Third Harmonic Generation (THG): Difference between revisions
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==Third Harmonic Generation in bulk Silicon== | |||
In this tutorial we will calculate third harmonic generation (THG) in bulk Silicon. | In this tutorial we will calculate third harmonic generation (THG) in bulk Silicon. | ||
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<br>Calculation of third harmonic generation proceeds in similar way to the SHG calculations. <br>DFT input can be found here ([http://www.attaccalite.com/lumen/tutorials/silicon_dft.tgz abinit] or [http://www.attaccalite.com/lumen/tutorials/silicon_qe.tgz |quantum espresso]). <br> We import the wave-functions as explained in the [[Real time approach to non-linear response]], then perform the setup using only 1000 plane waves. <br> | <br>Calculation of third harmonic generation proceeds in similar way to the SHG calculations. <br>DFT input can be found here ([http://www.attaccalite.com/lumen/tutorials/silicon_dft.tgz abinit] or [http://www.attaccalite.com/lumen/tutorials/silicon_qe.tgz |quantum espresso]). <br> We import the wave-functions as explained in the [[Real time approach to non-linear response]], then perform the setup using only 1000 plane waves. <br> | ||
==Removing symmetries== | |||
We are interested in the <math> \chi^{(3)}_{1111} </math> therefore we consider an external field in direction [1, 0, 0] (equivalent to [x,0,0]).<br /> | We are interested in the <math> \chi^{(3)}_{1111} </math> therefore we consider an external field in direction [1, 0, 0] (equivalent to [x,0,0]).<br /> | ||
We remove all the symmetries not compatible with the external field plus the time-reversal symmetry by doing <code>ypp -y</code>:<br /> | We remove all the symmetries not compatible with the external field plus the time-reversal symmetry by doing <code>ypp -y</code>:<br /> | ||
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<span style="color:red>RmTimeRev</span> # Remove Time Reversal | <span style="color:red>RmTimeRev</span> # Remove Time Reversal | ||
==Real-time simulations== | |||
Then you go in the FixSymm folder, run again the setup (as explained in the [[Linear response using Dynamical Berry Phase]]) and then generate the input file with the command <code>yambo_nl -u n -V qp -F input.in</code>:<br /> | Then you go in the FixSymm folder, run again the setup (as explained in the [[Linear response using Dynamical Berry Phase]]) and then generate the input file with the command <code>yambo_nl -u n -V qp -F input.in</code>:<br /> | ||
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<br /> | <br /> | ||
when the simulation will end, it will have produced the files <code>SAVE/ndb.Nonlinear</code>.<br /> | when the simulation will end, it will have produced the files <code>SAVE/ndb.Nonlinear</code>.<br /> | ||
Results can be | |||
==Analysis of the results== | |||
Results can be analyzed in the same way of the SHG, using the command <code>ypp_nl -u</code>:<br /> | |||
<br /> | <br /> | ||
nonlinear # [R] NonLinear Optics Post-Processing | |||
Xorder= 5 # Max order of the response functions | Xorder= 5 # Max order of the response functions | ||
% TimeRange | % TimeRange | ||
40 | -1.00000 | fs # Time-window where processing is done | |||
% | % | ||
ETStpsRt= 200 # Total Energy steps | ETStpsRt= 200 # Total Energy steps | ||
% EnRngeRt | % EnRngeRt | ||
0.00000 | 10.00000 | eV # Energy range | |||
% | % | ||
DampMode= "NONE" # Damping type ( NONE | LORENTZIAN | GAUSSIAN ) | DampMode= "NONE" # Damping type ( NONE | LORENTZIAN | GAUSSIAN ) | ||
DampFactor= 0.10000 eV # Damping parameter</pre> | DampFactor= 0.10000 eV # Damping parameter</pre> | ||
This time we increase the dephasing time to 40 fs in such a way to have a clean third-harminic response.<br /> | This time we increase the dephasing time to 40 fs in such a way to have a clean third-harminic response.<br /> | ||
Hereafter we report the result with the 8x8x8 k-points sampling and the converged result with the 24x24x24 k-points sampling: | Hereafter we report the result with the 8x8x8 k-points sampling and the converged result with the 24x24x24 k-points sampling: | ||
Revision as of 08:57, 19 October 2023
Third Harmonic Generation in bulk Silicon
In this tutorial we will calculate third harmonic generation (THG) in bulk Silicon.
Calculation of third harmonic generation proceeds in similar way to the SHG calculations.
DFT input can be found here (abinit or |quantum espresso).
We import the wave-functions as explained in the Real time approach to non-linear response, then perform the setup using only 1000 plane waves.
Removing symmetries
We are interested in the [math]\displaystyle{ \chi^{(3)}_{1111} }[/math] therefore we consider an external field in direction [1, 0, 0] (equivalent to [x,0,0]).
We remove all the symmetries not compatible with the external field plus the time-reversal symmetry by doing ypp -y:
fixsyms # [R] Reduce Symmetries % Efield1 1.00 | 0.00 | 0.00 | # First external Electric Field % % Efield2 0.00 | 0.00 | 0.00 | # Additional external Electric Field % #RmAllSymm # Remove all symmetries RmTimeRev # Remove Time Reversal
Real-time simulations
Then you go in the FixSymm folder, run again the setup (as explained in the Linear response using Dynamical Berry Phase) and then generate the input file with the command yambo_nl -u n -V qp -F input.in:
nloptics # [R NL] Non-linear optics % NLBands 1 | 7 | # [NL] Bands % NLstep= 0.0100 fs # [NL] Real Time step length NLtime=-1.000000 fs # [NL] Simulation Time NLintegrator= "CRANKNIC" # [NL] Integrator ("EULEREXP/RK4/RK2EXP/HEUN/INVINT/CRANKNIC") NLCorrelation= "IPA" # [NL] Correlation ("IPA/HARTREE/TDDFT/LRC/JGM/HF/SEX") NLLrcAlpha= 0.000000 # [NL] Long Range Correction % NLEnRange 0.200000 | 2.000000 | eV # [NL] Energy range % NLEnSteps= 6 # [NL] Energy steps NLDamping= 0.200000 eV # [NL] Damping %Field1_Dir 1.000000 | 0.000000 | 0.000000 | # [RT Field1] Versor Field1_kind= "SOFTSIN" # [NL ExtF] Kind(SIN|SOFTSIN|RES|ANTIRES|GAUSS|DELTA|QSSIN) Field1_Int= 0.1000E+8 kWLm2 # [NL ExtF] Intensity % GfnQP_E 0.600000 | 1.000000 | 1.000000 | # [EXTQP G] E parameters (c/v) eV|adim|adim %
We calculate the [math]\displaystyle{ \chi^{(3)}_{1111} }[/math] only on 6 frequencies, but calculations can be extended to larger frequency range.
We introduce a scissor operator of 0.6 eV in such a way to reproduce the gap of bulk silicon. Notice that we increased the field intensity in such a way to improve the ratio between non-linear response and numerical noise.
Now that you have created the file input.in you can run the non-linear optics calculation with the command:
yambo_nl -F input.in
when the simulation will end, it will have produced the files SAVE/ndb.Nonlinear.
Analysis of the results
Results can be analyzed in the same way of the SHG, using the command ypp_nl -u:
nonlinear # [R] NonLinear Optics Post-Processing Xorder= 5 # Max order of the response functions % TimeRange 40 | -1.00000 | fs # Time-window where processing is done % ETStpsRt= 200 # Total Energy steps % EnRngeRt 0.00000 | 10.00000 | eV # Energy range % DampMode= "NONE" # Damping type ( NONE | LORENTZIAN | GAUSSIAN )
DampFactor= 0.10000 eV # Damping parameter
This time we increase the dephasing time to 40 fs in such a way to have a clean third-harminic response.
Hereafter we report the result with the 8x8x8 k-points sampling and the converged result with the 24x24x24 k-points sampling:
File:Images/Si THG results.png
Plot data can be downloaded here.
