Near field against position-resolved plane waves and Parseval

← Verification · Thin films · Focused beam
Reference
near field against position-resolved plane waves and Parseval
Kind
method: an independent formulation inside this repo (a scattering matrix, a plane-wave superposition, a quadrature): proves the formulation
Calculated
E at points
Agreement
1e-10 (3e-4 Parseval quadrature)
A two-layer film (0.8 µm n = 1.6 + 0.05i, 2 µm n = 1.42) in air under a focused beam (NA 0.6/0.2, focus off-axis), 3 µm: |E|² along the depth Along x = 0.1, y = 0 µm from the air above, through both layers (0–0.8 and 0.8–2.8 µm) into the air below; x-polarized pupil, focus at (0.3, −0.2, 0.5) µm. The reference sums a 48 × 48 pupil grid of plane waves, each from position_resolved. The test also checks Parseval: the lateral integral of |E|² at a depth against the pupil's.
-1012340.20.40.60.811.21.41.61.8z [µm]|E|²
|E|², PyStratify |E|², position-resolved plane waves summed
Hover to read values.
  • largest relative difference: 3.44×10⁻¹⁵
  • PyStratify the lines, the reference the circles

Run it yourself: focused_checks.py · test_focused.py · figures.py · FOCUSED_CHECKS.md on GitHub, PyStratify 97e52a9