# PLaSK User Manual

#### Page Contents

- ThresholdSearchFourier2D

# ThresholdSearchFourier2D

<meta solver="ThresholdSearchFourier2D">

  Corresponding Python class: `meta.shockley.ThresholdSearchFourier2D`.

  Solver for threshold search of semiconductor laser in 2D Cartesian geometry.

  This solver performs thermo-electrical computations followed by determination ot threshold current and optical analysis in order to determine the threshold of a semiconductor laser. The search is performed by `scipy` root finding algorithm in order to determine the voltage and electric current ensuring no optical loss in the laser cavity.

  The optical computations are done with vector method based on 2D Fourier exansion.

  Attributes:

    - name (`required`) – Solver name.

  Contents:
    <geometry>

      Geometry settings for all solvers.

      Attributes:

        - thermal (`required`) – Geometry used by the thermal solver. (Cartesian2D geometry)

        - electrical (`required`) – Geometry used by the electrical, diffusion, and gain solvers. (Cartesian2D geometry)

        - optical (`required`) – Geometry used by the optical solver. (Cartesian2D geometry)

    <mesh>

      Mesh settings for all solvers.

      Attributes:

        - thermal (`required`) – Mesh used by the thermal solver. (mesh)

        - electrical (`required`) – Mesh used by the electrical solver. (mesh)

        - diffusion – Mesh used by the carriers diffusion solver. (mesh)

        - optical – Mesh used by the optical solver. (mesh)

        - empty-elements – Should empty regions (e.g. air) be included into electrical computations? (`default`, `include`, or `exclude`, default is `default`)

    <optical>

      Configuration of the optical solver

      Attributes:

        - size – Expansion size. (int, default 12)

        - refine – Number of refinement points for refractive index averaging. (int, default 32)

        - symmetry – Mode symmetry. Specify a symmetric field component here (e.g. ‘Etran‘, ‘Hx‘). (`none`, `Etran`, `Elong`, `Ex`, `Ey`, `Ez`, `Er`, `Ep`, `Et`, `El`, `Htran`, `Hlong`, `Hx`, `Hy`, `Hz`, `Hr`, `Hp`, `Ht`, or `Hl`, default is `none`)

        - smooth – Smoothing parameter for material boundaries (increases convergence). (float, default 0.0)

        - update-gain – If this attribute is set to ‘yes’, material parameters are always recomputed for layers with gain or permittivity provided by inEpsilon. This allows to set ‘lam0’ for better efficiency and still consider slight changes of wavelength, where it matters the most. (bool, default is `no`)

        - group-layers – Should similar layers be grouped for better performance. (bool, default is `yes`)

        - transfer – Layers transfer algorithm. Can be either reflection transfer, admittance transfer or automatic, in which case the reflection computations will use reflection transfer and eigenmode search is done with admittance transfer. (`auto`, `reflection`, or `admittance`, default is `auto`)

        - lam (`required`) – Emission wavelength. The effective index is searched for this wavelength. (float (nm))

        - mn – Lateral mode number (int, default 0)

        - dneff – Step, by which the effective index is swept while searching for the approximate mode. (float, default 0.02)

        - emission – Direction of the useful light emission. Necessary for the over-threshold model to correctly compute the output power. In this solver only top and bottom emission is possible. (`undefined`, `top`, or `bottom`, default is `undefined`)

    <root>

      Configuration of the root-finder used in threshold search.

      Attributes:

        - bcond (`required`) – Number of the voltage boundary condition to vary during the threshold search. (int)

        - vmin – Minimum voltage to search threshold for. It should be below the threshold. (float)

        - vmax – Maximum voltage to search threshold for. It should be above the threshold. (float)

        - vtol – Tolerance on voltage in the root search. (float (V), default 1e-05 V)

        - maxiter – Maximum number of root finding iterations. (int, default 50)

    <voltage>

      Voltage boundary conditions. See subsection Boundary conditions.

    <temperature>

      Temperature boundary conditions. See subsection Boundary conditions.

    <heatflux>

      Heat Flux boundary conditions. See subsection Boundary conditions.

    <convection>

      Convective boundary conditions. See subsection Boundary conditions.

      This boundary condition does not have value attribute. Use coeff for convection coefficient and ambient for ambient temperature instead.

    <radiation>

      Radiative boundary conditions. See subsection Boundary conditions.

      This boundary condition does not have value attribute. Use emissivity for surface emissivity and ambient for ambient temperature instead.

    <junction>

      Configuration of the effective model of p-n junction.

      Attributes:

        - beta# – Junction coefficients. This is an inverse of the junction thermal voltage. (float (1/V))

        - js# – Reverse bias current densities. (float (A/m2))

        - pnjcond – Initial vertical conductivity of the junctions. (float (S/m), default 5.0 S/m)

    <contacts>

      Properties of the contact layers.

      Attributes:

        - pcond – p-contact conductivity. (float (S/m), default 5.0 S/m)

        - ncond – n-contact conductivity. (float (S/m), default 50.0 S/m)

    <loop>

      Configuration of the self-consistent thermo-electric loop.

      Attributes:

        - skip-thermal – Skip thermal computations. The structure is assumed to have a constant temperature inittemp. This can be used to look for the threshold under pulse laser operation. (bool, default is `no`)

        - tfreq – Number of electrical iterations per single thermal step. As temperature tends to converge faster, it is reasonable to repeat thermal solution less frequently. (int, default 6)

        - inittemp – Initial temperature used for the first computation. (float (K), default 300 K)

        - maxterr – Maximum allowed temperature error. (float (K), default 0.05 K)

        - maxcerr – Maximum allowed current density error. (float (%), default 0.05 %)

    <tmatrix>

      Matrix configuration for the thermal solver.

      Attributes:

        - algorithm – Algorithm used for solving set of linear positive-definite equations. (`cholesky`, `gauss`, or `iterative`, default is `cholesky`)

      <iterative>

        Parameters for iterative matrix solver. PLaSK uses NSPCG package for performing iterations. Please refer to its documentation for explanation of most of the settings.

        Attributes:

          - maxit – Maximum number of iterations. (int, default 1000)

          - maxerr – Maximum iteration error. (float, default 1e-6)

          - noconv – Desired behavior if the iterative solver does not converge. (`error`, `warning`, or `continue`, default is `warning`)

          - accelerator – Accelerator used for iterative matrix solver. (`cg`, `si`, `sor`, `srcg`, `srsi`, `basic`, `me`, `cgnr`, `lsqr`, `odir`, `omin`, `ores`, `iom`, `gmres`, `usymlq`, `usymqr`, `landir`, `lanmin`, `lanres`, `cgcr`, or `bcgs`, default is `cg`)

          - preconditioner – Preconditioner used for iterative matrix solver. (`rich`, `jac`, `ljac`, `ljacx`, `sor`, `ssor`, `ic`, `mic`, `lsp`, `neu`, `lsor`, `lssor`, `llsp`, `lneu`, `bic`, `bicx`, `mbic`, or `mbicx`, default is `ic`)

          - nfact – This number initializes the frequency of partial factorizations. It specifies the number of linear system evaluations between factorizations. The default value is 1, which means that a factorization is performed at every iteration. (int, default 10)

          - ndeg – Degree of the polynomial to be used for the polynomial preconditioners. (int, default 1)

          - lvfill – Level of fill-in for incomplete Cholesky preconditioners. Increasing this value will result in more accurate factorizations at the expense of increased memory usage and factorization time. (int, default 0)

          - ltrunc – Truncation bandwidth to be used when approximating the inverses of matrices with dense banded matrices. An increase in this value means a more accurate factorization at the expense of increased storage. (int, default 0)

          - omega – Relaxation parameter. (float, default 1.0)

          - nsave – The number of old vectors to be saved for the truncated acceleration methods. (int, default 5)

          - nrestart – The number of iterations between restarts for the restarted acceleration methods. (int, default 100000)

        Preconditioner choices:
        `rich` | Richardson’s method
        `jac` | Jacobi method
        `ljac` | Line Jacobi method
        `ljacx` | Line Jacobi method (approx. inverse)
        `sor` | Successive Overrelaxation
        `ssor` | Symmetric SOR (can be used only with SOR accelerator)
        `ic` | Incomplete Cholesky (default)
        `mic` | Modified Incomplete Cholesky
        `lsp` | Least Squares Polynomial
        `neu` | Neumann Polynomial
        `lsor` | Line SOR
        `lssor` | Line SSOR
        `llsp` | Line Least Squares Polynomial
        `lneu` | Line Neumann Polynomial
        `bic` | Block Incomplete Cholesky (ver. 1)
        `bicx` | Block Incomplete Cholesky (ver. 2)
        `mbic` | Modified Block Incomplete Cholesky (ver. 1)
        `mbicx` | Modified Block Incomplete Cholesky (ver. 2)

        Accelerator choices:
        `cg` | Conjugate Gradient acceleration (default)
        `si` | Chebyshev acceleration or Semi-Iteration
        `sor` | Successive Overrelaxation (can use only SOR preconditioner)
        `srcg` | Symmetric Successive Overrelaxation Conjugate Gradient Algorithm (can use only SSOR preconditioner)
        `srsi` | Symmetric Successive Overrelaxation Semi-Iteration Algorithm (can use only SSOR preconditioner)
        `basic` | Basic Iterative Method
        `me` | Minimal Error Algorithm
        `cgnr` | Conjugate Gradient applied to the Normal Equations
        `lsqr` | Least Squares Algorithm
        `odir` | ORTHODIR, a truncated/restarted method useful for nonsymmetric systems of equations
        `omin` | ORTHOMIN, a common truncated/restarted method used for nonsymmetric systems
        `ores` | ORTHORES, another truncated/restarted method for nonsymmetric systems
        `iom` | Incomplete Orthogonalization Method
        `gmres` | Generalized Minimal Residual Method
        `usymlq` | Unsymmetric LQ
        `usymqr` | Unsymmetric QR
        `landir` | Lanczos/ORTHODIR
        `lanmin` | Lanczos/ORTHOMIN or Biconjugate Gradient Method
        `lanres` | Lanczos/ORTHORES or “two-sided” Lanczos Method
        `cgcr` | Constrained Generalized Conjugate Residual Method
        `bcgs` | Biconjugate Gradient Squared Method

    <ematrix>

      Matrix configuration for the electrical solver.

      Attributes:

        - algorithm – Algorithm used for solving set of linear positive-definite equations. (`cholesky`, `gauss`, or `iterative`, default is `cholesky`)

      <iterative>

        Parameters for iterative matrix solver. PLaSK uses NSPCG package for performing iterations. Please refer to its documentation for explanation of most of the settings.

        Attributes:

          - maxit – Maximum number of iterations. (int, default 1000)

          - maxerr – Maximum iteration error. (float, default 1e-6)

          - noconv – Desired behavior if the iterative solver does not converge. (`error`, `warning`, or `continue`, default is `warning`)

          - accelerator – Accelerator used for iterative matrix solver. (`cg`, `si`, `sor`, `srcg`, `srsi`, `basic`, `me`, `cgnr`, `lsqr`, `odir`, `omin`, `ores`, `iom`, `gmres`, `usymlq`, `usymqr`, `landir`, `lanmin`, `lanres`, `cgcr`, or `bcgs`, default is `cg`)

          - preconditioner – Preconditioner used for iterative matrix solver. (`rich`, `jac`, `ljac`, `ljacx`, `sor`, `ssor`, `ic`, `mic`, `lsp`, `neu`, `lsor`, `lssor`, `llsp`, `lneu`, `bic`, `bicx`, `mbic`, or `mbicx`, default is `ic`)

          - nfact – This number initializes the frequency of partial factorizations. It specifies the number of linear system evaluations between factorizations. The default value is 1, which means that a factorization is performed at every iteration. (int, default 10)

          - ndeg – Degree of the polynomial to be used for the polynomial preconditioners. (int, default 1)

          - lvfill – Level of fill-in for incomplete Cholesky preconditioners. Increasing this value will result in more accurate factorizations at the expense of increased memory usage and factorization time. (int, default 0)

          - ltrunc – Truncation bandwidth to be used when approximating the inverses of matrices with dense banded matrices. An increase in this value means a more accurate factorization at the expense of increased storage. (int, default 0)

          - omega – Relaxation parameter. (float, default 1.0)

          - nsave – The number of old vectors to be saved for the truncated acceleration methods. (int, default 5)

          - nrestart – The number of iterations between restarts for the restarted acceleration methods. (int, default 100000)

        Preconditioner choices:
        `rich` | Richardson’s method
        `jac` | Jacobi method
        `ljac` | Line Jacobi method
        `ljacx` | Line Jacobi method (approx. inverse)
        `sor` | Successive Overrelaxation
        `ssor` | Symmetric SOR (can be used only with SOR accelerator)
        `ic` | Incomplete Cholesky (default)
        `mic` | Modified Incomplete Cholesky
        `lsp` | Least Squares Polynomial
        `neu` | Neumann Polynomial
        `lsor` | Line SOR
        `lssor` | Line SSOR
        `llsp` | Line Least Squares Polynomial
        `lneu` | Line Neumann Polynomial
        `bic` | Block Incomplete Cholesky (ver. 1)
        `bicx` | Block Incomplete Cholesky (ver. 2)
        `mbic` | Modified Block Incomplete Cholesky (ver. 1)
        `mbicx` | Modified Block Incomplete Cholesky (ver. 2)

        Accelerator choices:
        `cg` | Conjugate Gradient acceleration (default)
        `si` | Chebyshev acceleration or Semi-Iteration
        `sor` | Successive Overrelaxation (can use only SOR preconditioner)
        `srcg` | Symmetric Successive Overrelaxation Conjugate Gradient Algorithm (can use only SSOR preconditioner)
        `srsi` | Symmetric Successive Overrelaxation Semi-Iteration Algorithm (can use only SSOR preconditioner)
        `basic` | Basic Iterative Method
        `me` | Minimal Error Algorithm
        `cgnr` | Conjugate Gradient applied to the Normal Equations
        `lsqr` | Least Squares Algorithm
        `odir` | ORTHODIR, a truncated/restarted method useful for nonsymmetric systems of equations
        `omin` | ORTHOMIN, a common truncated/restarted method used for nonsymmetric systems
        `ores` | ORTHORES, another truncated/restarted method for nonsymmetric systems
        `iom` | Incomplete Orthogonalization Method
        `gmres` | Generalized Minimal Residual Method
        `usymlq` | Unsymmetric LQ
        `usymqr` | Unsymmetric QR
        `landir` | Lanczos/ORTHODIR
        `lanmin` | Lanczos/ORTHOMIN or Biconjugate Gradient Method
        `lanres` | Lanczos/ORTHORES or “two-sided” Lanczos Method
        `cgcr` | Constrained Generalized Conjugate Residual Method
        `bcgs` | Biconjugate Gradient Squared Method

    <diffusion>

      Diffusion solver configuration.

      Attributes:

        - fem-method – Order of the finite-element method. (`linear` or `parabolic`, default is `parabolic`)

        - accuracy – Required relative accuracy. (float (%), default 0.01 %)

        - abs-accuracy – Required absolute minimal concentration accuracy. (float (cm-3), default 5000000000000000.0 cm-3)

        - maxiters – Maximum number of allowed iterations before attempting to refine mesh. (int, default 20)

        - maxrefines – Maximum number of allowed mesh refinements. (int, default 5)

        - interpolation – Current density interpolation method name. (`linear` or `spline`, default is `spline`)

    <gain>

      Gain solver parameters.

      Attributes:

        - lifetime – Average carriers lifetime. This parameter is used for gain spectrum broadening. (float (ps), default 0.1 ps)

        - matrix-elem – Value of the squared matrix element in gain computations. If it is not set it is estimated automatically. (float (eV×m0))

        - strained – Boolean attribute indicating if the solver should consider strain in the active region. If set to yes then there must a layer with the role “substrate“ in the geometry. The strain is computed by comparing the atomic lattice constants of the substrate and the quantum wells. (bool, default is `no`)

    <optical-root>

      Parameters of the horizontal root-finding algorithm.

      Attributes:

        - method – Root finding algorithm. (`muller`, `broyden`, or `brent`, default is `muller`)

        - tolx – Maximum change of the effective frequency parameter which is allowed for convergent solution. (float, default 1e-06)

        - tolf-min – Minimum value of the determinant sufficient to assume convergence. (float, default 1e-07)

        - tolf-max – Maximum value of the determinant required to assume convergence. (float, default 2e-05)

        - maxstep – Maximum step in one iteration of root finding. Significant for the Broyden’s method only. (float, default 0.1)

        - maxiter – Maximum number of root finding iterations. (int, default 500)

        - alpha – Parameter ensuring sufficient decrease of determinant in each step (Broyden method only). (float, default 1e-07)

        - lambda – Minimum decrease ratio of one step (Broyden method only). (float, default 1e-08)

        - initial-range – Initial range size (Muller method only). (complex, default 0.001)

    <output>

      Settings for the solver output.

      Attributes:

        - optical-res-x – Number of points along the horizontal axis for the saved and plotted optical field. (int, default 800)

        - optical-res-y – Number of points along the vertical axis for the saved and plotted optical field. (int, default 600)