# Linear and non-linear optics

### This page gives hints on how to compute linear and non-linear optical properties in the independent-particle approximation with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (SS,XG,YG)

Mentioned in help_features#7, help_optic#3.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.

### 1. Introduction.

Optical and non-linear optical properties can be computed with different levels of approximation.

The simplest (and fastest) approach relies on the independent-particle approximation (IPA): the electrons are supposed independent of each other when reacting to the optical perturbation (even if the initial computation of the band structure includes interactions in a mean-field sense, like with DFT). This approximation is also referred to as a "Sum-Over-States" approach (SOS). This neglects all electron-hole interaction (so no excitonic effects), but might provide meaningful results in many case, sometimes even quantitatively. A first problem is linked with the erroneous band gap of the material, but this might be corrected by a scissor approximation, see e.g. scissor@optic.

In ABINIT one can either work in the IPA (see below), or take into account the excitonic effects, see topic_BSE.

In the ABINIT package, there are two different utilities to compute optical response in the independent-particle approximation : optic and conducti. They have been developed independently of each other, and thus overlap significantly. The first one permits to cover the linear and non-linear optical properties as a function of the frequency. It provides the optical dielectric tensor, the second-harmonic generation (SHG) as well as the optical rectification tensor (or electro-optic tensor) - without the contribution from the nuclei displacements. For the further inclusion of the contribution from nuclei displacements, see topic_nonlinear.

The second utility "conducti" has more capabilities only at the linear level, but provides electronic conductivity, dielectric tensor, index of refraction, reflectivity, absorption, the thermal conductivity, and the thermopower (electron transport, high temperature, Kubo-Greenwood formalism) real as well as imaginary part.
Go to the top

### 2. Related lesson(s) of the tutorial.

- See The lesson on Optic, the utility that allows to obtain the frequency dependent linear optical dielectric function and the frequency dependent second order nonlinear optical susceptibility, in the simple "Sum-Over-State" approximation.
Go to the top

### 3. Related input variables.

Basic input variables:

... broadening@optic [BROADENING]
... ddkfile@optic [DDK FILE]
... domega@optic [Delta OMEGA]
... lin_comp@optic [LINear COMPonents]
... maxomega@optic [MAXimum value of OMEGA]
... nonlin_comp@optic [NON-LINear COMPonents]
... num_lin_comp@optic [NUMber of LINear COMPonents]
... num_nonlin_comp@optic [NUMber of NON-LINear COMPonents]
... scissor@optic [SCISSOR operator]
... tolerance@optic [TOLERANCE]
... wfkfile@optic [WaveFunction K FILE]
Go to the top

### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v4/Input: t56.in t57.in

tests/v67mbpt/Input: t52.in t53.in

tests/v7/Input: t41.in t42.in t47.in t48.in
Go to the top