QPM DFG in PPLN with chi2D

[tinolang]

This example shows how to simulate a quasi-phase matched (QPM) difference frequency generation  (DFG) in periodically poled lithium niobate (PPLN) using chi2D.

The QPM is realized by periodically alternating the sign of deff depending on z position during the simulation along z propagation. In the chi2D GUI this can be done by setting into the deff input field a formula instead of a value. Accepted are basically every inline Matlab syntax function. So in principle it is also possible to vary the deff with any function. In the following example it is a simple square function given by:

19.5.*(round((sin(2*pi * ( 1/31.1512e-6 .* z)) +1  )/2)*2-1)

The poling period is chosen to phase-match a DFG process amplifying a 1.6µm broadband seed pulse using a pump pulse with a wavelength of 1054nm. The idler is then generated at ~3µm. In this special example reasonable pulse energies and different chirps for the two pulses are chosen in order to get good temporal overlap.

It is important to choose a crystal length L together with a number of steps along z Nz in a way to get a step size which is a multiple of the poling periode.

L=num2str(1600*31.1512e-6/10,12) using 1600 steps and a poling periode 31.1512e-6

The full parameter set can be loaded into chi2D using this file:

PPLN_DFG_chi2D.mat

 

 

Results

The full spectrum, spanning from 150 nm till 4µm, before and after the nonlinear interaction of pump and seed in a 5 mm long PPLN:

 

Zoom in the amplified signal and the generated idler spectrum on a linear scale:

 

 

Discussion:

Due to the quite long crystal the acceptance bandwidth of the DFG is much smaller than the seed spectrum. Changing the poling period would change the amplified spectrum and the generated idler spectrum respectively. The chirp of signal and idler are opposite. This leads to either self-compression or temporal stretching of the signal and idler pulses caused by the dispersion of the crystal. Note: In principle every deff-function can be used, which would basically also allow for the simulation of a chirped poling period in order to get broadband amplification. However, since the step size in chi2D within one simulation run is fixed, a changing poling period can lead to artifacts. A proper way of simulating a chirped poling would be to use a variable step size which can be done using Chi3D. Please find the very same example done with chi3D here:

QPM DFG in PPLN with variable step size using chi3D