Modelling DFG in PPLN pumped by 800 nm

[jmorse2020]

Hello Nick,
I hope you're well and thanks for your work on this code. I am a PhD student tasked with modelling DFG in PPLN (MgO:LiNbO3) to 1) simulate the expected output from the crystal we have in our system and 2) use this to inform a decision on buying a new crystal aiming for higher conversion efficiency. In our lab we single pass the PPLN but our crystal is short (400 um), we think a longer crystal (500 - 1000 um) might improve our conversion efficiency, but want to back this up with simulations before making the order. Our system is designed to produce 3-4 um MIR light which we further amplify, and I think the idler overlaps with the pump and extends out to 1.1 um.
Currently I am struggling to get sensible outputs using the parameters of the crystal in our system. I was wondering if you have any advice on the PPLN modelling, since you mention it in your docs when demonstrating the for loops in the sequence console. In our lab I think we expect to see up to 10% conversion efficiency of the DFG process, so I hoped to see this reflected in the spectrum in the LWE outputs.

We amplify the output of our Ti:S in a single OPA stage (800 nm centred with 100 nm bandwidth approx.) to get around 10-30 uJ per pulse. After some dispersive optics, I estimated the GDD going in to be -1284 fs^2, giving us a few hundred fs pulse to pump the PPLN. I have estimated that we focus to a tight 40-50 um focal spot.
The poling period of our PPLN is technically chirped, i.e. the poling period increases linearly along the length of the crystal. This is something I will try to code in properly, but for now I am trying to see any results so I have been running either at a fixed poling period or have sampled up to four different periods with different for loops, with different poling periods in each from 19.4 um to 22 um. Here's my snippet for that:

set(1,19.4 )
set(2, 20.3)
set(3, 21.1)
set(4,22)
for(0.5100/v01,0){
nonlinear(d,d,d,v01,d)
rotate(180)
}
for(0.5100/v02,0){
nonlinear(d,d,d,v02,d)
rotate(180)
}
for(0.5100/v03,0){
nonlinear(d,d,d,v03,d)
rotate(180)
}
for(0.5100/v04,0){
nonlinear(d,d,d,v04,d)
rotate(180)
}

Also, since I have no information on this, I have set theta and phi both to zero. I think the polarisation is 0, however I am also running the simulations with this at 90 in case I have the axis wrong, and the process should be type-0 phase matched, so I'm expecting to see all DFG light produced in the same polarisation as the pump.

Any advice on DFG / DFG in PPLN modelling you can offer would be greatly appreciated.

Many thanks

[NickKarpowicz]

Hi there, I set up a simulation that I hope helps you get started: https://datashare.mpcdf.mpg.de/s/XMcalygSAJmsJ02

I set it up to use batch mode to scan the grating period so you can see the phase matching evolve.

For PPLN, it's important to set $\theta$ to 90 degress. The strong nonlinear coefficient is $d_{33}$, which requires all the fields to be along the z-axis of the crystal; for $\theta$=0 the field will always be in the x-y plane.

Generally, I have a few tips:

In my experience that might be a too much energy to send into a PPLN with tight focusing and a short pulse; they can damage quite easily. Especially with a 40 micron spot, you will likely have a lot of white light coming out... I'd start with looser focusing conditions. I used a 150 micron waist in the simulation, and it's still a bit strong. Remember that if your goal is to have a CEP-stable pulse coming out, you don't want to contaminate it with noisy light from self-phase modulation of the pump.

DFG also strongly depends on the pulse compression; you'll really want to tune the GDD of the input pulse to have a temporal focus in the crystal.

Anyway, I hope this helps, and good luck for the simulations and experiments!

Best wishes,
Nick

[jmorse2020]

Hi Nick,
This is great, thank you for the help with the simulations, and also the physics insights/advice!
Best wishes,
Jack