[fdfd.waveguide_2d_complex] add 2d complex modesolver

examples/eme_taper_pml_modes.py

@@ -0,0 +1,90 @@
+"""Build tracked complex/PML modal bases for a slowly varying taper."""
+
+from __future__ import annotations
+
+import numpy
+
+from meanas.fdmath import vec
+from meanas.fdfd import eme, scpml, waveguide_2d_complex
+
+
+WAVELENGTH = 1.55
+OMEGA = 2 * numpy.pi / WAVELENGTH
+SHAPE = (17, 17)
+SPACING = 0.25
+PML_CELLS = 3
+EPS_CLADDING = 1.45 ** 2
+EPS_CORE = 2.0 ** 2
+
+
+def build_grids() -> tuple[list[list[numpy.ndarray]], list[list[numpy.ndarray]]]:
+    """Build matching physical and complex-stretched transverse Yee grids.
+
+    Returns:
+        The real overlap grid followed by the PML-stretched solve grid.
+    """
+    physical = [[numpy.full(size, SPACING) for size in SHAPE] for _ in range(2)]
+    stretched = [[values.copy() for values in family] for family in physical]
+    for axis in (0, 1):
+        for polarity in (-1, +1):
+            stretched = scpml.stretch_with_scpml(
+                stretched,
+                axis=axis,
+                polarity=polarity,
+                omega=OMEGA,
+                epsilon_effective=EPS_CLADDING,
+                thickness=PML_CELLS,
+            )
+    return physical, stretched
+
+
+def build_epsilon(edge_fill: float) -> numpy.ndarray:
+    """Construct and vectorize one taper cross-section permittivity profile.
+
+    Args:
+        edge_fill: Fractional core fill used for the two cells beside the
+            central three-cell-wide core.
+
+    Returns:
+        Vectorized three-component relative permittivity field.
+    """
+    epsilon = numpy.full((3, *SHAPE), EPS_CLADDING)
+    center_x, center_y = (size // 2 for size in SHAPE)
+    epsilon[:, center_x - 1:center_x + 2, center_y] = EPS_CORE
+    mixed_epsilon = EPS_CLADDING + edge_fill * (EPS_CORE - EPS_CLADDING)
+    epsilon[:, center_x - 1:center_x + 2, center_y - 1] = mixed_epsilon
+    epsilon[:, center_x - 1:center_x + 2, center_y + 1] = mixed_epsilon
+    return vec(epsilon)
+
+
+def main() -> None:
+    """Solve, track, and summarize the sampled complex modal bases."""
+    physical_dxes, solve_dxes = build_grids()
+    z_coords = numpy.array([0.0, 5.0, 10.0])
+    bases = [
+        waveguide_2d_complex.solve_modes_near(
+            OMEGA,
+            solve_dxes,
+            build_epsilon(edge_fill),
+            target_wavenumbers=[1.45 * OMEGA],
+            modes_per_target=3,
+            candidate_margin=3,
+            overlap_dxes=physical_dxes,
+        )
+        for edge_fill in (0.30, 0.35, 0.40)
+    ]
+    tracked = waveguide_2d_complex.track_mode_path(bases)
+    sections = eme.mode_sections_from_bases(z_coords, tracked)
+
+    for z_coord, basis in zip(z_coords, tracked, strict=True):
+        print(
+            f'z={z_coord:5.1f}: '
+            f'beta={basis.wavenumbers[0]:.6g}, '
+            f'PML participation={basis.diagnostics.pml_participation[0]:.3f}, '
+            f'right residual={basis.diagnostics.right_residuals[0]:.2e}',
+        )
+    print(f'constructed {len(sections)} tracked EME sections with {len(sections[0].modes)} modes each')
+
+
+if __name__ == '__main__':
+    main()