non-linear response

[sitangshu]

Dear Sir,

I was trying to do a quick non-linear calculation using 4.3.1 version. Please excuse me for the queries as I am new to nonlinear calculations. I went through the papers on real time BSE in PRB by Claudio Attacallite an others. Initially, I am trying some simple problems with lumen also. It ran properly. But in 4.3.1 version, there are many advances that I am not able to understand. So my queries are for a real time linear response for a simple IPA and no long range correction:
I used the command: yambo_nl -u -F input.in

1. I removed all symmetries. Is that correct approach? TR removal seems to produce
<---> Detected 20 wrong symmetries (out of 24 )
[ERROR] STOP signal received while in :[03.01] Initialization
[ERROR] Use ypp -y to repair the symmetry group and restart Yambo


2. Information about first and additional external electric field are not there in ypp_nl. I guess this is in -q pn?

3. yambo_nl -u does not produce ExtF_kind= " ", Should I need to put this additionally? Also there is no NLstep, NLtime NLintegrator. Putting NLDamping = 0.000000, the code complains:
[ERROR] STOP signal received while in :[03.01] Initialization
[ERROR] Error damping=0 and NLtime<0!!

When I put some finite NLDamping value like 0.15 eV, the code runs and produce o.polarization_F1. When I plot y-plolarization vs time, the plot looks like a sine curve.
Am I doing correct?

With regards,
SItangshu

[sitangshu]

Forgot to attach the report file.

Thanks.
Sitangshu

[claudio]

Dear Sitangshu

please try to follow the tutorials available here:

http://www.attaccalite.com/lumen/tutorials.html

if you want to see more options in your input file, just add the -V nl flag

best
Claudio

[sitangshu]

Dear Professor Claudio,

Thank you for your response.
I am using lumen 1.3 version to compute real time IPA first. I am using silicon with 8 8 8 k sampling for testing purpose and obtained a 16 16 16 double-grid file.
Should I put this dg inside the folder FixSymm/SAVE/? There is already a folder SAVE after nscf-->p2y.
I am a bit confused here

Thank you Sir.

Regards,
Sitangshu

[claudio]

Dear Sitangshu

unfortunately, the double-grid method does not work for non-linear optics,
So if you want non-linear response on the 16x16x16 you have to use it directly.

best
Claudio

[sitangshu]

Dear Sir,

I recently came across a very interesting paper by the yambo /lumen developers: PRB 94, 035149 (2016). Please excuse me for the following silly (might be) questions. You see, I am new to this non-linear spectroscopy and in the learning stage:
After a long experience with lumen exercises, I tried to replicate my lumen results through yambo 4.3.1. And yes, I managed to do that.

What is actually bothering me now is how to recognize from the |X^(2)| and |X^(3)| spectra that whether the peaks are due to one photon, two photon or three photon process. I also went through the recent arxiv paper:1807.11797 on bulk hBN which also decode just by looking the spectra.
Incidentally, I also searched some books like (i) Boyed's, (ii) Ivan Pelant & Jan Valenta's but there is no clear description.
Do I have to see the quadratic behavior? or there are other ways to decode this mystery.
I would be very glad for your response.

[claudio]

Dear Sitangshu

I recently came across a very interesting paper by the yambo /lumen developers: PRB 94, 035149 (2016). Please excuse me for the following silly (might be) questions. You see, I am new to this non-linear spectroscopy and in the learning stage: After a long experience with lumen exercises, I tried to replicate my lumen results through yambo 4.3.1. And yes, I managed to do that.

very good

What is actually bothering me now is how to recognize from the |X^(2)| and |X^(3)| spectra that whether the peaks are due to one photon, two-photon or three-photon process.

This is a very good question, at present we do not have a tool to analyze |X^(2)| and |X^(3)| spectra, and analysis from the real-time simulation is complicated.
The only thing you can do it is to compare the spectra with the one of the imaginary dielectric constant calculated at \epsilon(w) and \epsilon(2w)
From the visual inspection you can see when a peak in the X^(2) coincide with a peak of the \epsilon(w) or \epsilon(2w) and from this comparison, you can assign
them to the one or two-photon transition.
I agree that this analysis is not rigorous, but at present, we do not have another tool to disentangle the different peaks.

I also went through the recent arxiv paper:1807.11797 on bulk hBN which also decode just by looking the spectra.

in the arxiv paper:1807.11797 you can find also symmetry analysis of the two-photon absorption peaks that help to understand them.

Incidentally, I also searched some books like (i) Boyed's, (ii) Ivan Pelant & Jan Valenta's but there is no clear description.
Do I have to see the quadratic behavior? or there are other ways to decode this mystery.
I would be very glad for your response.

the quadratic behavior is found in the polarization. Try to excite the system with a laser at a given frequency w and intensity E
than you have to study the polarization at 2w (in case of second harmonic) P(2w). If you repeat the calculation increasing the laser
intensity E, you will see the quadratic behavior of the polarization.

Notice that the X^2

X^2 (2w) = P(2w)/E^2(w)

is independent of the laser intensity.

best
Claudio

[sitangshu]

Thank you Professor Claudio, I will try this and will let you know.

With regards,
Sitangshu

[sitangshu]

Dear Sir,

Recently, we did a linear response calculation with a 2D C3v 3m symmetry system. We find the BSE and GW results to be quite convincing and are done on a 72 x 72 x 1 DG. We performed a real time analysis using a delta wave within the IPA without any scissor. The results obtained seems to be convincing.
Apparently, this is also a noncentrosymmetric system thus should have an SHG. We started to to do within IPA, and used the external electric field along 1 0 0 direction. We observed few things when SHG is evaluated:

1. A softsin is used. The Berry's polarization shows results only along two (in-plane) direction. This should be correct, as the third is along vacuum. Right?
2. The dephasing time used is 70 fs such the the signal is free from eigenmodes due to sudden turning of the E field. We saw a smooth polarization variation with time. However, at the end of the game, we observed that the X^(2) has got the real and imaginary values along x, y and z direction. Apparently, the z shows all zero values. This would perhaps be due to the zero polarization along z--> right?
3. How should I find the |X^(2)|? Should I square and then add all the real x and y and imaginary x and y respectively and then take a square root? Or only for x alone?
4. Is there any specific direction to obtain SHG? I did this with 1 0 0. Am I correct or should I have done with 1 1 0 ? I am not clear on this.
Can you please help me on this?

Regards,
Sitangshu

[claudio]

Dear Sitangshu

1. A softsin is used. The Berry's polarization shows results only along two (in-plane) direction. This should be correct, as the third is along vacuum. Right?

In non linear optics, we implemented only the response along the periodic directions.

2. The dephasing time used is 70 fs such the the signal is free from eigenmodes due to sudden turning of the E field. We saw a smooth polarization variation with time. However, at the end of the game, we observed that the X^(2) has got the real and imaginary values along x, y and z direction. Apparently, the z shows all zero values. This would perhaps be due to the zero polarization along z--> right?

Since z is a non-periodic direction the resonse in this direction is not calculated. Anyway for two-dimensional systems, this response is very small or zero by symmetry.

3. How should I find the |X^(2)|? Should I square and then add all the real x and y and imaginary x and y respectively and then take a square root? Or only for x alone?

if you use gnuplot just plot

p 'o.YPP-X_probe_order_2' u 1:(sqrt($2**2+$3**2)) w l

4. Is there any specific direction to obtain SHG? I did this with 1 0 0. Am I correct or should I have done with 1 1 0 ? I am not clear on this.
Can you please help me on this?

It depends on the symmetries of your system. Try to have a look to the Boyd book "Non-linear optics" or to
some paper on SHG in two-dimensional crystals, usually selection rules for the SHG are discussed in these papers.

best regards
Claudio Attaccalite