optics{ quantum_spectra{ } }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{no\;constraints}\)

This group specifies numerical properties of the quantum model used for computations of optical spectra base on the Fermi’s Golden Rule.

Note

Our algorithms and models controlled by keywords in this group are intensively developed. For this reason, related syntax may substantially change with each next release. Users of this group are highly encouraged to update the tool regularly with the new releases and to use our support system to give us feedback on any related issues.

Note

In the current versions, this group should not be used for modeling optical spectra for transitions between two separate 1-band models (e.g., quantum{ region{ Gamma{} } } and quantum{ region{ HH{} } }) or between a 1-band model and 6-band model (e.g., quantum{ region{ Gamma{} } } and quantum{ region{ kp_6band{ } } }). Computations within single models (e.g., only within quantum{ region{ kp_8band{ } } }, only within quantum{ region{ Gamma{} } }, etc.) are supported.

Dependencies

Maintained Keywords

The keywords below are available in at least one of currently published releases and are planned to be included also in the next release.

name

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{character\;string}\)

The name of already defined region in quantum{ region{ } } for which optical generation should be calculated. Multiple numerical parameters are inherited after the definitions in the quantum{ region{ } } referred to.

spin_align

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes for Pauli equation solved with 6-band or 8-band \(\mathbf{k} \cdot \mathbf{p}\) method, a spin-basis transformation is performed for each pair of quantum states (i, i+1), with i being an odd number, such that matrix representation of the Pauli operator \(\hat{\mathbf{\sigma}}\) multiplied by a selected versor (along the \(z\) direction in 3D, and the \(x\) direction in 1D and 2D) becomes diagonal in the subspace defined by these two states. With other words, spinor compositions of degenerate (due to lack of magnetic field) pairs of quantum states are chosen as if magnetic field was parallel to the \(z\) direction (3D) or \(x\) direction (1D, 2D). This procedure is triggered before running an algorithm computing optical spectra.

interband

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

Compute optical transitions dominating in interband transitions, typically conduction band to valence band transitions.

intraband

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

Compute optical transitions dominating in intraband transitions, typically conduction band to conduction band transitions.

interband_approximation

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Only terms of the type \(<c|p|v>\) and \(<v|p|c>\) are taken into account (\(c=s\) and \(v=x,y,z\))

intraband_approximation

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Only terms of the type \(<c|p|c>\) and \(<v|p|v>\) are taken into account (\(c=s\) and \(v=x,y,z\))

enable_hole_hole

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If yes then transitions within valence bands are included according to applied classification.

enable_electron_hole

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If yes then transitions between conduction and valence bands are included according to applied classification.

enable_electron_electron

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If yes then transitions within conduction bands are included according to applied classification.

use_kp8_EP

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If yes then uses the \(P\) parameter from 8-band \(\mathbf{k} \cdot \mathbf{p}\) material data is used to compute the strength of optical transitions when computing the spectra between 2 states computed within 1-band model, and when computing the spectra with conduction band expressed within 1-band model and valence bands within 6-band \(\mathbf{k} \cdot \mathbf{p}\) model.

energy_threshold

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{eV}\)

  • default: 1e-6

Only transitions between states with at least this energy difference are regarded when computing optical spectra.

transition_threshold

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{eV}\)

  • default: 1e-6

Only transitions between states with at least this optical intensity are regarded when computing optical spectra. Increasing the value can reduce computational time but may neglect weak optical transitions.

occupation_threshold

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{-}\)

  • default: 0.0

Only transitions between states with at least this occupation are regarded when computing optical spectra. Increasing the value can reduce computational time but may neglect weakly occupied states.

occupation_ignore

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Ignore the occupation of states when computing optical spectra: Valence bands and conduction bands are considered to be fully occupied and fully empty, respectively.

Warning

This feature is under development.

Attention

Occupation and classification of states are currently performed independently for carrier densities and for optical spectra.

occupation_zero_fermilevel

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

This keyword is active when occupation_ignore is set to no. In semi-classical current calculations, the quasi-Fermi level may depend on position. Optical spectra, on the other, hand are computed using a quantum mechanical model with where single states involved in the transitions exhibit non-locality (wave functions) resulting in their existence in areas with different quasi-Fermi levels assigned. As the model for the spectra assumes a specific quasi-Fermi level for each state, the inconsistency arises. Using this keyword set to yes resolves this inconsistency by taking both quasi-Fermi levels equal zero. Taking it no, position dependent occupation number is computed.

Warning

This feature is under development.

occupation_interpolate_invfermi

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

This keyword is active when occupation_ignore and occupation_zero_fermilevel are set to no. If yes then Fermi levels are interpolated between k-points before applying to the integrating algorithm which may increase accuracy of numerical \(k_\parallel\) space integration.

Warning

This feature is under development.

classify_states

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

Classifies states as electrons if energy is higher than average value of minimum of the conduction band and maximum of the valence, \((EC_{min} + EV_{max})/2\), plus classification_threshold.

classification_threshold

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: no constraints

  • unit: \(\mathrm{eV}\)

  • default: 0.0

A parameter shifting the reference energy for the classification of the states.

excitons{ }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{maximum\;1}\)

Include excitonic effects.

Attention

Excitons are implemented only for 1D simulations.

excitons{ num_exciton_levels }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {1, ..., 10}

  • unit: \(\mathrm{-}\)

  • default: 1

Number of exciton levels included in the model.

excitons{ coulomb_enhancement }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If set to yes, then the Coulomb enhancement factor, also known as the Sommerfeld factor, is taken into account.

spontaneous_emission

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Calculate spontaneous emission rate using the momentum matrix element obtained by 8-band kp model. (This feature is not yet implemented in 3D simulation.)

output_energies

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output energy dispersion for every transition.

output_occupations

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output occupation dispersion for every transition.

output_transitions

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output transition strength for every transition.

output_spinor_components

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output the spinor components for each state at each \(k_\parallel\) point (only relevant in multi-band \(\mathbf{k} \cdot \mathbf{p}\) calculations).

Note

In 1-dimensional systems the axis of quantization for the angular momentum is x, in 3D z.

output_spectra{ }

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • items: \(\mathrm{exactly\;1}\)

Control of optical spectra output

output_spectra{ output_components }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {0, 1, 2}

  • unit: \(\mathrm{-}\)

  • default: 0

If its value is set different from zero, this attribute generates an output of state-to-state spectral components of any type of spectra triggered by the keywords output_spectra{ absorption_coeff }, output_spectra{ decadic_absorption_coeff }, output_spectra{ gain }, output_spectra{ decadic_gain }, and output_spectra{ emission }. If set to 1 then components with vanishing or nearly vanishing values are omitted in the output. If set to 2 then all components are outputted.

Warning

Setthing this attribute to 2 may lead to a big number of files being written.

output_spectra{ absorption_coeff }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If set to yes, then the optical absorption coefficient expressed in \(\mathrm{cm^{-1}}\) is outputted.

output_spectra{ decadic_absorption_coeff }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, then the optical absorption coefficient is expressed in \(\mathrm{dB/}\mu\mathrm{m}\) is outputted.

output_spectra{ gain }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If set to yes, then the optical gain coefficient expressed in \(\mathrm{cm^{-1}}\) is outputted.

output_spectra{ decadic_gain }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, then the optical gain coefficient expressed in \(\mathrm{dB/}\mu\mathrm{m}\) is outputted.

output_spectra{ emission }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If set to yes, then emission spectrum is outputted.

output_spectra{ spectra_over_energy }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

Output spectra with respect to the energy.

output_spectra{ spectra_over_frequency }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output spectra with respect to the frequency.

output_spectra{ spectra_over_wavelength }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output spectra with respect to the wavelength.

output_spectra{ spectra_over_wavenumber }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

Output spectra with respect to the wave number.

output_spectra{ photon_spectra }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: yes

If set to yes, then spectrum of photon number is outputted with one of the following units \(1/cm^2/s/eV\), \(1/cm^2/s/nm\), \(1/cm^2/s/THz\), or \(1/cm^2/s/cm^{-1}\).

output_spectra{ power_spectra }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, then photon power spectrum is outputted with units \(W/cm^2\).

polarization{ }

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • items: \(\mathrm{no\;constraints}\)

Define polarization of incoming light for which optical absorption spectrum should be calculated.

Important

polarization{ name }

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{character\;string}\)

name attached to output files with computed spectra for the defined polarization

polarization{ re }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{vector\;of\;3\;real\;numbers}\)

  • values: no constraints

  • unit: \(\mathrm{-}\)

  • default: [0.0, 0.0, 0.0]

real part of the polarization vector

polarization{ im }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{vector\;of\;3\;real\;numbers}\)

  • values: no constraints

  • unit: \(\mathrm{-}\)

  • default: [0.0, 0.0, 0.0]

imaginary part of the polarization vector

refractive_index

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: (0.0, ...)

  • unit: \(\mathrm{-}\)

  • default: substrate

Specify constant refractive index for the simulation of the optical spectra.

normalization_volume

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: (0.0, ...)

  • unit: \(\mathrm{nm^{dimension}}\)

  • default: related quantum region

Specifies normalization volume for the optical spectra.

min_energy

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{eV}\)

  • default: 0.0

lower energy bound for optical spectra

max_energy

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e-3, ...)

  • unit: \(\mathrm{eV}\)

  • default: 2.0

upper energy bound for optical spectra

energy_resolution

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e-6, ...)

  • unit: \(\mathrm{eV}\)

  • default: 1e-3

Spacing between subsequent energy grid points.

energy_broadening_gaussian

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e-6, ...)

  • unit: \(\mathrm{eV}\)

Set the broadening to value greater than 0.0 to make the Gaussian broadening

\[\mathcal{L}(E-E_0)=\frac{1}{\sqrt{2\pi}\sigma}\exp{\big(-\frac{(E-E_0)^2}{2\sigma^2}\big)}\]

included to the calculation of the optical spectrums. The specifed value is read as the FWHM \(\Gamma=2\sqrt{\ln 2}\cdot\sigma\).

(In 1D and 2D, both Lorentzian and Gaussian can be used simultaneously. In 3D, either of these broadenings must be included.)

energy_broadening_lorentzian

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e-6, ...)

  • unit: \(\mathrm{eV}\)

Set the broadening to value greater than 0.0 to make the Lorentzian broadening

\[\mathcal{L}(E-E_0)=\frac{1}{\pi}\frac{\Gamma/2}{(E-E_0)+(\Gamma/2)^2}\]

included to the calculation of the optical spectrums. The specifed value is read as the FWHM \(\Gamma\).

kramers_kronig{ }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{maximum\;1}\)

If specified, then Kramers-Kronig relations are used to evaluate real part of dielectric function and dispersion of complex refractive index based on previously computed imaginary part of dielectric function.

Attention

Available Hamiltonians, defined within 1-band, 6-band, or 8-band \(\mathbf{k} \cdot \mathbf{p}\) models, will contribute to the imaginary part of dielectric function \(\varepsilon_{i}\) only with transitions close to the \(\Gamma\) point, therefore, underestimating the spectrum at higher energies. As Kramers-Kronig relations are non-local, the transformation of such \(\varepsilon_{i}\) is reproducing real part of dielectric function \(\varepsilon_{r}\) accurately only up to slow-varying background. The missing background accounts for not-computed high-energy \(\varepsilon_{i}\). Therefore only local features of real part of dielectric function are accessible within the transformation.

To handle this problem, the missing background can be approximated analytically assuming additional contributions from \(\varepsilon_{i}\) at high energies with parameters: kramers_kronig{ im_epsilon_extension }, kramers_kronig{ im_epsilon_rescale }, kramers_kronig{ delta_static_epsilon }, and kramers_kronig{ delta_position }. These contributions are not shown in the \(\varepsilon_{i}\) output, but their effect is present in \(\varepsilon_{r}\) output.

Note

Specific values of parameters: kramers_kronig{ im_epsilon_extension }, kramers_kronig{ im_epsilon_rescale }, kramers_kronig{ delta_static_epsilon }, and kramers_kronig{ delta_position } have to be fitted individually for every device. No tables for materials nor devices are available.

kramers_kronig{ im_epsilon_extension }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{eV}\)

  • default: 0.0

If kramers_kronig{ im_epsilon_extension } is set to non-zero value then \(\varepsilon_{i}\) computed at max_energy multiplied by kramers_kronig{ im_epsilon_rescale } is assumed for \(\varepsilon_{i}\) in an energy range from max_energy to max_energy \(+\) kramers_kronig{ im_epsilon_extension }. Effectively a rectangle is attached to the end of the spectra with width of kramers_kronig{ im_epsilon_extension } and height of the \(\varepsilon_{i}\) at max_energy multiplied by kramers_kronig{ im_epsilon_rescale }, to be used in Kramers-Kronig transformation.

kramers_kronig{ im_epsilon_rescale }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: (0.0, ...)

  • unit: \(\mathrm{-}\)

  • default: 1.0

This parameter is rescaling value used to approximate constant \(\varepsilon_{i}\) at high energies, from max_energy to max_energy \(+\) kramers_kronig{ im_epsilon_extension }. When kramers_kronig{ im_epsilon_rescale } \(=1\) then exactly \(\varepsilon_{i}\) at max_energy is used.

kramers_kronig{ delta_static_epsilon }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.0, ...)

  • unit: \(\mathrm{-}\)

  • default: 0.0

If this attribute is set to non-zero value then delta-function multiplied by the value is added to \(\varepsilon_{i}\) at energy kramers_kronig{ delta_position } to be used in Kramers-Kronig transformation.

kramers_kronig{ delta_position }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: (0.0, ...)

  • unit: \(\mathrm{eV}\)

This parameter is defining position of the delta function added to \(\varepsilon_{i}\).

kramers_kronig{ use_for_absorption }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, then computed refractive index is used to calculate absorption. Otherwise, constant value is used.

kramers_kronig{ use_for_emission }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, then the computed refractive index is used to calculate emission. Otherwise, constant value is used.

k_integration{ }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{maximum\;1}\)

Group defining numerical parameters of integration over the states in the space of the wave vector \(k_\parallel\) space.

k_integration{ relative_size }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e-3, 1.0]

  • unit: \(\mathrm{-}\)

  • default: 1e-1

Size of the integrated volume of the \(k_\parallel\) space expressed as relative value to the size of the First Brillouin Zone

k_integration{ num_points }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {1, 2, 3, ..., 100}

  • unit: \(\mathrm{-}\)

  • default: 4

Number of points counted from \(k=0\) to the border of considered \(k_\parallel\) space along \(k_\parallel=k_y\) or \(k_z\) excluding the point at \(k=0\). The Schrödinger equation is solved for optical spectra at the grid with the “radius” as described above. The transition intensities are computed at these points and later used in the integration procedure.

k_integration{ num_integrationpoints }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {1, 2, 3, 4, ...}

  • unit: \(\mathrm{-}\)

  • default: 180

Number of integration points in the \(k_\parallel\) defining an independent grid analogously as the attribute k_integration{ num_points }.

Spline interpolation at the grid defined with k_integration{ num_integrationpoints } of all quantities necessary for computation of the optical spectra is performed in the \(k_\parallel\) space based on solution obtained at the grid defined with the attribute k_integration{ num_points }. The transition intensities and energies resulting from this interpolation are integrated and included in the optical spectra.

Warning

Assigning too small value to k_integration{ num_integrationpoints } may result in artificial oscillatory results in the spectra.

k_integration{ force_k0_subspace }

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: yes; no

  • default: no

If set to yes, \(k_\parallel\) integration is modified in a way that only states for point \(k=0\) are computed exactly, whereas for all other k points the wave functions are computed in the subspace of the solutions for the \(k=0\). Computational speed is notably improved as a result of this approximation. Therefore enlarging the number of eigenvalues included in the computation becomes more feasible.

Attention

This approximation should be used carefully as it reduces accuracy of computed optical spectra.

Examples

We can generally write the electric field of a traveling wave propagating to \(\mathbf{k}\) direction as follows:

\[\begin{split}\begin{aligned} \mathbf{E}(\mathbf{r};t) = & [E_x\hat{\mathbf{x}}+E_y\hat{\mathbf{y}}+E_z\hat{\mathbf{z}}] e^{\imath[\mathbf{k}\mathbf{r}-\omega t]} \\ = & \begin{bmatrix} E_x \\ E_y \\ E_z \end{bmatrix} e^{\imath[\mathbf{k}\mathbf{r}-\omega t]} = \left( \begin{bmatrix} \mathrm{Re}(E_x) \\ \mathrm{Re}(E_y) \\ \mathrm{Re}(E_z) \end{bmatrix} + \imath \begin{bmatrix} \mathrm{Im}(E_x) \\ \mathrm{Im}(E_y) \\ \mathrm{Im}(E_z) \end{bmatrix} \right) e^{\imath[\mathbf{k}\mathbf{r}-\omega t]} \end{aligned}\end{split}\]

where \(E_{x/y/z}\) are complex numbers.

re=[ , , ] and im = [ , , ] correspond to the first and second column in the last line.

# linearly polarized light in x direction.
# name is used for the file names of the output.
polarization{ name = "x"        re = [1,0,0]                 }

# linearly polarized light in y direction
polarization{ name = "y"        re = [0,1,0]                 }

# linearly polarized light in z direction
polarization{ name = "z"        re = [0,0,1]                 }


# TM mode.
# This naming might be useful when analyzing heterostructure
# grown in x direction.
polarization{ name = "TM"        re = [1,0,0]                }

# TE mode
polarization{ name = "TEy"       re = [0,1,0]                }

# TE mode
polarization{ name = "TEz"       re = [0,0,1]                }


# (sigma+) circularly polarized light around the x axis
polarization{ name = "y+iz"     re = [0,1,0]   im = [0,0, 1] }

# (sigma-) circularly polarized light around the x axis
polarization{ name = "y-iz"     re = [0,1,0]   im = [0,0,-1] }


# an example for an arbitrary polarization direction
polarization{ name = "x1y1z2"   re = [1,1,2]                 }