# TDExternalFields

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#### TDExternalFields

Section Time-Dependent
Type block

The block TDExternalFields describes the type and shape of time-dependent external perturbations that are applied to the system, in the form $f(x,y,z) \cos(\omega t + \phi (t)) g(t)$, where $f(x,y,z)$ is defined by by a field type and polarization or a scalar potential, as below; $\omega$ is defined by omega; $g(t)$ is defined by envelope_function_name; and $\phi(t)$ is the (time-dependent) phase from phase.

These perturbations are only applied for time-dependent runs. If you want the value of the perturbation at time zero to be applied for time-independent runs, use TimeZero = yes.

Each line of the block describes an external field; this way you can actually have more than one laser (e.g. a "pump" and a "probe").

There are two ways to specify $f(x,y,z)$ but both use the same omega | envelope_function_name [| phase] for the time-dependence. The float omega will be the carrier frequency of the pulse (in energy units). The envelope of the field is a time-dependent function whose definition must be given in a TDFunctions block. envelope_function_name is a string (and therefore it must be surrounded by quotation marks) that must match one of the function names given in the first column of the TDFunctions block. phase is optional and is taken to be zero if not provided, and is also a string specifying a time-dependent function.

(A) type = electric field, magnetic field, vector_potential

For these cases, the syntax is:

%TDExternalFields
type | nx | ny | nz | omega | envelope_function_name | phase
%

The vector_potential option (constant in space) permits us to describe an electric perturbation in the velocity gauge. The three (possibly complex) numbers (nx, ny, nz) mark the polarization direction of the field. By default, (nx, ny, nz) are defined in Cartesian space. However, it is possible for solids to define them using the Miller indices. This can be achieved by defining the block MillerIndicesBasis.

(B) type = scalar_potential

%TDExternalFields
scalar_potential | "spatial_expression" | omega | envelope_function_name | phase
%

The scalar potential is any expression of the spatial coordinates given by the string "spatial_expression", allowing a field beyond the dipole approximation.

For DFTB runs, only fields of type type = electric field are allowed for the moment, and the type keyword is omitted.

A NOTE ON UNITS:

It is very common to describe the strength of a laser field by its intensity, rather than using the electric-field amplitude. In atomic units (or, more precisely, in any Gaussian system of units), the relationship between instantaneous electric field and intensity is: $I(t) = \frac{c}{8\pi} E^2(t)$.

It is common to read intensities in W/cm$^2$. The dimensions of intensities are [W]/(L$^2$T), where [W] are the dimensions of energy. The relevant conversion factors are:

Hartree / ($a_0^2$ atomic_time) = $6.4364086 \times 10^{15} \mathrm{W/cm}^2$

eV / ( Å$^2 (\hbar$/eV) ) = $2.4341348 \times 10^{12} \mathrm{W/cm}^2$

If, in atomic units, we set the electric-field amplitude to $E_0$, then the intensity is:

$I_0 = 3.51 \times 10^{16} \mathrm{W/cm}^2 (E_0^2)$

If, working with Units = ev_angstrom, we set $E_0$, then the intensity is:

$I_0 = 1.327 \times 10^{13} (E_0^2) \mathrm{W/cm}^2$

Options:

• electric_field:
The external field is an electric field, the usual case when we want to describe a laser in the length gauge.
• magnetic_field:
The external field is a (homogeneous) time-dependent magnetic field.
• vector_potential:
The external field is a time-dependent homogeneous vector potential, which may describe a laser field in the velocity gauge.
• scalar_potential:
The external field is an arbitrary scalar potential, which may describe an inhomogeneous electrical field.

Source information

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