wavesolve.FEsolver

This page contains the documentation for the FEsolver submodule, which functionally defines different kinds of waveguides, enables the creation of custom waveguides, and handles mesh generation for finite element analysis.

Solve

wavesolve.FEsolver.solve_waveguide(mesh, wl, IOR_dict, Nmax=6, target_neff=None, solve_mode='sparse')

given a mesh, propagation wavelength, and refractive index dictionary, solve for the scalar modes.

Parameters:

• mesh – mesh object corresponding to waveguide geometry

• wl (float) – wavelength, defined in the same units as mesh point positions

• IOR_dict (dict) – a dictionary assigning different named regions of the mesh different refractive index values

• Nmax (int) – return only the <Nmax> largest eigenvalue/eigenvector pairs

• target_neff (float or None) – search for modes with indices close to but below this value. if None, target_neff is set to the maximum index in the guide.

• solve_mode (str) – use ‘sparse’ or ‘dense’ matrices when solving

Returns:

a tuple containing:

• eigvals: array of eigenvalues, descending order

• eigvecs: array of corresponding eigenvectors (waveguide modes)

Return type:

(tuple)

wavesolve.FEsolver.solve_waveguide_vec(mesh, wl, IOR_dict, Nmax=6, target_neff=None, solve_mode='mixed')

given a mesh, propagation wavelength, and refractive index dictionary, solve for the vector modes.

Parameters:

• mesh – mesh object corresponding to waveguide geometry

• wl (float) – wavelength, defined in the same units as mesh point positions

• IOR_dict (dict) – a dictionary assigning different named regions of the mesh different refractive index values

• Nmax (int) – return only the <Nmax> largest eigenvalue/eigenvector pairs

• target_neff (float or None) – search for modes with indices close to but below this value. if None, target_neff is set to the maximum index in the guide.

• solve_mode (str) – ‘mixed’ combines a sparse linear solve and a dense eigensolve. ‘dense’ uses dense matrices for everything; default ‘mixed’

Returns:

a tuple containing:

• eigvals: array of eigenvalues, descending order

• eigvecs: array of corresponding eigenvectors (waveguide modes)

Return type:

(tuple)

Plot

wavesolve.FEsolver.plot_scalar_field(mesh, field, show_mesh=False, ax=None, res=100, bounds=None)

plot a scalar field

Parameters:

• mesh – finite element mesh

• field (array) – a 1D array corresponding to a scalar-valued field (e.g. eigenmode)

• show_mesh (bool) – set True to additionally plot the mesh geometry

• ax (matplotlib.axes or None) – optionally put the plots on an axis. if one axis is given, only the transverse part is plotted. if (ax0,ax1) is given, the longitudinal component is also plotted. if None, axes are made for both.

• res (int) – grid resolution, make tuple to set xres and yres separately

• bounds – 4-element array [xmin,xmax,ymin,ymax], setting plot boundary.

wavesolve.FEsolver.plot_vector_field(mesh, field, show_mesh=False, ax=None, arrows=True, res=100, bounds=None, dec_factor=4)

plot a vector field - transverse and longitudinal components.

Parameters:

• mesh – finite element mesh

• field (array) – a 1D array corresponding to a vector-valued field (e.g. eigenmode) which encodes both transverse and longitudinal components

• show_mesh (bool) – set True to additionally plot the mesh geometry

• ax (matplotlib.axes or None) – optionally put the plots on mpl axis. if one axis is given, only the transverse part is plotted. if (ax0,ax1) is given, the longitudinal component is also plotted. if None, axes are made for both.

• arrows (bool) – whether or not to overplot field arrows

• res (int) – grid resolution, make tuple to set xres and yres separately

• bounds – 4-element array [xmin,xmax,ymin,ymax], setting plot boundary.

• dec_factor (int) – decimation factor for arrow plotting

Evaluate

wavesolve.FEsolver.evaluate(point, field, mesh)

evaluate a field sampled over a finite element mesh at a given point.

Parameters:

• point – an [x,y] point, or an Nx2 array of points

• field – a real-valued field represented on a finite-element mesh

• mesh – the FE mesh, which has been sorted with sort_mesh().

Returns:

the field evaluated at point(s)

Return type:

(float or array)

wavesolve.FEsolver.evaluate_grid(pointsx, pointsy, field, mesh)

evaluate a field defined over a finite element mesh on a cartesian grid.

Parameters:

• pointsx – a 1D array of x points

• pointsy – a 1D array of y points

• field – a real-valued field represented on a finite-element mesh

• mesh – the FE mesh, which has been sorted with sort_mesh().

Returns:

a 2D or 3D array corresponding to field (scalar or vectorial), evaluated on the grid.

Return type:

(array)

Misc.

wavesolve.FEsolver.count_modes(w, wl, IOR_dict)

count the number of guided (non-spurious) modes. This function only works well for weakly guiding waveguides!

Parameters:

• w (array) – array of eigenvalues corresponding to the modes, assumed decreasing.

• wl (float) – wavelength

• IOR_dict (dict) – a dictionary assigning different named regions of the mesh different refractive index values

wavesolve.FEsolver.isvectorial(field, mesh)

determine if field is a vector or scalar field

Parameters:

• field (array) – electric field evaluated on a finite element mesh

• mesh – the finite element mesh

wavesolve.FEsolver.sort_mesh(mesh)

create a bounding volume hierarchy tree for mesh and pass it into to mesh.tree. this is required for evaluations of fields on meshes. you usually don’t need to call this manually.

Parameters:

mesh – finite element mesh

wavesolve.FEsolver.get_eff_index(wl, w)

get effective refractive index from wavelength wl and eigenvlaue w

Parameters:

• wl (float) – wavelength

• w (float or array) – eigenvalue(s)

wavesolve.FEsolver.resample(field, mesh, newmesh)

resample a finite element field onto a new mesh

Parameters:

• field – the finite element field to be resampled.

• mesh – the finite element mesh on which <field> is defined.

• newmesh – the new finite element mesh <field> should be sampled on.