Ideas for improving SHG efficiency in Q-switched DPSS laser?

[brianpe]

I just won't go away. I've been working on improving SHG efficiency of a home made DPSS laser. I've made a ton of progress (entire saga here) but I'm not seeing the conversion efficiencies I expect.

My test setup is a single 40W fiber array focused to a .5% doped Nd:YVO4 crystal that is 15mm long. This output is focused via curved mirrors to a Cr:YAG crystal with an initial transmission of 90%. The pulsed output of this is sent to a 10mm KTP crystal that is temperature tuned with pretty close to .1ºC stability. All of this is intracavity. The beam into the KTP is parallel except for some focusing caused by thermal lensing.

I am pumping the array with a maximum of 30A which yields an optical pump input of just under 16W. The pump is cooled, but not temperature controlled. The Nd:YVO4 is not cooled at all but is held in a good copper block. The block gets warm after a while but not hot to the touch.

I've temperature tweaked the KTP to get the best phase matching I can -- and it is sensitive. A 1ºC change in temperature yields a 3x change in output power.

I calculate I should be able to get about 4W of green output with this setup, but I am seeing about 1.5W.

The idea behind how this cavity is setup is that it takes advantage of thermal lensing in the vanadate. As lensing increases, the waist inside the Cr:YAG can either increase or decrease depending on where I place the crystal (the two mirrors are 200mm and 150mm and form a modified confocal cavity. The focal point of this cavity moves as lensing increases). The waist inside the. KTP always decreases, making efficiency increase. The idea is to balance these two so that as the power goes up I continue to hit as close to the KTP conversion peak as is optimal. If thermal lensing is ignored, the incoming beam to the KTP is parallel. I've added in the additional angle caused by thermal lensing to the calculations but it doesn't make much of a difference.

Calculations:

• Continuous wave IR output is spot on with my calculations.
• The Cr:YAG repetition rate is off by a significant amount (almost 2x) but seems to vary widely depending on the cavity setup. In some cavities it is only off by < 20%.
• Average output power for IR matches measurements pretty well...which is a little odd because this uses the repetition rate.
• SHG is where it all falls apart. In both CW and Q-switched, I calculate a significant upturn in efficiency due to thermal lensing pinching the waist in the KTP. But the measured data is much more in line with calculations when I ignore thermal lensing. Note that the measured power does have some of the curve associated with lensing. This is why I was suspecting a phase mismatch, but I feel I've got this pretty dialed in:

It's possible my math is just off. But if there are ideas I'm missing here I'd love to hear them.

[Farbe]

It might not be very helpful, but I want to ask you:

Did you take the wavelength drift of the pump array into account?
The pump will drift up with higher currents which might ruin your absorption coefficient, resulting in less thermal load -> less thermal lensing despite higher input power.


You could check for this by measuring the undoubled output before the KTP.

You may even did that because I am not really sure if you meant that by:

• Continuous wave IR output is spot on with my calculations.

Did you mean the 1064nm CW output is matching your expectations or your pump array Pout vs Current?

Are you able to confirm the pulsed output length / peak power without KTP?

Cr:YAG also shows thermal lensing, did you take that into account?

[brianpe]

Thx for the reply, and good questions.

I did not take wavelength drift into account but I measured it over the weekend and it drifts .4nm between pump threshold and 30A. It does read a little low (806.8nm) so I may be over cooling. I only have one TEC controller in this setup and I am reserving it for the KTP. Nor have I factored in thermal lensing for either the KTP or the Cr:YAG. I did find a thermo-optic coefficient published for KTP, but couldn't find one for Cr:YAG.

I ran a series of measurements with the cavity configured as CW, IR Q-Switched and doubled Q-switched:



"Spot On" is maybe hyperbole (it's been better with different cavities), but for CW and IR Q-switched my simulation is an OK predictor. For SHG...not so much. The SHG and CW output largely overlap -- the reason the SHG for the high conversion rates here is that I just chose a stock 20% output coupler for the IR. SHG efficiency here should be about 30%.

I also measured the repetition rate of both IR and SHG through the power range. The pulse width is about 100ns (I calculate 54ns) and from average power, pulse width and rate I can estimate peak power to be about 675W for IR and 250W for SHG:



There are a few interesting things I observed while taking measurements:

Thermal Lensing

Thermal lensing is not instant. I takes a few seconds, and since I am not cooling the vanadate it never really reaches steady state. All these average powers are taken from the "peak" reading of my meter. I realize that should mean that the power increases for the SHG case as I'm using lensing to my advantage, but it doesn't. Now that I say that there definitely have been some measurements I've taken in the past where the power climbs. These were at pretty moderate power levels. I need to get back to that and think about it more.

My calculations predict at about 28A of pump current I will start to see cavity destabilization due to lensing. This is really clear with the SHG -- The output drops to zero after about five seconds. I was worried this was leaving a large intracavity flux that could do damage, but now I think the intracavity beam was also probably extinguished since I'm losing stabilization.

Repetition Rate

The repetition rate for IR is an OK match for what I calculate but the SHG is way off and shows a much steeper slope. I think this is because I am not getting the conversion I expect so the cavity inversion does not drop as low as the simulation expects.

The calculated repetition rate for IR shows a logarithmic trend. In this cavity the Cr:YAG waist is staying pretty constant, but the beam waist in the vanadate is decreasing. This causes the overall density in the Cr:YAG to go down with lensing.

Looking at the graph the measured rate for IR is more linear than I predict. I think this means I'm not seeing the lensing I expect here. This may be due to my measurement technique: I was taking a rate reading about 3s after starting the pumps. This may not be long enough. I suspect to get this close I'm going to have to temperature regulate the vanadate.

Anyway, thx for reading.

[Farbe]

Regarding Cr:YAG lensing:
https://sci-hub.ru/10.1109/CLEOE.1998.719150
However you should also be able to use the values for undoped YAG, they should be very close to almost exactly the same.

Pump Wavelength:
Yes you cool your diodes too much. You can expect better absorption if your wavelength is higher but you will also need more current and power at higher temps for the same Pump output.
Did you check how much isn't absorbed? It might be good as it is depending on your crystal length.


Thermal Lensing:
I am not certain that you will see a steady climb. I didn't calculate anything but my gut tells me that the time constant of the small pumped mode volume inside the crystal is so small that you aren't going to see a climb.
You could calculate the time by getting the pumped volume + density to get heat capacity and check for "how long does it take to heat up".

I would expect that this time will be very short maybe just a few hundred ms. But thats just my gut feeling after all. Maybe worth a quick calculation or even better a quick thermal simulation in fusion.

I simulated stuff like that in fusion to get me a better understanding when my crystal will break. (von Mises stresses).

You have written on your site:

The paper uses fiber coupled pump lasers that keep the polarization aligned. I’m not: I’m using large multi-mode fibers and the polarization is random. The way I’ve handled this is to assume 50% at ordinary and 50% at extraordinary, calculate the dioptric of both, and take the average. It’s still not great.

I think taking the average might be a bad assumption.
Both polarization components get absorbed differently in the medium.
The one with the lower absorption coefficient gets "deeper" into the crystal resulting In a wider spread of power along its z-axis. The other one gets absorbed much faster resulting in more loading of the input face of the crystal.
Same for assuming a single wavelength for absorption calculations.

Nd:YVO4 shows different coefficients for both polarization, I am not sure how much, a quick google couldnt tell me.

I integrated my diode spectrum and absorption spectrum and used that to find how much power is absorbed in each 0,5mm z-length of crystal to get a better estimate of temperature and stress.

Assuming 50% random polarization seems fine.

However, that seems to be a non issue as your CW IR power is "good".

Maybe some astigmatism in the thermal lens because of bad pump mode / cavity mode overlap?
How much bigger is your pump compared to the mode?

Is your crystal mounted stress free? Does it get cooled on all sides?

Did you adjust the laser under full output lasing conditions or at/close to threshold? (Thinking: You might be in a local maximum)

[brianpe]

Thanks! I will get back to some of the deeper ideas here after I can run some math / simulations.

I took a few quick measurements tonight and...

My spectrometer needs to be recalibrated. Running with SHG the spectrum shows 529, 806, 1060 nm. So the spectrometer is off by about 3nm. I have a calibration source and can recalibrate it. I could still use some temp regulation on the pump because after a few minutes of runtime the spectrometer shows 811nm, but until it outpaces the TEC it's OK.

Thank you for finding that description on my blog about how I'm calculating thermal lensing. The blog post is outdated and I no longer do this. I was confused between different polarizations (s vs p) and ordinary vs extraordinary rays. I thought they were talking about the same thing but they're not. The way I calculate this now is to still assume 50% each s and p, calculate the net crystal absorption from the absorption coefficients for each polarization, and use that along with dn/DT for ordinary rays to calculate the thermal lens. This doesn't account for the lens depth into the crystal like you mentioned. I don't know if I need to factor in dn/DT for extraordinary rays here. It's a much smaller value but I'm sure there is some contribution given the random polarization.

I had assumed the laser would stop altogether when I reach lensing that should be unstable but it appears to just start dropping power, which is why I doubted the much larger lensing value.

I found something interesting. You mentioned crystal absorption of the pump light so I measured it: one of the mirrors on the crystal is already HT @ 808 in preparation for dual end pumping. I measured the 808 light coming through it and it was much larger than I expected: approx 300mW for a 3W pump beam. What's more, the value rapidly decreased once the laser was running....exactly like my power drop I thought was due to thermal lensing. I measured just the pump and it's a solid 3W. I removed the crystal and again a solid 3W. I put the crystal back in place and the problem went away. Leakage through the mirror was only about 5mw (and some of that could be 1064 leakage...mirrors aren't perfect). While I do see some power drop when I run, it is much more consistent now and doesn't rapidly drop like it used to. The crystal looks like it is in the same place....not sure what I changed.

Crystal mount: this bench setup is using a crystal out of a Coherent Avia and I'm just using the Avia mount. This is mount is cooled on "2 1/2" sides: two sides are solid and the bottom has a bit of a groove in it. The crystal is held in place with thermal silicone which gives some compliance. The mount I have for the finished laser is custom but uses the same cooling mechanism. Instead of thermal silicone I'm using a conforming graphite pad. This gives decent conductivity while adding some compliance so it's not too rigid.

This cavity does have a fair amount of astigmatism. There are two concave mirrors at about a 12º angle and this causes the cavity mode to be elliptical. Within the crystal and with zero lensing the mode is ~330µm x 600µm. I am pumping this with a 400µm beam. I can improve the astigmatism by increasing the distance between the curved mirrors by a couple of mm. When I do this the cavity destabilizes with a little less lensing, so I've optimized to tolerate higher lensing at the expense of worse astigmatism. My mathematics does not account for the elliptical mode, however, and I am doing the math based on a 330µm mode waist (these are all radii). This should actually calculate a little low because there is some pump loss from 400 to 330, but in reality one dimension will be able to use the full 400.

I adjusted the cavity above threshold, but not with the power turned up very high. Nor have I tried to adjust the pump / mode overlap while the power is up. Probably worth some experimentation there.

[Farbe]

Did you check your 1064nm beam profile/shape?

some pump loss from 400 to 330, but in reality one dimension will be able to use the full 400.

This immediately rings a bell.

Having the pump smaller than the mode waist will put your mode inside the thermal aberrations from the thermal lens.

Most designs sacrifice some efficiency to make sure the pump is always bigger than the mode waist to reduce the amount of "thermal aberrations"
Or they at least try to match it as closely as possible.


Your design might suffer from aberrations on only one axis. This could even cause TM01 or so oscillations because the 400 vs 330um axis could even be big enough to cause higher modes to appear and therefore make the M² worse resulting in bigger spot sizes in your SHG crystal.

The astigmatism will also cause bigger spot sizes / lower energy densitys in your SHG. Did you take that into account?

[brianpe]

Lots of good stuff here and lots of experimentation.

First: Cr:YAG Lensing

I'm really not sure I'm doing this right, but I did calculate lensing in the Cr:YAG and re-modeled the cavity factoring it in. Lensing in the Cr:YAG does increase the radius of the beam waist in the KTP so this will affect SHG efficiency.

I'm not sure the way I'm calculating the Cr:YAG lensing is correct. First, to estimate absorption I looked at the emission spectra for Cr:YAG and calculated absorption based on an input 1064nm beam and the peak emission around 1450nm. Then, I used the population inversion at the point where the Cr:YAG bleaches to calculate the beam power. I considered this a constant since the YAG always saturates at the same intensity. This misses some excited state absorption but I'm assuming that's small. With this I calculate 151cm of thermal lensing from the Cr:YAG. I also tried the case where all of the 1064nm light was absorbed and this yielded 30cm of lensing. I'm not sure if either of these is right. I do see some drop off in power output as a result, but it is very minor compared to what I measure.

I also found a paper that included equations for the time constant for thermal lens generation. You're correct: the lens evolves very quickly (~3ms for the time constant so by 30ms the lens is pretty established).

Pump Mode Overlap (Mode Filling Factor)

Excellent that you pointed out the thermal lens aberrations. I tried two different collimator setups: I tried a large 700µm pump radius and a smaller 526µm radius. The 700µm radius is 100µm larger than the largest mode waist so it should have no aberrations. The 526µm is smaller than the largest mode, but has headroom as the mode shrinks due to lensing. At 1000cm of lensing 526µm is larger than the cavity mode.

Also, with the 700µm waist I tweaked the Cr:YAG placement to maximize the power output. I also fed this new position back into my calculations and found it very interesting that it makes little difference to my calculations but quite a lot of difference in measured power output:



I ran these same mesurements for the 526µm pump waist, using my new optimized Cr:YAG position. Better power than before, but still starts to fade after 2.5w. Also, with both of these pump waists I calculate that I can max out my bench supply before I start having problems with lensing.




Astigmatism
All my math assumes circular beam profiles. I've worked around the astigmatism by trying to choose the conservative or worst case values from the ellipse. This isn't terribly accurate but I was hoping it was good enough to predict performance. I've also been assuming an M^2 of 1, which I'm sure is too high. As a test, I increased M^2 to see if I can make my calculations match my measurements. And I can....but I have to set M^2 to 80. Is that even possible?



There's something in the setup that is just preventing me from getting decent harmonic conversion past about 2.5w.

[brianpe]

I think the cavity may be mode hopping. I built a new cavity this weekend that uses 400mm/200mm mirrors to constrict the beam. This yields a pretty mediocre waist constriction in the Cr:YAG but a 5x constriction in the KTP. Calculations show this cavity is very tolerant to lensing and the green output should be similar with and without taking lensing into account. I really wanted to see here if my lensing math is off.

Well, this cavity is not great. I can't generate over 1.2w of power but it does demonstrate very clearly what might be happening in the other cavity: mode hopping. I added an expanding lens after the output coupler to make the beam larger and I can clearly see it hop as I turn the current up. By 30A the beam is a real mess. I was able to tame this with a spatial filter but the alignment is not perfect down the bore and I don't have an extra x-y positioner, so I wasn't really able to dial it in very well. The power output didn't suddenly spike with this in place but it did clean up the beam.

I think I need to spend a little time refining the cavity design so it doesn't change too much during lensing. I found this paper on optimizing saturable absorbers for thermal lensing; hopefully it's a valuable read.

[Farbe]

Hey!

Nice to see your progress!

And I can....but I have to set M^2 to 80. Is that even possible?

Are you talking about the cavity mode or the pump mode here?
I would guess that the pump source M² is even worse than 80.
Considering a single 5W 450nm diode is close to M² 1,5x30.

Your pump module is likely a huge multi emitter setup.
So very likely that your M² is >80x80

A FAP800 with 40W has an NA of 0,14 and a 800um fibre. That equates to M² > 210!

I would think that the cavity mode would be better, but it depends on how well you keep the overlap / in which regions the energy density is high enough to cause oscillation.

[brianpe]

Are you talking about the cavity mode or the pump mode here?

I meant cavity mode. At higher powers this cavity was a real mess, but I don't think it was that much of a mess. The power fluctuations at higher intensities look somewhat sinusoidal, but I wonder if this is mode hopping and each mode affects SHG conversion differently:



That paper I cited has some really interesting math in it for calculating the thermal lens of Cr:YAG when used as a saturable absorber. It's going to be a bear integrating that into my simulation -- in my case the thermal lens of the YAG is going to affect downstream SHG efficiency, which then changes the effective output coupling and pulse rates, so it feeds back into the Cr:YAG thermal lens calculations. I'm also using two pieces of software: Rezonator for cavity stability and Gaussian beam analysis, and then the data from that is fed into a Matlab simulation for the rest. Those equations require coupling between Matlab and Rezonator. I wonder if LasCAD can do this and what a single license costs...