Note: At 10:20, I incorrectly assert that the linewidth measured on the ESA is 5MHz and that the inherent linewidth of the laser therefore must by 2.5MHz. The mistake is that the 5MHz is only the distance from the peak to where the spectral power drops by 3dB. When measuring linewidth, we actually care about the full 3dB width, which in this case would be 10 MHz. Therefore, the actual inherent linewidth of the laser is 5MHz.
Thanks! I was wondering about that! At 4:35, you wrote the same expression for the linewidth of both the AOM and 100km spool output, but are they supposed to be the same? Is the linewidth of the ESA is twice the linewidth of the two (just the sum of the linewidths)?
I think the first linewidth near 200MHz is more due to environment noise so they are similar and is actually Gaussian shape, more porper way might be to use the sidewings to fit for Lorentizian shape to get actual linewidth. Very nice demonstration!
I have a question, on your other video: "Distributed Feedback Laser (DFB) demonstration" , you show us how the spectrum of the laser is on a OSA, we could see the distribution there. Why do we then need this setup, could we not just measure the linewidth on that? (I think I miss something fundamental :( )
@@jusm5139 Typical grating based OSA's have minimum resolutions (several GHz) that are much larger than the typical linewidth of diode lasers (several MHz). Therefore, measuring the linewidth with such an OSA is like trying to use a regular ruler to measure the width of a hair. An OSA that relies on interferring the incoming signal with a built-in laser can achieve a better resolution, which approaches that of DFB lasers, but the resulting plot has a width, which is determined by both the linewidth of the DFB and that of the internal laser, which makes the DFB width tricky to extract. The setup in this video is nice because it only involves the laser itself, thus making the result easy to interpret. Typical ESA's have minimum resolutions of a few Hz, which allows them to measure highly stable lasers; just add a longer delay line to ensure that the highly stable signals in the two branches have decorrelated enough when they reach the PD.
@@yourfavouriteta Thank you for your quick reply!! This makes it more clear. I still to grasp some things, I will try to read more literature on the "decorrelated" part, also to be able to calculate out at what delay a certain laser is 'decorrelated' , must be some way to measure a minimum delay for it. But for now, thanks a lot and when possible keep these videos coming, I really enjoy your videos and triggers thinking! Thank you!
@@jusm5139 You're welcome! One of my recent videos actually explains how the linewidth of a laser comes about in the first place: ua-cam.com/video/qcpKBbtCguQ/v-deo.html An ideal laser would have a phase that increases linearly over time according to cos(wt). Alternatively, we can say that a laser is "single frequency" if the derivative of the argument inside the cosine function is a constant. If the derivative is not constant, but changes over time, the frequency will be changing over time. With this in mind, a realistic laser basically has a phase that both "increases linearly" (due to the carrier frequency) AND additionally undergoes a 1D random walk over time. Therefore, if you know the phase at t=0, you can reliably predict the phase at t=dt, but this prediction becomes less reliable the more time passes. For sufficiently large time delays, the original phase at t=0 provides no information about the phase at t=T. The experiment here takes laser light at two very different times (thanks to the delay line), interferes them and looks at the average spectrum of the interference. If we see a Lorentzian shape, we can be sure that the time delay is large enough for the two copies to be completely decorrelated. The (Schawlow-Townes) linewidth of this Lorentzian is the inverse of the coherence time and can in fact be calculated from knowledge of the laser parameters: www.rp-photonics.com/Schawlow-Townes_linewidth.pdf See also this excellent paper on linewidths: www.mdpi.com/1424-8220/24/11/3656
Thank you for useful video. Is this measurement setup configured by PM fiber better than non-PM? I expect PM-setup gets higher signal intensity at the photodiode.
Glad that you like it! Using PM fiber does not provide a significant advantage. To ensure maximum interference between the reference signal and the signal from the AOM, they just need to have the same polarization at the photodiode, which can easily be ensured by using a regular polarization controller placed in one of the "arms" as shown at 6:08. Since the exact SOP does not matter as long as it's the same for both signals, the paddles can be adjusted until maximum interference is achieved.
Really nice informative video! Thank you! However, how would you stabilize the laser frequency over time for some high precision spectroscopy measurement?
I am glad you found it helpful! Laser diodes with linewidths below 1MHz are commercially available for around $1.000. More expensive models in the low kHz range are also available. Depending on your application and budget, these might be sufficient. Alternatively, you can stabilize a laser to an external cavity. The idea is that two highly reflective mirrors with high mechanical and thermal stability create a Fabry-Peroy cavity with extremely narrow lines. Let's assume that this FP cavity line width is 0.1kHz. If you shine a 1MHz laser centered on one of the FP lines into this cavity, the light that comes out will be filtered and have a 0.1kHz linewidth. If this light is sent back into the source of the 1MHz laser light, it will be amplified and sent back to the FP cavity for another "round trip". Eventually, the filtered light inside the 0.1kHz range will "steal" all the available power in the laser source, effectively changing it from 1MHz to 0.1kHz. One detriment is that the central frequency of the laser source must be aligned with one of the FP lines for this trick to work, which makes the system less tunable.
You're welcome, glad you found it useful. I don't think using a MMF would be advantageous. If two (or more) transverse modes propagating with different speeds are present in the system, I think both of the signals they produce will contribute to the measurement simultaneously, making the result more difficult to interpret.
Hmm, could be many different things. If possible, please tell me the following: 1) What is the driving frequency of the AOM and what is the frequency spacing from the main peak to the many peaks you mention? Can you post a link to the spec sheet of the AOM and to the function generator you use for driving it? 2) What type of laser are you testing? Can you post a link to the spec sheet? Maybe it emits light at more than one frequency? This can also be checked with a high resolution optical spectrum analyzer if its resolution is higher than the spacing between the peaks you are observing. 3) What current are you driving the laser with? If driven with too high current, the electric field in the gain medium may become so strong that four-wave-mixing occurs, where new frequency components are generated. If FWM is the problem you can check it with an optical spectrum analyzer and remove the problem by reducing the driving current. Note that changing the current will alter the gain of the medium and therefore change the linewidth a bit. 4) What photodiode are you using? What is its bandwidth (maximum operational frequency) and saturation power? If a very intense sinusoidal optical signal hits a photodiode so the saturation level is exceeded, the generated electrical signal may get "clipped", which causes spurious frequency components to appear. For example, a clipped 200MHz signal will cause extra frequency components at 400MHz, 600MHz and so on. You can check this by reducing the incident power. 5) Try running the linewidth measurement setup with the laser turned off. The electrical spectrum analyzer may be experiencing interference from other devices in your laboratory.
Can someone answer this At 690 nm if laser linewidth 0.06 cm^-1 then if the laser is frequency tripled to get a wavelength 230 nm then what would be the laser linewidth
EDIT: The explanation below is incorrect, please see this video for the correct answer: ua-cam.com/video/qcpKBbtCguQ/v-deo.html In short, THG will actually increase the original linewidth by a factor 3^2=9 and not sqrt(3) as asserted below. That's a good question! Here's how to think about it: Suppose you take turn launching three ideal CW lasers at 99THz, 100THz and 101THz, where each has zero linewidth into the same system causing THG. They will end up at 297THz, 300THz and 303THz respectively. You can see that the spacing between them started out being 1THz, which ultimately gets tripled to 3THz. This thought experiment shows that we generally expect the linewidth of a realistic laser to increase, but we should be careful about drawing conclusions about the exact amount from it, since nonlinear effects involve all its frequencies interacting with each other! In reality, each frequency in the spectrum does not simply get tripled. Rather, the spectrum undergoes a "triple convolution" with itself. Let's assume that you have a laser with a Gaussian lineshape that is undergoing SHG. Convolving two Gaussians simply results in adding their variances, so in terms of standard deviations, s: s_final = sqrt(s1^2+s2^2) = sqrt(2)s_initial, if s1=s2. Similarly, we would expect the final standard deviation for THG to be sqrt(3) higher than the initial one. Of course, this is only exactly true for a Gaussian lineshape (which is often more "Lorentzian" in practice), but it should be a good approximation. Here is a paper that explores something related to your question but for SHG: opg.optica.org/oe/fulltext.cfm?uri=oe-32-3-3266&id=545631 Check out the Q&A section of this article: www.rp-photonics.com/frequency_doubling.html This spec sheet for a commercial UV laser utilizing THG also indicates an approximate sqrt(3) increase in linewidth for the output compared to the input: www.sirah.com/wp-content/uploads/documents/THG.pdf
@@e-skills2120 By the way: Mathematically, we need to do a convolution, because in the time domain, the amount of THG field depends on E^3. From Fourier theory, we know that multiplying in the time domain is equivalent to doing convolutions in the frequency domain.
@@yourfavouriteta Thanks a lot for a clear and descriptive answer with reference. It was so kind of you, means a lot Once again thank you for the response
@@josephthomas3791 For this detection method, we need the light in the two arms to be decorrelated. In other words, we compare two "samples" of the same electric field that are so far apart in time that their relative phase is 0% due to the predictable oscillations at the carrier frequency and 100% due to random-walk fluctuations in the phase. It is the spectrum of these fluctuations that give rise to the Lorentzian lineshape. With a 100km delay fiber, any laser with a coherence time shorter than roughly 100km/c~300μs will give rise to a Lorentzian lineshape on the ESA. Since c/100km~3kHz, we can also say that this setup makes it easy to measure lasers with a linewidth over 3kHz. If we tried to use this setup for measuring a laser with a 500Hz linewidth, the light in each arm would not be fully decorrelated and the ESA would not show a Lorentzian, but a sharp "spike" with "sidelobes". This shape can be deacribed analytically to obtain the "true" linewidth, but it's often easier to simply add more delay fiber. The only cost is that the delayed field experiences higher loss, so the final signal will be weaker.
I was not previously familiar with that method, but after looking into it, I think the answer is yes, provided that the three lasers have approximately the same linewidth: www.wriley.com/3-CornHat.htm
Note: At 10:20, I incorrectly assert that the linewidth measured on the ESA is 5MHz and that the inherent linewidth of the laser therefore must by 2.5MHz. The mistake is that the 5MHz is only the distance from the peak to where the spectral power drops by 3dB. When measuring linewidth, we actually care about the full 3dB width, which in this case would be 10 MHz. Therefore, the actual inherent linewidth of the laser is 5MHz.
Thanks! I was wondering about that!
At 4:35, you wrote the same expression for the linewidth of both the AOM and 100km spool output, but are they supposed to be the same? Is the linewidth of the ESA is twice the linewidth of the two (just the sum of the linewidths)?
I think the first linewidth near 200MHz is more due to environment noise so they are similar and is actually Gaussian shape, more porper way might be to use the sidewings to fit for Lorentizian shape to get actual linewidth. Very nice demonstration!
Interesting idea! Makes sense that if one diode is more sensitive to external noise, "smearing" could occur in the spectrum.
I have a question, on your other video: "Distributed Feedback Laser (DFB) demonstration" , you show us how the spectrum of the laser is on a OSA, we could see the distribution there.
Why do we then need this setup, could we not just measure the linewidth on that? (I think I miss something fundamental :( )
@@jusm5139 Typical grating based OSA's have minimum resolutions (several GHz) that are much larger than the typical linewidth of diode lasers (several MHz). Therefore, measuring the linewidth with such an OSA is like trying to use a regular ruler to measure the width of a hair.
An OSA that relies on interferring the incoming signal with a built-in laser can achieve a better resolution, which approaches that of DFB lasers, but the resulting plot has a width, which is determined by both the linewidth of the DFB and that of the internal laser, which makes the DFB width tricky to extract.
The setup in this video is nice because it only involves the laser itself, thus making the result easy to interpret. Typical ESA's have minimum resolutions of a few Hz, which allows them to measure highly stable lasers; just add a longer delay line to ensure that the highly stable signals in the two branches have decorrelated enough when they reach the PD.
@@yourfavouriteta Thank you for your quick reply!! This makes it more clear.
I still to grasp some things, I will try to read more literature on the "decorrelated" part, also to be able to calculate out at what delay a certain laser is 'decorrelated' , must be some way to measure a minimum delay for it.
But for now, thanks a lot and when possible keep these videos coming, I really enjoy your videos and triggers thinking! Thank you!
@@jusm5139 You're welcome! One of my recent videos actually explains how the linewidth of a laser comes about in the first place:
ua-cam.com/video/qcpKBbtCguQ/v-deo.html
An ideal laser would have a phase that increases linearly over time according to cos(wt). Alternatively, we can say that a laser is "single frequency" if the derivative of the argument inside the cosine function is a constant. If the derivative is not constant, but changes over time, the frequency will be changing over time.
With this in mind, a realistic laser basically has a phase that both "increases linearly" (due to the carrier frequency) AND additionally undergoes a 1D random walk over time. Therefore, if you know the phase at t=0, you can reliably predict the phase at t=dt, but this prediction becomes less reliable the more time passes. For sufficiently large time delays, the original phase at t=0 provides no information about the phase at t=T.
The experiment here takes laser light at two very different times (thanks to the delay line), interferes them and looks at the average spectrum of the interference. If we see a Lorentzian shape, we can be sure that the time delay is large enough for the two copies to be completely decorrelated. The (Schawlow-Townes) linewidth of this Lorentzian is the inverse of the coherence time and can in fact be calculated from knowledge of the laser parameters:
www.rp-photonics.com/Schawlow-Townes_linewidth.pdf
See also this excellent paper on linewidths:
www.mdpi.com/1424-8220/24/11/3656
@@yourfavouriteta
Thank you for useful video.
Is this measurement setup configured by PM fiber better than non-PM?
I expect PM-setup gets higher signal intensity at the photodiode.
Glad that you like it!
Using PM fiber does not provide a significant advantage. To ensure maximum interference between the reference signal and the signal from the AOM, they just need to have the same polarization at the photodiode, which can easily be ensured by using a regular polarization controller placed in one of the "arms" as shown at 6:08. Since the exact SOP does not matter as long as it's the same for both signals, the paddles can be adjusted until maximum interference is achieved.
@@yourfavouriteta Thank you for your reply!
I understand to use polarization controller.
Really nice informative video! Thank you! However, how would you stabilize the laser frequency over time for some high precision spectroscopy measurement?
I am glad you found it helpful!
Laser diodes with linewidths below 1MHz are commercially available for around $1.000. More expensive models in the low kHz range are also available. Depending on your application and budget, these might be sufficient.
Alternatively, you can stabilize a laser to an external cavity. The idea is that two highly reflective mirrors with high mechanical and thermal stability create a Fabry-Peroy cavity with extremely narrow lines. Let's assume that this FP cavity line width is 0.1kHz. If you shine a 1MHz laser centered on one of the FP lines into this cavity, the light that comes out will be filtered and have a 0.1kHz linewidth. If this light is sent back into the source of the 1MHz laser light, it will be amplified and sent back to the FP cavity for another "round trip". Eventually, the filtered light inside the 0.1kHz range will "steal" all the available power in the laser source, effectively changing it from 1MHz to 0.1kHz.
One detriment is that the central frequency of the laser source must be aligned with one of the FP lines for this trick to work, which makes the system less tunable.
Thanku for the info. Can we use multi mode fiber for this setup?
You're welcome, glad you found it useful.
I don't think using a MMF would be advantageous. If two (or more) transverse modes propagating with different speeds are present in the system, I think both of the signals they produce will contribute to the measurement simultaneously, making the result more difficult to interpret.
Good. when I tested, there were many peaks near the peak. what was the reason
Hmm, could be many different things. If possible, please tell me the following:
1) What is the driving frequency of the AOM and what is the frequency spacing from the main peak to the many peaks you mention? Can you post a link to the spec sheet of the AOM and to the function generator you use for driving it?
2) What type of laser are you testing? Can you post a link to the spec sheet? Maybe it emits light at more than one frequency? This can also be checked with a high resolution optical spectrum analyzer if its resolution is higher than the spacing between the peaks you are observing.
3) What current are you driving the laser with? If driven with too high current, the electric field in the gain medium may become so strong that four-wave-mixing occurs, where new frequency components are generated. If FWM is the problem you can check it with an optical spectrum analyzer and remove the problem by reducing the driving current. Note that changing the current will alter the gain of the medium and therefore change the linewidth a bit.
4) What photodiode are you using? What is its bandwidth (maximum operational frequency) and saturation power? If a very intense sinusoidal optical signal hits a photodiode so the saturation level is exceeded, the generated electrical signal may get "clipped", which causes spurious frequency components to appear. For example, a clipped 200MHz signal will cause extra frequency components at 400MHz, 600MHz and so on. You can check this by reducing the incident power.
5) Try running the linewidth measurement setup with the laser turned off. The electrical spectrum analyzer may be experiencing interference from other devices in your laboratory.
Can someone answer this
At 690 nm if laser linewidth 0.06 cm^-1 then if the laser is frequency tripled to get a wavelength 230 nm then what would be the laser linewidth
EDIT: The explanation below is incorrect, please see this video for the correct answer:
ua-cam.com/video/qcpKBbtCguQ/v-deo.html
In short, THG will actually increase the original linewidth by a factor 3^2=9 and not sqrt(3) as asserted below.
That's a good question! Here's how to think about it:
Suppose you take turn launching three ideal CW lasers at 99THz, 100THz and 101THz, where each has zero linewidth into the same system causing THG. They will end up at 297THz, 300THz and 303THz respectively. You can see that the spacing between them started out being 1THz, which ultimately gets tripled to 3THz.
This thought experiment shows that we generally expect the linewidth of a realistic laser to increase, but we should be careful about drawing conclusions about the exact amount from it, since nonlinear effects involve all its frequencies interacting with each other! In reality, each frequency in the spectrum does not simply get tripled. Rather, the spectrum undergoes a "triple convolution" with itself.
Let's assume that you have a laser with a Gaussian lineshape that is undergoing SHG. Convolving two Gaussians simply results in adding their variances, so in terms of standard deviations, s:
s_final = sqrt(s1^2+s2^2) = sqrt(2)s_initial,
if s1=s2. Similarly, we would expect the final standard deviation for THG to be sqrt(3) higher than the initial one. Of course, this is only exactly true for a Gaussian lineshape (which is often more "Lorentzian" in practice), but it should be a good approximation.
Here is a paper that explores something related to your question but for SHG:
opg.optica.org/oe/fulltext.cfm?uri=oe-32-3-3266&id=545631
Check out the Q&A section of this article:
www.rp-photonics.com/frequency_doubling.html
This spec sheet for a commercial UV laser utilizing THG also indicates an approximate sqrt(3) increase in linewidth for the output compared to the input:
www.sirah.com/wp-content/uploads/documents/THG.pdf
@@e-skills2120 By the way: Mathematically, we need to do a convolution, because in the time domain, the amount of THG field depends on E^3. From Fourier theory, we know that multiplying in the time domain is equivalent to doing convolutions in the frequency domain.
@@yourfavouriteta
Thanks a lot for a clear and descriptive answer with reference.
It was so kind of you, means a lot
Once again thank you for the response
@@e-skills2120 You're welcome!
Why interferometer one arm is having 100 km can I have lower length ?
@@josephthomas3791 For this detection method, we need the light in the two arms to be decorrelated. In other words, we compare two "samples" of the same electric field that are so far apart in time that their relative phase is 0% due to the predictable oscillations at the carrier frequency and 100% due to random-walk fluctuations in the phase. It is the spectrum of these fluctuations that give rise to the Lorentzian lineshape.
With a 100km delay fiber, any laser with a coherence time shorter than roughly 100km/c~300μs will give rise to a Lorentzian lineshape on the ESA. Since c/100km~3kHz, we can also say that this setup makes it easy to measure lasers with a linewidth over 3kHz.
If we tried to use this setup for measuring a laser with a 500Hz linewidth, the light in each arm would not be fully decorrelated and the ESA would not show a Lorentzian, but a sharp "spike" with "sidelobes". This shape can be deacribed analytically to obtain the "true" linewidth, but it's often easier to simply add more delay fiber. The only cost is that the delayed field experiences higher loss, so the final signal will be weaker.
Could You use "Three-Cornered-Hat" approach with three independent lasers?
I was not previously familiar with that method, but after looking into it, I think the answer is yes, provided that the three lasers have approximately the same linewidth:
www.wriley.com/3-CornHat.htm
Thank you so much.
You're welcome!
Nice try. The 2nd laser may suffer from more 1/f noise than the 1st one.