Negative two photon absorption

[Zhengran Wu]

Dear all,

I am learning to calculate two photon absorption (TPA) with Yambo. For Si, the TPA peaks I calculated are locate at half the linear absorption peak. For GaAs, the first TPA peak is also consistent with some experiments. It seems really a nice tool for TPA calculation.

But I found the calculated TPA goes down to negative value when the energy lies in the right half part of the linear absorption peak. This tendency appears both for Si and GaAs. For another material "MA" I am concerned about, it is also negative. (see the attachment)

I noticed that in the two TPA work: PHYSICAL REVIEW B 98, 165126 (2018); PHYSICAL REVIEW B 96, 245109 (2017), the TPA are always above zero.

Is is a convergence problem? Or is there something wrong with the post process TPA script?

Any advices would be appreciated.

input and output files for TPA of Si: https://mailsucaseducn-my.sharepoint.co ... Q?e=TeDGa4

Bests
Zhengran

[claudio]

Dear Zhengran

how did you extract TPA? the calculation of TPA is quite involved.

It requires many calculations at different frequencies for different intensities,
then you have to collect all the results and subtract the different terms as explained in Eq. 18 of https://journals.aps.org/prb/pdf/10.110 ... .98.165126

In practice you have to use Eq. 18 separately for each frequency

I will try to make a tutorial on this.... but I need some time

best
Claudio

[Zhengran Wu]

Dear Claudio,

I did three separate calculations for field intensities I, I/4, I/16 with the same frequency range. Then I collected the "o.YPP-X_probe_order_1" for the three intensities and renamed them: o.YPP-X_probe_int_1_order_1 (X1_int1, for I), o.YPP-X_probe_int_2_order_1 (X1_int2, for I/4), o.YPP-X_probe_int_3_order_1 (X1_int3, for I/16).

The X3(w: w, w, -w) for TPA was calculated using:

X3(w: w, w, -w) = 8/3 * ( X1_int1 - 3*X1_int2 + 2*X1_int3 ) / (E**2)

where E=E'/(3*10**4), E' is "Efield Amplitude" in r_nloptics.

To transform X3(w: w, w, -w) to intensity dependent refractive index n2 and two photon absorption beta, I used Eq. A.3 and A.4 of https://doi.org/10.1016/j.optcom.2014.03.005. The complex linear refractive index was extracted from o.YPP-X_probe_int_1_order_1.

Are these steps correct? Do I need to do more calculation for other intensities to eliminate the fourth and fifth order contributions?

the related input/output files and the python script for extracting TPA are here : https://mailsucaseducn-my.sharepoint.co ... Q?e=eaiXWE


Bests
Zhengran

[claudio]

Dear Zhengran

your calculations seems correct to me.
Plase send me your input files DFT+pseudo and Yambo for one particular case, for example Silicon
and I will make some test.

best
Claudio

[claudio]

Dear Zhengran

unfortunately I had not time to perform these test, I just want give you a possible suggestion
try to reduce the de-phasing term and see if this solve the problem

best
Claudio

[Zhengran Wu]

Dear Claudio,

I found that the negative two photon absorption coefficient appears when there are linear absorption, that is, negative TPA above band gap.
If I shift the band gap Eg' to higher energy Eg using "GfnQP_E" tag, the corresponding TPA locate between Eg' and Eg will change from negative to positive.

Why the TPA calculation seems invalid when linear absorption exists?

In practice, since the damping can not be zero and there are finite linear absorption value below band gap, the negative TPA will still appear below band gap. Can I shift the experimental band gap Eg_exp to a much larger value "Eg_exp + E_shift", then shift the resulted TPA spectrum with " - E_shift/2 " to avoid the negative value? I have tried this way and got the TPA all positive below Eg_exp. But is this physically meaningful?


Bests
Zhengran

[claudio]

Dear Zhengran

I understand the problem, at present I do not have a solution, for the case we studied the result was positive.
I will try to make some test end of august when I will be back from vacations.
The idea of shift the gap is exact for linear response, it could work also for two-photon absorption but now sure 100%.
Otherwise you can also try different Richard extrapolations formulas
using E, E/2 e 2E or other combination of field intensities.

best
Claudio

ps I asked other developers to comment on this post, I hope they will add other possible solutions

[Ignacio Alliati]

Dear Zhengran,

I'm happy to try and reproduce the error. Could you please provide the relevant files for Silicon?
That is,

• input, report and output files of Yambo

• SAVE directory if possible

• inputs and outputs of DFT

• pseudopotentials

Regards,
Ignacio.

[Ignacio Alliati]

Dear Zhengran,

Just an update. I've calculated TPA for Silicon in the region 0.2 - 5 eV (gap at 3.17 eV) and found no negative signal. I'll wait for your files to try and reproduce the error.

Regards,
Ignacio.

[Zhengran Wu]

Dear Ignacio,

Thank you so much for testing for me!

The relevant files are put in the link:
https://mailsucaseducn-my.sharepoint.co ... g?e=rjmkte

best
Zhengran