Hanbury Brown and Twiss effect question

[LmdL]

Hi,
I just recorded 3000 patches.
There were patches with photons:

Patches with noise only:

And patches with some strange "noise" (296 patches out of 3000):

I supposed that pattern in last picture is a kind of noise (i.e. didn't count it for photons).
Photon number distribution over all 3000 patches:

Mean: 0.7257. Variance: 0.8027.Combined into 60 bins, 50 patches each bin:

Mean: 36.2833. Variance: 41.9692.So, I suppose, "my" Martienssen lamp doesn't work?
Somehow, I still think the problem is in the second light path. When I put out the diffuser - I see almost identical Airy discs on both light paths, but when I return it back - on the short path I see big speckles, but nothing is on the long path. Or it's just becomes too faint to see.

 

[LmdL]

By the way, before collecting the patches I slightly changed the "Martienssen lamp" part in my experimental setup. Now it looks like this:

Laser L1 produces a beam that passes through ND neutral density filter and is focused by L2 lens on the side of the D1 diffuser that is rotated by MT motor. Speckle pattern produced passes through a 2um PH pinhole and converged by L3 lens into plane wave.
Plane wave was set up without rotating diffuser and density filter mounted - for simplicity. Then I just inserted them back in.
In addition, I added a converging lens between BS2 beam splitter and a PMT in order to focus the combined beam into PMT.

 

[Cthugha]

I do not think that the second beam is the problem right now. It might be bad (it is a huge delay), but at these timescales, the effect should be visible just looking at the first beam alone.

Actually I think your lamp might be working. You assume a coherence time of 350 ns. You average the photon number over a time window of 2048 points which means your effective time resolution is somewhere around 1.6 microseconds. As your coherence time is much faster than your time resolution, you should only see a drastically reduced HBT peak and the variance should also not bee much larger than the mean. If the values are correct, I would expect a peak with a magnitude of roughly 10 to 20% of the real value seen with good temporal resolution. So can you subdivide each patch into smaller patches of, say, 160 ns and check, whether the mean and variance change? You might run into the problem of having pretty low photon numbers here, so I am not sure whether it is really necessary to use a 2 micron pinhole in the speckle pattern. It sounds like that may reduce your intensity really strongly. Do you have a larger pinhole or an iris or something like that?

 

[LmdL]

Hi,
Yeah, you are right. I somehow missed the fact that each patch is already longer than expected coherence time. I performed a new measurement - recorded 3000 patches again with the following changes:
1. Increased coherence time, by reducing rotation rate of the diffuser.
2. Replaced a 2um pinhole with a 15um one.

Results are as following. Bins graphs in increasing order of number of patches each bin contains:

Statistics:

First of all, I see no sense why variance/mean ratio is ~4 for most of bin size variations. Is it because 2 beams are actually involved and not 1?
Secondly, ratio is decreasing as bin time length increases, but it feels like it does so, because bins number decreases.

 

[Cthugha]

The ratio indeed is quite large. Can you block the second beam? It might (and should) cause some interferences and extra variance and the correct photon statistics can be identified from one beam alone.

Besides that, two possible issues come to my mind: If the disk is rotating slowly, additional noise may be introduced if the rotation does not go at exactly the same velocity all the time. And maybe more important: You need to sample the scattering disk evenly. So you want your total collection time to be orders of magnitude longer than your coherence time. Otherwise you just sample a part of the probability distributions. Usually a total collection time of at least 1000 coherence times is used.

 

[LmdL]

Blocked the second beam and recorded 5000 patches (overall signal time is about ~8msec). Supposing that coherence time is in usec range this should be enough. Actually I don't know how to measure the coherence time, so I supposed it is in the range of 0.3nsec - 5usec.

Statistics:

Frustrating...
Is there a way to measure the coherence time directly? With help of oscilloscope or something?
By the way, patches are not taken continuously. There is a dead time between each 2 patches FPGA takes. Shouldn't it a be a problem for statistics?

Secondly, each peak in the 2048 graph can represent a photon or many photons. If photon reaches the PMT and it shows a peak (detection of that photon), and there is an additional photon hits a PMT at that time - I'll never know.

For example, is there really only 8 photons here?
So this can be a reason for poor statistics as well. In addition, I think that was a reason for ratio ~1 in my first patches collection, because there I used a 2um pinhole and therefore a chance that each peak represents only 1 photon is quite high.
Of course, in correlation measurements (between the two PMTs) it won't be so important, as for photon counting.
Finally, maybe a stupid question, but still: I use a 532nm laser pointer as light source. As I know, these diode lasers use second harmonics to double the frequency. From what I know about second harmonics, it produces a linear polarized light. May it be the reason I didn't get the peaks? Because from multiple reflections from the mirrors, second beam may have lost a majority of "correlated" photons before reaching the PMT.
I will try to replace the green pointer with HeNe laser and see if anything changes.
And one more thing. As you already saw, all parts in my system are "in-axis", which means that majority of the light I detect, came in a straight line from the laser after passing a diffuser. But if it came in a straight line - it wasn't diffused. Is it worth to slightly "tilt" the laser, so light that enters the pinhole is for sure a diffused one? Something like this:

Or in this case I will get something similar to LED and I actually need the "main" beam?

And, of course, thank you for help! It is very appreciated.

 

[Cthugha]

The dead time in between patches should not be a problem. The problem with the missing photon number resolution of PMTs is well known, but as long as the intensity is sufficiently low that the probability to have two photons arriving at the same time is small, the error you get should be small, too.

He-Ne lasers are usually polarized, too. You will always lose some polarization when using mirrors. If you want to counteract that, you may put another polarizer in, but at this stage the effect should not bee too bad.

However, it is very likely that going off-axis will be necessary. Usually I collect off-axis to ensure that no unscattered light is collected, but tilting the laser will work, too. That might decrease your intensity drastically, so might want to consider a different pinhole.

Also, if you do not trust your laser or detector or setup (instabilities will of course change the statistics), you may do the same experiment using just the bare laser and check, whether the variance roughly equals the mean here. If so, you can at least trust your setup.

 

[LmdL]

Thanks! I'll try to tilt the laser / move a pinhole off axis. I can just remove the ND filter in order to compensate in light intensity.

 

[LmdL]

Hi Cthugha,
Almost a year has passed, but I'm still "fighting" with my setup to get the effect. Meanwhile - no luck. I hope maybe you can find a mistake in my setup.
For now my experimental setup is as following:

1. Laser. I use a green laser pointer (exactly the one listed here: http://www.ebay.com/itm/331280017127)
2. Short focal length (5mm) lens and a 2 micron pinhole. Laser light focuses into a pinhole and a nice Airy pattern is generated.
3. Iris. In one of the previous posts you said different modes fluctuate independently and all but one mode should be filtered out. This is done by Iris in this step. After an Airy pattern generation by a pinhole (central disk and rings around it), Iris allows to the central disk only to pass, filtering out the rings in Airy pattern.
4. Lens. This lens converges the light and focuses it on the rotating ground glass diffuser.
5. Rotating ground glass diffuser. Generates speckle pattern. I set rotation rate to be slow, about 1 full rotation in a second, because as I understand, the faster the rotation, more the light behaves like a Poisson (laser/coherent light) and less like Bose-Einstein (thermal light).
6. Black screen with a small aperture. Allows to pass only a small amount of the speckle pattern. Currently, the aperture is about 1mm diameter. At this distance the speckle size is about this size as well. Should I decrease the aperture so it will be much smaller than the average speckle size?
7. Non-polarizing 50/50 beam splitter. Divides the beam into two.
8 and 9. Lenses with 5cm focal length in order to focus the light on the PMTs.
10 and 11. PMTs. I use R7400U HAMAMATSU PMTs (described here: http://ctf3-tbts.web.cern.ch/ctf3-tbts/instr/PMT/R7400U_TPMH1204E07.pdf)

After that, as already described, I record the signals from both PMTs and perform a correlation between them in MATLAB (with xcorr(PMT1,PMT2) function).
Actually, I got once a nice peak around zero point in the correlation (because distance to the PMTs is equal), but on the second run - it didn't appear again.

Hope you can help me on mistakes in a setup, or how to improve the setup to get the effect easier.
Thank you!

 

[Cthugha]

Sorry to hear that you are still struggling. Let me see what we can find.

1. Laser. I use a green laser pointer (exactly the one listed here: http://www.ebay.com/itm/331280017127)
2. Short focal length (5mm) lens and a 2 micron pinhole. Laser light focuses into a pinhole and a nice Airy pattern is generated.
3. Iris. In one of the previous posts you said different modes fluctuate independently and all but one mode should be filtered out. This is done by Iris in this step. After an Airy pattern generation by a pinhole (central disk and rings around it), Iris allows to the central disk only to pass, filtering out the rings in Airy pattern.
4. Lens. This lens converges the light and focuses it on the rotating ground glass diffuser.

Sounds good to me. What is the focus length of the lens used in step 4? A lens with short focal length may give you a bigger speckle pattern.

5. Rotating ground glass diffuser. Generates speckle pattern. I set rotation rate to be slow, about 1 full rotation in a second, because as I understand, the faster the rotation, more the light behaves like a Poisson (laser/coherent light) and less like Bose-Einstein (thermal light).

No, this is incorrect. The rotation rate just determines your coherence time. It is pretty much always a very bad idea to choose a slow rotation rate. At 1 Hz, the coherence time is most likely longer than your total recording time for one patch, so you will not get a peak.

6. Black screen with a small aperture. Allows to pass only a small amount of the speckle pattern. Currently, the aperture is about 1mm diameter. At this distance the speckle size is about this size as well. Should I decrease the aperture so it will be much smaller than the average speckle size?

I am somewhat surprised. 1mm is very small for the speckles. Could you use a shorter lens in step 4 or a rougher ground glass disk to get larger speckles?

7. Non-polarizing 50/50 beam splitter. Divides the beam into two.
8 and 9. Lenses with 5cm focal length in order to focus the light on the PMTs.
10 and 11. PMTs. I use R7400U HAMAMATSU PMTs (described here: http://ctf3-tbts.web.cern.ch/ctf3-tbts/instr/PMT/R7400U_TPMH1204E07.pdf)

Sounds fine.

After that, as already described, I record the signals from both PMTs and perform a correlation between them in MATLAB (with xcorr(PMT1,PMT2) function).
Actually, I got once a nice peak around zero point in the correlation (because distance to the PMTs is equal), but on the second run - it didn't appear again.

So what is your average count rate now? Does the patch still basically consist of many zeros and few signal peaks? If so, just using xcorr might not be the best way to do the analysis. You used some different binnings before. Could you calculate mean(PMT1.*PMT2)/(mean(PMT1)*mean(PMT2)) and tell me what you get? The result should usually be somewhere between 1 and 2.

 

[LmdL]

What is the focus length of the lens used in step 4?

I use the one with 19mm focus length. It's the shortest I have.

I am somewhat surprised. 1mm is very small for the speckles.

I have all my setup on a small optical table (around 1 meter in length overall), so there is no large distances to light to propagate to get large speckles (distance between diffuser and a black screen with aperture is 38cm). I actually measured mine with ruler and it's about 3-5mm speckle size. Moreover, I played with distance between lens and diffuser and speckle size grows in a strange way. In the beginning it is very small bright and dark dots. Moving the diffuser it gets larger when at some moment it just becomes large blurred bright areas separated by a narrow dark contours. I put the distance so speckles are large and more or less round, before they become a large blurred areas.

or a rougher ground glass disk to get larger speckles?

I use the widest one. It's written on it "light shaping diffuser 10 deg". I have 5 deg, 1 deg and 0.5 deg, but these are worse. This diffuser is not the "milk glass" one, but I compared it to the "milky glass 120 grit" one, and it acts the same. I have one from this set (50mm diameter, 10 deg):
https://www.newport.com/Light-Shaping-Diffusers/141131/1033/info.aspx#tab_Overview

So what is your average count rate now? Does the patch still basically consist of many zeros and few signal peaks?

Each patch I measure is 2048 points. Each point is 0.8 ns. So each patch is a time window of ~1.6 microseconds.
Each patch contains more or less from 0 to 10 photon counts. I inserted ND filter, because I have very sensitive amplifiers (after PMTs), that not allow to me to have large count rates - it just burns out, like it happened to previous one.

Could you calculate mean(PMT1.*PMT2)/(mean(PMT1)*mean(PMT2)) and tell me what you get?

I recorded 1000 patches in slowest rotation and 1000 patches in fastest rotation of diffuser I could achieve.
Statistics are as following:
1. Slowest rotation.

Average(PMT#1) = 7.055
Average(PMT#2) = 0.591
Average(PMT#1*PMT#2) = 4.083
So the ratio you asked for is 0.98

2. Fastest rotation.

Average(PMT#1) = 4.335
Average(PMT#2) = 0.562
Average(PMT#1*PMT#2) = 2.977
So the number you requested is 1.22

So I have some questions:
1. Looks like the distribution is still Poisson and not Bose-Einstein. But I can shift the distribution to the left and therefore get more Bose-Einstein like distribution just by inserting another ND filter. Isn't it?
2. PMT#2 gets much less counts. Is it a problem? Maybe I should put a linear polarizer before a beam splitter?
3. In some articles (and original Martienssen article as well) people put additional pinholes of ~50um in front of the PMTs, because they explain that PMT collecting area should me much less than a speckle size. In my case this, I believe, is done by the black screen with small aperture.
In addition, when they put a ~50um pinholes in front of the PMTs, how can they be sure these pinholes are symmetric, i.e. pass the same spot of the speckle? Its impossible to see that by eye to adjust their position.
Thanks!

 

[Cthugha]

I use the one with 19mm focus length. It's the shortest I have.

Ok, sounds good.

Each patch I measure is 2048 points. Each point is 0.8 ns. So each patch is a time window of ~1.6 microseconds.
Each patch contains more or less from 0 to 10 photon counts. I inserted ND filter, because I have very sensitive amplifiers (after PMTs), that not allow to me to have large count rates - it just burns out, like it happened to previous one.

Ok, so photon detections are rare events. Good.

Average(PMT#1) = 7.055
Average(PMT#2) = 0.591
Average(PMT#1*PMT#2) = 4.083
So the ratio you asked for is 0.98

Just one question. These are the mean photon numbers per patch (consisting of 2048 data points each), right?

Average(PMT#1) = 4.335
Average(PMT#2) = 0.562
Average(PMT#1*PMT#2) = 2.977
So the number you requested is 1.22

Ok. The number you just calculated is the second-order correlation function. It is 2 for thermal light and 1 for coherent light. Interestingly, a faster rotation rate gets you there somewhat. In the second case, the distribution also already looks a bit more Bose-Einstein like. Now there are several possible reasons, why you do not arrive at full thermal statistics:

1) The coherence time of your light is way shorter than your temporal resolution. That is unlikely, I guess.
2) You collect light from more than one speckle. In that case increasing speckle size or decreasing the colection window might help.
3) The distance from the ground glass disk to the two PMTs is slightly different.
4) You have too much stray light background. What is your dark count rate?

1. Looks like the distribution is still Poisson and not Bose-Einstein. But I can shift the distribution to the left and therefore get more Bose-Einstein like distribution just by inserting another ND filter. Isn't it?

No, that does not help. At low photon numbers, the Poissonian and the Bose-Einstein distribution just start to look pretty similar. You cannot get thermal light just by making the light dimmer.

2. PMT#2 gets much less counts. Is it a problem? Maybe I should put a linear polarizer before a beam splitter?

Whether that is a problem depends on your dark count rate, but balancing the count rates is always a good idea.

3. In some articles (and original Martienssen article as well) people put additional pinholes of ~50um in front of the PMTs, because they explain that PMT collecting area should me much less than a speckle size. In my case this, I believe, is done by the black screen with small aperture.
In addition, when they put a ~50um pinholes in front of the PMTs, how can they be sure these pinholes are symmetric, i.e. pass the same spot of the speckle? Its impossible to see that by eye to adjust their position.

In my opinion the main role of these pinholes is stray light suppression. If you have a problem with the dark count rate, placing more pinholes close to the PMTs will surely help. The dark count rate should be as small as possible, if possible even orders of magnitude smaller than your real count rate.

 

[LmdL]

These are the mean photon numbers per patch (consisting of 2048 data points each), right?

Yes. I calculated number of photons in each patch (time window of 1.6 microseconds) for each PMT and then did the statistics in Excel.

You have too much stray light background. What is your dark count rate?

I will measure the dark count rate this evening and post the results.

In my opinion the main role of these pinholes is stray light suppression.

I just thought, maybe they don't even need to put the pinholes such that they pass the same speckle? Because if pinholes pass the same speckle I will just get the Poisson statistics and I want to correlate between different speckles. That's why it should be placed on different speckles and then I don't need to adjust them to be ideally symmetrical.

 

[Cthugha]

Yes. I calculated number of photons in each patch (time window of 1.6 microseconds) for each PMT and then did the statistics in Excel.

Ok, so you reduced your effective time resolution to 1.6 microseconds.

I will measure the dark count rate this evening and post the results.

Great!

I just thought, maybe they don't even need to put the pinholes such that they pass the same speckle? Because if pinholes pass the same speckle I will just get the Poisson statistics and I want to correlate between different speckles. That's why it should be placed on different speckles and then I don't need to adjust them to be ideally symmetrical.

No. You want the same speckle. The scattering process is what gives you the thermal distribution. If you correlate between two different speckles you will get two Bose-Einstein distributions which are uncorrelated with each other, so the counting statistics will be much closer to Poissonian when picking different speckles.

 

[LmdL]

No. You want the same speckle. The scattering process is what gives you the thermal distribution. If you correlate between two different speckles you will get two Bose-Einstein distributions which are uncorrelated with each other, so the counting statistics will be much closer to Poissonian when picking different speckles.

Then, I don't understand.
First, I then can just leave the diffuser with no rotation at all, move both PMTs to measure the same speckle and measure only that speckle over the time. But then, I actually will get the Poisson distribution, because non-rotating diffuser is same like no diffuser at all, i.e. coherent light.
Secondly, I'm very surprised how this author:
http://search.proquest.com/docview/1552496353
which uses single mode fibers that collect the light and transfer it to the PMTs, could setup those fibers (core radius of 5um, p.43) in such a precision to collect the same speckle (coherence length of 130um, so I suppose speckle size is on this length scale as well) or setup a 50um pinholes to collect the same speckle (p. 45).

 

[Cthugha]

First, I then can just leave the diffuser with no rotation at all, move both PMTs to measure the same speckle and measure only that speckle over the time. But then, I actually will get the Poisson distribution, because non-rotating diffuser is same like no diffuser at all, i.e. coherent light.

But by doing so, you will not get changing photon numbers and just the photon statistics of the input beam. Of course you want to see different speckles over time, but at each instant you want both diodes to see the same speckle.

Secondly, I'm very surprised how this author:
http://search.proquest.com/docview/1552496353
which uses single mode fibers that collect the light and transfer it to the PMTs, could setup those fibers (core radius of 5um, p.43) in such a precision to collect the same speckle (coherence length of 130um, so I suppose speckle size is on this length scale as well) or setup a 50um pinholes to collect the same speckle (p. 45).

On p.45 first-order coherence is studied, which just requires fixed phases. On page 55/56, you find a measurement of the second-order correlation function. As you can see in figure 3.8. you really need to place the fibers with an accuracy of about 100 micrometers to get a g2 of approximately 2, which is the smoking gun for having created (pseuso)thermal light.

 

[LmdL]

As you can see in figure 3.8. you really need to place the fibers with an accuracy of about 100 micrometers to get a g2 of approximately 2, which is the smoking gun for having created (pseuso)thermal light.

You are right. Now I see it.

I performed the dark current measurement. Firstly I measured 1000 patches in a regular way, then I blocked the small aperture on the black screen, while leaving all the rest as it was (including working laser and rotating diffuser) so any leaks of light will be accounted in the dark current measurement and recorded another 1000 patches.
Statistics with open aperture:

(by the way G2 = 1.05)

Statistics with blocked aperture:

So I guess I'm fine with the noise.

 

[LmdL]

Hi Cthugha,
Thank you very much for your help! I finally got it! I'm so happy.

The problem was in a pinholes size in front of the PMTs. They were too large, included many orders, and as you already stated many times, each order fluctuates independently, so the overall fluctuations cancel out. I put a single mode fibers (5 um) instead of pinholes, which lead the light to the PMTs.

 

[Swamp Thing]

LmdL, congrats on your successful experiment.

About those last two plots, what is the X-axis? Is it the distance between the 5 um pickup fibres, or is it a time offset ? How is the axis scaled?
I have not fully understood the HBT thing, but curious to understand what's going on.

 

[LmdL]

Hi Swamp Thing,
In my case I have 2 signals recorded as a function of time. Then I correlate between the signals (run xcorr(CH1,CH2) in MATLAB). So the correlation in pictures above are as a function of time delay between photon arrivals to each PMT. Since correlation is peaked at 0, the PMTs are equidistant from the source, so the correlated photons arrive simultaneously to the PMTs. So the answer to your question: x-axis represent a time delay between signals at two PMTs.
Now, I can move one of the PMTs longitudinally, so there will be a time delay between photons arrivals. At some point introduced distance will be too large and correlation will nullify since photons will no longer be correlated. This way I can measure a temporal coherence.
Or I can move one of the PMTs transversely and measure a correlation peak height as function of the distance. At some point it will nullify, since at this point photons are no longer correlated (PMTs will no longer measure the same speckle). This way I can measure a spatial coherence.

 

[Swamp Thing]

Thanks, LmdL.

The x-axis is labeled -1e4 to 1e4. That is in what units?

With the diffuser not moving, there is a very slight change in correlation between 0.85 to 0.95 approx. Is this an artifact, or is it theoretically expected?

 

[LmdL]

The x-axis is labeled -1e4 to 1e4. That is in what units?

Signals were recorded with oscilloscope at 2.5Ghz/s. That is, each point in a signal is a 0.4ns. The x-axis is a time delay between signals. So roughly speaking, -1e4 to 1e4 on the graph is from -4us time delay, through 0 time delay and to 4us time delay between signals.

With the diffuser not moving, there is a very slight change in correlation between 0.85 to 0.95 approx. Is this an artifact, or is it theoretically expected?

I'm not sure what you mean. Did you mean the "triangle" slope of the whole graph?

 

[Cthugha]

Congratulations on successfully building the setup. :)

Are you going to investigate something special with it?

 

[Swamp Thing]

Did you mean the "triangle" slope of the whole graph?

Yes, I meant the triangle slope of the first graph. With no rotation, it should be like any good laser beam - i.e. independent Poisson processes - so the two detectors should ideally be uncorrelated ??

 

[LmdL]

Congratulations on successfully building the setup. :)
Are you going to investigate something special with it?

Thanks! I actually need to design a FPGA board to measure the photon bunching for mini telescope design, since having an oscilloscope is not always possible. So before I start with FPGA desing, I needed to get the effect in the lab to test FPGA work on.

Yes, I meant the triangle slope of the first graph.

The "triangle" feature you see is an artifact of the correlation between finite signals.
Suppose you have finite signals:
Signal 1: 1 1 1 1 1
Signal 2: 1 1 1 1 1
On the on hand, you can think that since signals are constant, their correlation is constant too, since no matter what the delay between the signals, the correlation is same.
But on the other hand, since signals are finite, each time you shift one with respect to the other, in order to multiply them in the correlation process, the edges of each signal will multiply 0 and therefore will not contribute to the correlation value at given delay point. The more delay you introduce - the more values at edges are multiplied by 0. Therefore you get maximum in the middle, and less and less towards the edges.
For the example above, the correlation in the middle (0 delay between signals) is 1*1+1*1+1*1+1*1+1*1 = 5.
With 1 value shifted you get 1*0+1*1+1*1+1*1+1*1+0*1 = 4
and so forth. So for this case you will have the correlation: 1 2 3 4 3 2 1, which is rectangular pattern.

Therefore, correlation of features in each signal that are more or less constant (mostly the noise), will result in a rectangular feature in the correlation graph. And what's what you see in both graphs (non rotating and rotating diffuser). The feature that is different between the 2 graphs is an additional peak in the rotating diffuser case, which corresponds to the photon bunching.