Second Harmonic Generation

by Dmitrii Nabok for exciting boron

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

$SETUP-excitingroot.sh  Please get first familiar with the input parameters related to shg element. Note that all required components of the second order susceptibility tensor$\chi_{abc}^{2}(-2\omega,\omega,\omega)$can be specified by adding corresponding chicomp combinations (1=x, 2=y, 3=z). As an example, we present the results for$| \chi_{xyz}^{2}(-2\omega,\omega,\omega) |\$ (output file CHI_MODULE_123.OUT)

##### 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)