Photonics_TM_FDFD#

class Photonics_TM_FDFD(omega, geometry, chi=None, des_mask=None, ji=None, ei=None, chi_background=None, sparseQCQP=True, A0=None, s0=None, c0=0.0)[source]#

Bases: Photonics_FDFD

TM polarization FDFD photonics problem (Cartesian or Polar).

Parameters:

  • omega (complex)

  • geometry (CartesianFDFDGeometry | PolarFDFDGeometry)

  • chi (complex | None)

  • des_mask (ndarray[tuple[int, ...], dtype[bool]] | None)

  • ji (ndarray[tuple[int, ...], dtype[complexfloating]] | None)

  • ei (ndarray[tuple[int, ...], dtype[complexfloating]] | None)

  • chi_background (ndarray[tuple[int, ...], dtype[complexfloating]] | None)

  • sparseQCQP (bool)

  • A0 (ndarray[tuple[int, ...], dtype[complexfloating]] | csc_array | None)

  • s0 (ndarray[tuple[int, ...], dtype[complexfloating]] | None)

  • c0 (float)

EM_solver#

Electromagnetic field solver.

Type:

dolphindes.maxwell.TM_FDFD | None

QCQP#

QCQP instance for optimization.

Type:

dolphindes.cvxopt.qcqp.SparseSharedProjQCQP |

Ginv#

Inverse Green’s function (sparse QCQP).

Type:

csc_array or None

G#

Green’s function (dense QCQP).

Type:

ndarray of complex or None

M#

Maxwell operator.

Type:

csc_array or None

EM_solver#

Electromagnetic field solver.

Type:

TM_FDFD or TM_Polar_FDFD or None

structure_objective#

Function for structure optimization objective.

Type:

Callable

Methods Summary

get_chi_inf()

Get the inferred susceptibility from the QCQP dual solution.

setup_EM_operators()

Set up electromagnetic operators for the design region and background.

setup_EM_solver([geometry])

Set up the FDFD electromagnetic solver with given geometry.

structure_objective_dense(dof, grad)

Structural optimization objective and gradient when sparseQCQP=False.

structure_objective_sparse(dof, grad)

Structural optimization objective and gradient when sparseQCQP=True.

Methods Documentation

get_chi_inf()[source]#

Get the inferred susceptibility from the QCQP dual solution.

Return type:

ndarray[tuple[int, …], dtype[complexfloating]]

setup_EM_operators()[source]#

Set up electromagnetic operators for the design region and background.

Notes

This method creates the appropriate operators based on whether sparse or dense QCQP formulation is used: - For sparse QCQP: Creates Ginv (inverse Green’s function) and M operators - For dense QCQP: Creates G (Green’s function) operator

Requires self.des_mask to be defined.

Raises:

AttributeError – If des_mask is not defined.

Return type:

None

setup_EM_solver(geometry=None)[source]#

Set up the FDFD electromagnetic solver with given geometry.

Parameters:

geometry (CartesianFDFDGeometry or PolarFDFDGeometry) – Geometry specification. If None, uses self.geometry.

Return type:

None

Notes

Creates a TM_FDFD or TM_Polar_FDFD solver instance and stores it in self.EM_solver.

structure_objective_dense(dof, grad)[source]#

Structural optimization objective and gradient when sparseQCQP=False.

Specifications exactly the same as structure_objective_sparse.

Parameters:

  • dof (ndarray of float) – Pixel-wise structure degrees of freedom.

  • grad (ndarray of float) – Gradient storage array.

Returns:

obj – Design objective value.

Return type:

float

structure_objective_sparse(dof, grad)[source]#

Structural optimization objective and gradient when sparseQCQP=True.

Follows convention of the optimization package NLOPT: returns objective value and stores gradient with respect to objective in the input argument grad.

Parameters:

  • dof (ndarray of float) – Pixel-wise structure degrees of freedom over the design region as specified by self.des_mask. dof[j] is a linear interpolation between dof[j] = 0 (self.chi_background) and dof[j] = 1 (self.chi_background + self.chi)

  • grad (ndarray of float) – Adjoint gradient of the design objective with respect to dof. Specify grad = [] if only the objective is needed. Otherwise, grad should be an array of the same size as dof; upon method exit grad will store the gradient.

Returns:

obj – The design objective for the structure specified by dof.

Return type:

float