Sources

Sources#

fmmax.amplitudes_for_fields(ex: Array, ey: Array, hx: Array, hy: Array, layer_solve_result: LayerSolveResult, brillouin_grid_axes: Tuple[int, int] | None = None) → Tuple[Array, Array][source]#

Computes the amplitudes for fields.

If brillouin_grid_axes is not None, the fields are expected to be given for a supercell containing one or more unit cells, i.e. for a calculation with in-plane wavevector generated by basis.brillouin_zone_in_plane_wavevector. The shape of the supercell is inferred from the batch shape of the layer_solve_result and the specified brillouin_grid_axes.

Parameters:

ex – The x-oriented electric field on the real-space grid, with a trailing batch dimension.
ey – The y-oriented electric field on the real-space grid, with shape (..., nx, ny, num_fields).
hx – The x-oriented magnetic field on the real-space grid.
hy – The y-oriented magnetic field on the real-space grid.
layer_solve_result – The eigensolve result for the layer containing the fields.
brillouin_grid_axes – The batch axes corresponding to the Brillouin zone grid.

Returns:

The forward and backward wave amplitudes.

fmmax.amplitudes_for_source(jx: Array, jy: Array, jz: Array, s_matrix_before_source: ScatteringMatrix, s_matrix_after_source: ScatteringMatrix) → Tuple[Array, Array, Array, Array, Array, Array][source]#

Computes wave amplitudes resulting from an internal source.

The configuration of the calculation is depicted below. A source is located at the interface of two layers. The layer stacks before and after the source are named as such. The function computes the amplitudes of forward-going and backward-going waves at various locations within the stack, also depicted below.

                    source _____
                                |
 __before_______________________V___after_____________________

|             |     |           |           |     |           |
|   layer 0   | ... |  layer i  |   layer   | ... |  layer N  |
| start layer |     |           |   i + 1   |     | end layer |
|             |     |           |           |     |           |

                     -> a_i      -> a_i+1          -> a_N
        b_0 <-            b_i <-    b_i+1 <-

Parameters:

jx – The x-oriented dipole amplitude; must be at least rank-3 with a trailing batch dimension.
jy – The y-oriented dipole amplitude, with shape matching jx.
jz – The z-oriented dipole amplitude, with shape matching jx.
s_matrix_before_source – The scattering matrix for the layer substack before the source, having no overlap with the after-source substack. Scattering matrix pairs returned by scattering.stack_s_matrices_interior may not be directly used.
s_matrix_after_source – The scattering matrix for the layer substack after the source.

Returns:

backward_amplitude_0_end: The backward-going wave amplitude at the end: of the first layer.
forward_amplitude_before_start: The forward-going wave amplitude at the: start of the layer preceding the source.
backward_amplitude_before_end: The backward-going wave amplitude at the: end of the layer preceding the source, i.e. just before the source.
forward_amplitude_after_start: The forward-going wave amplitude at the: start of the layer following the source, i.e. just after the source.
backward_amplitude_after_end: The backward-going wave amplitude at the: end of the layer following the source.
forward_amplitude_N_start: The forward-going wave amplitude at the start: of the final layer.

Return type:

The wave amplitudes

fmmax.dirac_delta_source(location: Array, in_plane_wavevector: Array, primitive_lattice_vectors: LatticeVectors, expansion: Expansion) → Array[source]#

Returns the coefficients for a delta source at the specified location.

This function is appropriate for creating sources to be used with amplitudes_for_source.

Parameters:

location – The location of the source, with shape (num_sources, 2) and the trailing axis giving the x and y location. Location (0, 0) is at the corner of the unit cell.
in_plane_wavevector – The in-plane wavevevector for the calculation, which gives the offset of the plane wave decomposition. Has shape (..., 2) with possible batch dimensions.
primitive_lattice_vectors – The primitive lattice vectors of the unit cell.
expansion – The Fourier expansion used for the calculation.

Returns:

The coefficients, with the shape (..., expansion.num_terms, num_sources).

fmmax.gaussian_source(fwhm: Array, location: Array, in_plane_wavevector: Array, primitive_lattice_vectors: LatticeVectors, expansion: Expansion) → Array[source]#

Returns the coefficients for a Gaussian source at the specified location.

This function is appropriate for creating sources to be used with amplitudes_for_source.

Parameters:

fwhm – The full-width at half-maximum for the Gaussian source.
location – The location of the source, with shape (num_sources, 2) and the trailing axis giving the x and y location. Location (0, 0) is at the corner of the unit cell.
in_plane_wavevector – The in-plane wavevevector for the calculation, which gives the offset of the plane wave decomposition. Has shape (..., 2) with possible batch dimensions.
primitive_lattice_vectors – The primitive lattice vectors of the unit cell.
expansion – The Fourier expansion used for the calculation.

Returns:

The coefficients, with the shape (..., expansion.num_terms, num_sources).

fmmax.shifted_rotated_fields(field_fn: Callable[[Array, Array, Array], Tuple[Tuple[Array, Array, Array], Tuple[Array, Array, Array]]], x: Array, y: Array, z: Array, beam_origin_x: Array, beam_origin_y: Array, beam_origin_z: Array, polar_angle: Array, azimuthal_angle: Array, polarization_angle: Array) → Tuple[Tuple[Array, Array, Array], Tuple[Array, Array, Array]][source]#

Computes the fields on a rotated coordinate system.

Given fields_fn(xf, yf, zf) -> (exf, eyf, ezf), (hxf, hyf, hzf) which returns the fields in the field coordinate system, returns the fields at coordinates (x, y, z), which are rotated from (xf, yf, zf), by the specified polar_angle, azimuthal_angle, and polarization_angle.

For example, a beam propagating in the zf direction, polarized in the xf direction will be propagating in the direction specified by polar_angle and azimuthal_angle, with polarization rotated about the propagation direction by polarization_angle.

Parameters:

field_fn – Function which returns the fields in the field coordinate system. The fields should be for a beam propagating in the zf direction, i.e. in the z-direction of the beam coordinate system.
x – x-coordinates of the desired output fields.
y – y-coordinates of the desired output fields.
z – z-coordinates of the desired output fields.
beam_origin_x – The x-origin of the beam coordinate system in the (x, y, z) unit system.
beam_origin_y – The y-origin of the beam coordinate system.
beam_origin_z – The z-origin of the beam coordinate system.
polar_angle – The rotation angle about the y-axis.
azimuthal_angle – The rotation angle about the z-axis.
polarization_angle – The rotation angle about the propagation axis.

Returns:

The fields ((ex, ey, ez), (hx, hy, hz)) at the specified coordinates.

Sources

Contents

Sources#