Second-Harmonic Generation

by Dmitrii Nabok for exciting oxygen

Purpose: In this tutorial you will learn how to initialize and perform calculations of the second order susceptibility tensor with exciting. As an example, we compute the second-harmonic generation (SHG) spectrum of GaAs.

### Second harmonic generation

Copy and paste the following exciting input data into input.xml.

<input>

<title>GaAs SHG</title>

<structure speciespath="$EXCITINGROOT/species"> <crystal> <basevect>5.3435 5.3435 0.0000</basevect> <basevect>5.3435 0.0000 5.3435</basevect> <basevect>0.0000 5.3435 5.3435</basevect> </crystal> <species speciesfile="Ga.xml" rmt="2.0"> <atom coord="0.00 0.00 0.00"/> </species> <species speciesfile="As.xml" rmt="2.0"> <atom coord="0.25 0.25 0.25"/> </species> </structure> <groundstate do="fromscratch" rgkmax="7.0" ngridk="8 8 8" xctype="LDA_PW" nempty="10" > </groundstate> <properties> <momentummatrix/> <shg wmax="0.3" wgrid="400" swidth="0.004" etol="1.d-4" scissor="0.0423" tevout="true" > <chicomp>1 2 3</chicomp> </shg> </properties> </input>  Make sure to set$EXCITINGROOT to the correct exciting root directory in the speciespath attribute using the command

$SETUP-excitingroot.sh  Please get first familiar with the input parameters related to the shg element. Note that all required components of the second-order susceptibility tensor$\chi_{abc}^{(2)}(-2\omega,\omega,\omega)$can be specified by adding corresponding chicomp combinations where$a,b$, and$c$stand for the Cartesian indices (1=x, 2=y, 3=z). Run exciting in the usual way. $ time exciting_smp &


As an example, we present results for $\chi_{xyz}^{(2)}(-2\omega,\omega,\omega)$ (which can be found in the output file CHI_123.OUT). Note that this file contains information about the frequency dependence of the real, imaginary, and absolute value of the corresponding tensor component given in the units of 10-7 esu. In the literature, one would often find the second-order susceptibility in the units of nm/V. Please notice the conversion factor: 1 nm/V = 23.86x10-7 esu. For tutorial purposes, the results could be visualized by executing

\$ PLOT-SHG.py CHI_123.OUT


The resulting plot is saved in the files PLOT.png and PLOT.eps, which should look like the following image:

##### Exercise
• Converge the SHG spectrum with respect to ngridk.
• Try different components of the SHG susceptibility tensor noting that many of them are actually zero due to crystal symmetry.

### Literature

• J. L. P. Hughes and J. E. Sipe, Phys. Rev. B 53, 10751 (2003)
• S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003)
• S. Sharma and C. Ambrosch-Draxl, Physica Scripta T109, 128 (2004)