The coherence length is much longer than the manufacturer claims

[gvgpg66]

TL;DR Summary

The problem is that the coherence length of a laser I am experimentally measuring is much longer than the manufacturer claims and has an oscillating visibility.

Let me explain the situation: I have an experimental setup consisting mainly of a Michelson interferometer, so I want to use it to measure the coherence length for two different situations, when the beam is focused on a mirror and when it is focused on a sample. Therefore, before analyzing the behavior with the sample, I needed to measure the coherence length of the continuous wave laser with λ_0=532 nm, which is a Thor Labs laser (https://www.thorlabs.com/thorproduct.cfm?partnumber=CPS532). From the product data sheet, I was able to extract the bandwidth from a graph of its spectrum, which is about Δλ≈0.6 nm. So, from with the coherence length equation: Lc=(λ_0)^2/Δλ→Lc≈0.5 mm.

Thus, in the lab I should observe the interference pattern only along a moving mirror path of at least 0.25 mm, so that the difference between the arms (twice) is equal to the coherence length. Before doing so, I measured the coherence length of a pulsed laser with a similar λ, which I used to find the point t_0 (where both arms have the same length). In that case I had no problem and got a length of about 0.24 mm. Then, I changed the laser, but I noticed that the interference pattern did not disappear at any point along the entire mirror path, which is 139 mm, implying an optical path difference of almost 270 mm. This was extremely weird to me, as I had expected to see the interference pattern only over a short distance.

By taking pictures of the interference pattern for different mirror displacements, the 2D array information can be integrated along the axis in the direction of the fringes to find a function containing an average of the pattern intensity for each displacement. Such functions can be fitted according to the following equation to find the amplitude (A) with respect to displacement: I(x)=A⋅(1+cos(2πf⋅x+ϕ))+C,here x is the displacement along the image (2D array).

The amplitude of the interference pattern changes as the mirror moves, but it never disappears. Taking the data in a shorter interval, it can be seen that the frequency is even higher, this being the true periodic behavior of the amplitude (confirmed by the rest of the measurements that were made in even shorter intervals). The same can be observed when calculating the visibility by means of the equation: V=(I_{max}−I_{min})/(I_{max}+I_{min}).

At first I thought it might be that the laser is not really single mode, causing this kind of behavior, since another laser from Thor Labs does exactly this (See manual, section 5.6, page 31: https://www.thorlabs.com/drawings/2...44C1A4565AEE004/EDU-MINT2_M-EnglishManual.pdf). However, after a careful examination, it was verified that the laser is indeed single mode, so this idea loses support. So, it may be due to something related to the experimental setup:

I have a Michelson interferometer, the mirror that moves is a retroreflector mirror and it is on a motorized stage. This was done in an attempt to increase the distance the mirror could move and to find the point at which the interference pattern disappeared, without success. I added some ND filters in the output to attenuate the power and to be able to photograph the pattern to perform the analysis as mentioned above. In both cases, with or without the retroreflector mirror or camera, the periodic behavior of the visibility of the interference pattern is maintained over the entire displacement distance.

In the most recent setup, the beam is focused on a sample and then goes through a spatial filtering process, and it has also been verified that it remains collimated. Even in this new setup, the aforementioned behavior is still present. So, with all this information, my question to you is what could be causing this periodic behavior of the interference pattern visibility, which is maintained along the entire mirror displacement distance even though the coherence length is presumably much shorter according to the manufacturer.

 

[.Scott]

Although I am not entirely clear on your test setup, I think extracting the bandwidth from the spectrum graph may be misleading. It is only a "typical" graph and the exposure time in the spectrograph was likely on the order of milliseconds. So for any given nsec, the bandwidth may be much, much narrower.
Also, that graph was created with a Thorlab CCS100 with a resolution of 0.5nm.

 

[berkeman]

TL;DR Summary: The problem is that the coherence length of a laser I am experimentally measuring is much longer than the manufacturer claims and has an oscillating visibility.

(See manual, section 5.6, page 31: https://www.thorlabs.com/drawings/2...44C1A4565AEE004/EDU-MINT2_M-EnglishManual.pdf).

 

[gvgpg66]

View attachment 354176

Sorry, this is the real link: https://lenlasers.ru/upload/iblock/485/EDU_MINT2_M_Manual.LLS.pdf , page 29

 

[gvgpg66]

Although I am not entirely clear on your test setup, I think extracting the bandwidth from the spectrum graph may be misleading. It is only a "typical" graph and the exposure time in the spectrograph was likely on the order of milliseconds. So for any given nsec, the bandwidth may be much, much narrower.
Also, that graph was created with a Thorlab CCS100 with a resolution of 0.5nm.

I see what you mean, I was just looking for some kind of reference to work from, but I know it's quite possible that the coherence length was different. But I didn't expect it to be that long, that's the real question, because I was able to measure the interference pattern along almost 60 cm of optical path, so that's my question.

 

[Gleb1964]

I know that those type 532nm DPSS laser people using in LUPI (laser unequal path interferometer) with a several meters difference in a path length between the arms. The fringe visibility may variate along the path according to a multiple resonator lengths.
Can be that the spec bandwidth is related to multimode operation just nor resolved by spectrometer while you are running in a single mode.

 

[gvgpg66]

I know that those type 532nm DPSS laser people using in LUPI (laser unequal path interferometer) with a several meters difference in a path length between the arms. The fringe visibility may variate along the path according to a multiple resonator lengths.
Can be that the spec bandwidth is related to multimode operation just nor resolved by spectrometer while you are running in a single mode.

I understand, that would generate a change in the visibility of the pattern. But, using a grating I checked to see if I could observe another mode in the laser, but even at a great distance I could only identify a single mode. So the fact that I can see this behavior when there is only one mode is something that I have a hard time understanding.

 

[Andy Resnick]

From the product data sheet, I was able to extract the bandwidth from a graph of its spectrum, which is about Δλ≈0.6 nm. So, from with the coherence length equation: Lc=(λ_0)^2/Δλ→Lc≈0.5 mm.

That tracks- the rule-of-thumb is that the coherence length is about 2x the cavity dimensions, which makes sense for a diode laser.

Thus, in the lab I should observe the interference pattern only along a moving mirror path of at least 0.25 mm, so that the difference between the arms (twice) is equal to the coherence length. Before doing so, I measured the coherence length of a pulsed laser with a similar λ, which I used to find the point t_0 (where both arms have the same length). In that case I had no problem and got a length of about 0.24 mm. Then, I changed the laser, but I noticed that the interference pattern did not disappear at any point along the entire mirror path, which is 139 mm, implying an optical path difference of almost 270 mm. This was extremely weird to me, as I had expected to see the interference pattern only over a short distance.

I agree, this is confusing. However, I do question your use of a pulsed laser here- is that the only other laser you have access to?

My first thought is that the interference pattern is arising from something other than the adjustable path length difference- could it be coming from the collimating optics, for example?

 

[Gleb1964]

Thorlabs has two similar 532nm DPSS lasers, one 4.5mW and another 0.9 mW. If you look at the second laser spec, it has laser spectrum taken with much higher resolution. They are using Fourier spectrometer with 0.25cm ^-1 (or 0.007nm) bandwidth instead of diode array spectrometer with 0.25nm band.

I think that both lasers have approximately the same spectrum. I would expect more powerful laser generates more spectral lines.

It seems that spectrometer with resolution 0.007nm does not resolve single lines. Assuming 0.007nm line width that gives about 1cm coherence length, but it probably much longer.

 

[gvgpg66]

That tracks- the rule-of-thumb is that the coherence length is about 2x the cavity dimensions, which makes sense for a diode laser.


I agree, this is confusing. However, I do question your use of a pulsed laser here- is that the only other laser you have access to?

My first thought is that the interference pattern is arising from something other than the adjustable path length difference- could it be coming from the collimating optics, for example?

In the next few days I will try using another laser to see if the same thing happens, with that I will be able to discard whether this behavior comes from the setup or if it arises from the laser, as soon as I have the answer I will return with my observations!

 

[gvgpg66]

Thorlabs has two similar 532nm DPSS lasers, one 4.5mW and another 0.9 mW. If you look at the second laser spec, it has laser spectrum taken with much higher resolution. They are using Fourier spectrometer with 0.25cm ^-1 (or 0.007nm) bandwidth instead of diode array spectrometer with 0.25nm band.

View attachment 354197

I think that both lasers have approximately the same spectrum. I would expect more powerful laser generates more spectral lines.

It seems that spectrometer with resolution 0.007nm does not resolve single lines. Assuming 0.007nm line width that gives about 1cm coherence length, but it probably much longer.

It is a very strong possibility, in fact at first I thought that the laser I really had was the CPS532-C2, since that would fit better with what I was observing. However, I have now fully confirmed that the laser I have is the CPS532 with a much higher power. To verify this, I have contacted ThorLabs directly to inquire more about the laser, hoping that they will give me some additional information that can clarify what may be happening.