90 lines
2.9 KiB
Python
90 lines
2.9 KiB
Python
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"""Build tracked complex/PML modal bases for a slowly varying taper."""
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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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WAVELENGTH = 1.55
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OMEGA = 2 * numpy.pi / WAVELENGTH
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SHAPE = (17, 17)
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SPACING = 0.25
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PML_CELLS = 3
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EPS_CLADDING = 1.45 ** 2
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EPS_CORE = 2.0 ** 2
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def build_grids() -> tuple[list[list[numpy.ndarray]], list[list[numpy.ndarray]]]:
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"""Build matching physical and complex-stretched transverse Yee grids.
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Returns:
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The real overlap grid followed by the PML-stretched solve grid.
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"""
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physical = [[numpy.full(size, SPACING) for size in SHAPE] for _ in range(2)]
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stretched = [[values.copy() for values in family] for family in physical]
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for axis in (0, 1):
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for polarity in (-1, +1):
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stretched = scpml.stretch_with_scpml(
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stretched,
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axis=axis,
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polarity=polarity,
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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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)
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return physical, stretched
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def build_epsilon(edge_fill: float) -> numpy.ndarray:
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"""Construct and vectorize one taper cross-section permittivity profile.
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Args:
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edge_fill: Fractional core fill used for the two cells beside the
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central three-cell-wide core.
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Returns:
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Vectorized three-component relative permittivity field.
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"""
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epsilon = numpy.full((3, *SHAPE), EPS_CLADDING)
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center_x, center_y = (size // 2 for size in SHAPE)
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epsilon[:, center_x - 1:center_x + 2, center_y] = EPS_CORE
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mixed_epsilon = EPS_CLADDING + edge_fill * (EPS_CORE - EPS_CLADDING)
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epsilon[:, center_x - 1:center_x + 2, center_y - 1] = mixed_epsilon
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epsilon[:, center_x - 1:center_x + 2, center_y + 1] = mixed_epsilon
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return vec(epsilon)
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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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OMEGA,
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solve_dxes,
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build_epsilon(edge_fill),
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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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]
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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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for z_coord, basis in zip(z_coords, tracked, 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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)
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print(f'constructed {len(sections)} tracked EME sections with {len(sections[0].modes)} modes each')
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if __name__ == '__main__':
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main()
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