[docs] document scattering conventions and frozen-basis workflows
Update examples for sampled-interface tapers, explicit physical CPML spacing, copied SCPML widths, and the consolidated complex mode solver. Document breaking API changes, overlap measures, and PML convergence.
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10 changed files with 152 additions and 29 deletions
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@ -1,5 +1,5 @@
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"""
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Local-mode CMT example for a continuously varying rib-waveguide taper.
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Sampled-interface EME example for a continuously varying rib-waveguide taper.
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This example keeps geometry construction outside `meanas.fdfd.eme`: it samples a
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width taper at several cross-sections, solves and normalizes each local mode with
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@ -112,14 +112,15 @@ def print_summary(
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print('sampled taper effective indices:', ', '.join(f'{value:.5f}' for value in neffs))
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print(f'abrupt endpoint reflection |S_00|^2 = {abs(abrupt_s[0, 0]) ** 2:.6f}')
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print(f'abrupt endpoint transmission |S_{n_modes},0|^2 = {abs(abrupt_s[n_modes, 0]) ** 2:.6f}')
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print(f'taper CMT reflection |S_00|^2 = {abs(taper_s[0, 0]) ** 2:.6f}')
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print(f'taper CMT transmission |S_{n_modes},0|^2 = {abs(taper_s[n_modes, 0]) ** 2:.6f}')
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print(f'taper CMT total output power = {numpy.sum(abs(taper_s[:, 0]) ** 2):.6f}')
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print(f'taper reflection |S_00|^2 = {abs(taper_s[0, 0]) ** 2:.6f}')
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print(f'taper transmission |S_{n_modes},0|^2 = {abs(taper_s[n_modes, 0]) ** 2:.6f}')
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print(f'taper total output power = {numpy.sum(abs(taper_s[:, 0]) ** 2):.6f}')
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def main() -> None:
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sections, neffs, _omega, dxes_2d = solve_taper_sections()
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taper_s = eme.get_taper_s(sections, dxes=dxes_2d)
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prepared = eme.prepare_taper(sections, dxes=dxes_2d)
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taper_s = eme.evaluate_taper_s(prepared)
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abrupt_s = eme.get_s(
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sections[0].modes,
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sections[0].wavenumbers,
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@ -5,7 +5,7 @@ from __future__ import annotations
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import numpy
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from meanas.fdmath import vec
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from meanas.fdfd import eme, scpml, waveguide_2d_complex
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from meanas.fdfd import eme, scpml, waveguide_2d
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WAVELENGTH = 1.55
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@ -34,6 +34,7 @@ def build_grids() -> tuple[list[list[numpy.ndarray]], list[list[numpy.ndarray]]]
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omega=OMEGA,
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epsilon_effective=EPS_CLADDING,
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thickness=PML_CELLS,
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max_imag_ratio=1.0,
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)
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return physical, stretched
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@ -61,29 +62,48 @@ def main() -> None:
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"""Solve, track, and summarize the sampled complex modal bases."""
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physical_dxes, solve_dxes = build_grids()
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z_coords = numpy.array([0.0, 5.0, 10.0])
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bases = [
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waveguide_2d_complex.solve_modes_near(
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epsilon_samples = [build_epsilon(edge_fill) for edge_fill in (0.30, 0.35, 0.40)]
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solved = [
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waveguide_2d.solve_modes_near(
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OMEGA,
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solve_dxes,
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build_epsilon(edge_fill),
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epsilon,
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target_wavenumbers=[1.45 * OMEGA],
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modes_per_target=3,
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candidate_margin=3,
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overlap_dxes=physical_dxes,
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)
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for edge_fill in (0.30, 0.35, 0.40)
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for epsilon in epsilon_samples
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]
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bases = [basis for basis, _diagnostics in solved]
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tracked = waveguide_2d.track_mode_path(bases, overlap_dxes=physical_dxes)
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tracked_diagnostics = [
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waveguide_2d.compute_mode_diagnostics(
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basis,
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OMEGA,
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solve_dxes,
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epsilon,
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target_wavenumbers=[1.45 * OMEGA],
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overlap_dxes=physical_dxes,
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)
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for basis, epsilon in zip(tracked, epsilon_samples, strict=True)
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]
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tracked = waveguide_2d_complex.track_mode_path(bases)
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sections = eme.mode_sections_from_bases(z_coords, tracked)
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prepared = eme.prepare_taper(sections, physical_dxes)
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# Fields and interface overlaps are reused: these are frozen-basis length
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# sweeps. Wavelength-dependent beta overrides would also freeze the fields.
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length_sweep = [eme.evaluate_taper_s(prepared, z_coords=z_coords * scale)
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for scale in (0.8, 1.0, 1.2)]
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for z_coord, basis in zip(z_coords, tracked, strict=True):
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for z_coord, basis, diagnostics in zip(z_coords, tracked, tracked_diagnostics, strict=True):
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print(
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f'z={z_coord:5.1f}: '
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f'beta={basis.wavenumbers[0]:.6g}, '
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f'PML participation={basis.diagnostics.pml_participation[0]:.3f}, '
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f'right residual={basis.diagnostics.right_residuals[0]:.2e}',
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f'PML participation={diagnostics.pml_participation[0]:.3f}, '
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f'right residual={diagnostics.right_residuals[0]:.2e}',
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)
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print(f'constructed {len(sections)} tracked EME sections with {len(sections[0].modes)} modes each')
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print('frozen-basis length sweep |T_00|:', [float(abs(ss[len(tracked[0]), 0])) for ss in length_sweep])
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if __name__ == '__main__':
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@ -145,7 +145,7 @@ def main() -> None:
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# PMLs in every direction
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pml_params = [
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[cpml_params(axis=dd, polarity=pp, dt=dt, thickness=pml_thickness, epsilon_eff=n_air ** 2)
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[cpml_params(axis=dd, polarity=pp, dt=dt, dx=dx, thickness=pml_thickness, epsilon_eff=n_air ** 2)
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for pp in (-1, +1)]
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for dd in range(3)]
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update_E, update_H = updates_with_cpml(cpml_params=pml_params, dt=dt, dxes=dxes, epsilon=epsilon, dtype=complex)
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@ -203,7 +203,7 @@ def main() -> None:
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dxes_fdfd = copy.deepcopy(dxes)
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for pp in (-1, +1):
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for dd in range(3):
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stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_air ** 2, thickness=pml_thickness)
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dxes_fdfd = stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_air ** 2, thickness=pml_thickness)
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# Compare the extracted phasor to the FDFD operator on the stretched grid,
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# not the unstretched Yee spacings used by the raw time-domain update.
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A = e_full(omega=omega, dxes=dxes_fdfd, epsilon=epsilon)
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@ -273,7 +273,7 @@ def main2():
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# PMLs in every direction
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pml_params = [
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[cpml_params(axis=dd, polarity=pp, dt=dt, thickness=pml_thickness, epsilon_eff=n_cladding ** 2)
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[cpml_params(axis=dd, polarity=pp, dt=dt, dx=dx, thickness=pml_thickness, epsilon_eff=n_cladding ** 2)
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for pp in (-1, +1)]
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for dd in range(3)]
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update_E, update_H = updates_with_cpml(cpml_params=pml_params, dt=dt, dxes=dxes, epsilon=epsilon, dtype=complex)
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@ -330,7 +330,7 @@ def main2():
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dxes_fdfd = copy.deepcopy(dxes)
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for pp in (-1, +1):
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for dd in range(3):
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stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_cladding ** 2, thickness=pml_thickness)
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dxes_fdfd = stretch_with_scpml(dxes_fdfd, axis=dd, polarity=pp, omega=omega, epsilon_effective=n_cladding ** 2, thickness=pml_thickness)
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# Residuals must be checked on the stretched FDFD grid, because the FDTD run
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# already includes those same absorbing layers through CPML.
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A = e_full(omega=omega, dxes=dxes_fdfd, epsilon=epsilon)
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