Electric field direction for a given X3 component (THG)

[jiejiang]

Dear Yambo,

https://wiki.yambo-code.eu/wiki/index.p ... tion_(THG)
explains how to choose the external field direction for different X3 (THG).

For my case, I do not know how to setup E-filed directions for X*xyy, X*xyx, and X*yyx.
I am wondering for a given X component (X*abc), how to decide E-filed direction, i.e.,
coefficients of the linear combination of the Cartesian axes. For example, is E-field direction
of (110) for X*xyy, X*xxy, X*xyx, or another component?

Any suggestions and/or references will be great.

Thanks,
Jie

[claudio]

Dear Jie

this is a very good question. I'm not sure I have a good answer, but you can try

1) if can put the field in the direction (1, 1, 0 ) and then study the Xhi3 along x and y
I guess it should contain:

X3_x = X*xyy + X*xxy + X*xxx + X*yyy + X*yyx + X*yxx + X*xyx + X*yxy
Y3_x = Y*xyy + Y*xxy + Y*xxx + Y*yyy + Y*yyx + Y*yxx + Y*xyx + Y*yxy

some of these will be zero or equivalent by symmetries, and maybe you can extract then one you are searching for.
And/our you can sum/subtract the different X3 you get from Yambo using fields in different directions, for example for a field in x you get

X3_x = X*xxx
X3_y = Y*xxx
and in y you get

X3_x = X*yyy
X3_y = Y*yyy

these can be subtracted from the previous ones to remove components you do not want.

2) you can put two different external fields, and then try to post-process the result in some smart way
see the example of pump and probe
https://wiki.yambo-code.eu/wiki/index.p ... _and_Probe
in this case you can also think to use Richarson extrapolation, changing the intenty of the fields in x or y direction to eliminate
some components of X3. See the example for two-photon absorption
https://wiki.yambo-code.eu/wiki/index.p ... absorption

best
Claudio

ps I think the first solution is the best, you fied calculate X3_xxxx and X3_yyy then the X3 with the field in (1,1,0)
and remove this diagonal components, the rest should be simplified with symmetries

[jiejiang]

Dear Claudio,

Great. Your answers are very helpful.

Thanks,
Jie