm trying to figure out why.

I heard somewhere that this can happen if there are some deterministic processes present, but I can't find any information on it and have no idea what that process would be. My only theory is that the light is polarized, and that there might be some polarization dependence for example in the BS.

Any help or information on what can be causing this high g(2)-value would be very helpful. Thank you!

 

[Paul Colby]

Does the value of $g(2)$ change with sample rate or rotation rate? Also, is it a single mode or multimode fiber? This could explain a time dependent correlation of the splitter.

 

[kvantarina]

Does the value of $g(2)$ change with sample rate or rotation rate? Also, is it a single mode or multimode fiber? This could explain a time dependent correlation of the splitter.

It's a single mode fiber, and I've only tried two different rotation rates (7 Hz and 70 Hz) and the value at t=0 is similar (but the width of the peak as a function of time varies of course). I haven't checked if it's exactly the same though. I could try run it again tomorrow and check more carefully. The sample rate is more than high enough to not smear out the peak.

How and why would the peak value depend on the rotation rate?

 

[Paul Colby]

I've done some photon counting in the dim past so I may not understand the experiment correctly. My guess is your experimental setup has two photo detectors monitoring two outputs of a fiber beam splitter being fed by a single mode fiber? The input is laser light reflected from the rotating rough surface which will cause the intensity at each detector to fluctuate in a correlated manner. Other than this the count rate fluctuations between detectors at $t=0$ should be uncorrelated. Sorry if this is way off base.

 

[Cthugha]

There are several possible issues that may result in modified values of g2(0).
First, I assume that your HBT uses two SPADs and you are doing coincidence counting in start-stop mode? How do you normalize your correlation function? Of course at long times the normalized correlation function should go towards 1, but this requires pretty low count rates because otherwise pile-up effects occur, which result in an artificial suppression of coincidence counts at large delays, which in turn result in g2(0) being too large because the normalization is off. This can be checked by monitoring g2(0) at different laser intensities.

Also, what is the shape of your g2(tau)? Does it go down towards 1 monotonously? If the rotating ground glass disk is mounted a bit off-center, the local velocity of the disk at the laser spot will change with time, which may result in a changed g2(0). However, this will usually also result in some periodic structure in g2(tau).

Is your laser a HeNe-laser or a diode? These are not really notorious for mode competition, but some may emit on several modes. If you have mode competition, this will already increase the g2(0) of your laser. Hitting a rotating ground glass disk with light that is already noisy will result in a g2(0) above 2. However, you can easily check that by measuring g2(0) of the bare laser.

Besides that, any long-term instability, pointing instability or slow drift will tend to increase g2, but I guess you already checked whether your count rates are constant over time. From my own experience, I can tell that fibers and fiber BS may be incredibly sensitive to even slight motion. I always used to fix them on the optical table using duct tape.

What are the coherence times of your pseudothermal light source at 7 Hz and 70 Hz by the way?

 

[kvantarina]

There are several possible issues that may result in modified values of g2(0).
First, I assume that your HBT uses two SPADs and you are doing coincidence counting in start-stop mode? How do you normalize your correlation function? Of course at long times the normalized correlation function should go towards 1, but this requires pretty low count rates because otherwise pile-up effects occur, which result in an artificial suppression of coincidence counts at large delays, which in turn result in g2(0) being too large because the normalization is off. This can be checked by monitoring g2(0) at different laser intensities.

Almost. Using two SPAD's and doing coincidence counting but not in start-stop mode. I use 50 ns coincidence windows and control the delay electronically. At the moment I've just normalized to the coincidence counts at large tau's. I've measured it for different input powers/count rates but not investigated all the data carefully yet so I will do that, thank you, to see if it varies.

Also, what is the shape of your g2(tau)? Does it go down towards 1 monotonously? If the rotating ground glass disk is mounted a bit off-center, the local velocity of the disk at the laser spot will change with time, which may result in a changed g2(0). However, this will usually also result in some periodic structure in g2(tau).

The shape is beautiful, looks just like it should. It's just the height that's weird. But I've only measured for tau's up to about hundred times the coherence time/FWHM of the peak. Should I measure for larger delay times?

Is your laser a HeNe-laser or a diode? These are not really notorious for mode competition, but some may emit on several modes. If you have mode competition, this will already increase the g2(0) of your laser. Hitting a rotating ground glass disk with light that is already noisy will result in a g2(0) above 2. However, you can easily check that by measuring g2(0) of the bare laser.

Aha! I did not know that. Will check with the bare (HeNe) laser immediately. Thank you! Why does mode competition increase g2(0)?

Besides that, any long-term instability, pointing instability or slow drift will tend to increase g2, but I guess you already checked whether your count rates are constant over time. From my own experience, I can tell that fibers and fiber BS may be incredibly sensitive to even slight motion. I always used to fix them on the optical table using duct tape.

What are the coherence times of your pseudothermal light source at 7 Hz and 70 Hz by the way?

Why do these factors increase g2(0)? The count rates are fairly constant but there is definitely some instability. How high variations in count rates can you allow without significantly affecting g2? Can I suppress it by normalizing to the single count rates? Sorry, it should be 7 Hz and 35 Hz, and they are around 8 µs and 1.6 µs.

 

[Cthugha]

The shape is beautiful, looks just like it should. It's just the height that's weird. But I've only measured for tau's up to about hundred times the coherence time/FWHM of the peak. Should I measure for larger delay times?

No, that should be fine. I guess that g2 is flat after about ten times the FWHM anyway, right?

Aha! I did not know that. Will check with the bare (HeNe) laser immediately. Thank you! Why does mode competition increase g2(0)?

g2(0) is essentially a measure of the photon number noise of your light fields in terms of its variance. It provides the conditional probability to detect a second photon after you just measured one compared to a light source with the same mean photon count rate that just emits fully independent photons. Now mode competition means that two modes of the light field will compete for the same gain medium. If one mode is stronger, it will suppress the other and vice versa. If the stronger mode becomes the weaker mode at some point, the intensity of that mode will change. In terms of g2(0) this means that if you detect a photon from a mode, it is most likely that it is the dominant mode right now because the emitted intensity in that instant is above the mean intensity. However, that also means that the probability to detect another photon shortly afterwards will also be enhanced. This results in an increased value of g2.

Why do these factors increase g2(0)? The count rates are fairly constant but there is definitely some instability. How high variations in count rates can you allow without significantly affecting g2? Can I suppress it by normalizing to the single count rates? Sorry, it should be 7 Hz and 35 Hz, and they are around 8 µs and 1.6 µs.

The machanisms are the same as above. Any amount of variation of the mean photon number will increase g2. For large enough mean photon numbers, you can estimate g2 as 1+(photon number variance)/(mean photon number^2). (for low count rates you have to consider an additional -(1/mean photon number)).
Normalization to the single count rates might help if you have really slow fluctuations present.

 

[kvantarina]

Thank you Cthugha! Your answers are very helpful. Will go do some work in the lab now see if I can connect the dots in what's causing this.