[docs] clarify FDFD-to-FDTD field reconstruction

README.md

@@ -194,6 +194,10 @@ For a broadband or continuous-wave FDTD run:
    part of the simulation, and compare the extracted phasor to the FDFD field or
    residual.
 
+This is the primary FDTD/FDFD equivalence workflow. The phasor extraction step
+filters the time-domain run down to the guided `+\omega` content that FDFD
+solves for directly, so it is the cleanest apples-to-apples comparison.
+
 ### Real-field reconstruction workflow
 
 For a continuous-wave real-valued FDTD run:
@@ -211,4 +215,14 @@ For a continuous-wave real-valued FDTD run:
    pieces to see whether the remaining mismatch is actually in the mode or in
    weak nonguided tails.
 
+This is a stricter diagnostic, not the primary equivalence benchmark. A raw
+monitor slice contains both the guided field and the remaining orthogonal
+content on that plane,
+
+$$ E_{\text{monitor}} = E_{\text{guided}} + E_{\text{residual}} , $$
+
+so its full-plane instantaneous error is naturally noisier than the extracted
+phasor comparison even when the underlying guided `+\omega` content matches
+well.
+
 `examples/waveguide_real.py` is the reference implementation of this workflow.

docs/index.md

@@ -26,6 +26,15 @@ Relevant starting examples:
   mode-weighted, and guided-mode / residual comparisons
 - `examples/fdfd.py` for direct frequency-domain waveguide excitation
 
+For solver equivalence, prefer the phasor-based examples first. They compare
+the extracted `+\omega` content of the FDTD run directly against the FDFD
+solution and are the main accuracy benchmarks in the test suite.
+
+`examples/waveguide_real.py` answers a different, stricter question: how well a
+late raw real snapshot matches `Re(E_\omega e^{i\omega t})` on a monitor plane.
+That diagnostic is useful, but it also includes orthogonal residual structure
+that the phasor comparison intentionally filters out.
+
 The API pages are better read as a toolbox map and derivation reference:
 
 - Use the [FDTD API](api/fdtd.md) for time-domain stepping, CPML, phasor

examples/waveguide_real.py

@@ -9,9 +9,12 @@ FDFD" workflow:
 3. solve the matching FDFD problem from the analytic source phasor, and
 4. compare late real monitor slices against `fdtd.reconstruct_real_e/h(...)`.
 
-Unlike the complex-source examples, this script does not use phasor extraction
+Unlike the phasor-based examples, this script does not use extracted phasors as
-as the main output. The comparison target is the real field itself, with both
+the main output. It is a stricter diagnostic: the comparison target is the raw
-full-plane and mode-weighted monitor errors reported.
+real field itself, with full-plane, mode-weighted, guided-mode, and orthogonal-
+residual errors reported. Strong phasor agreement can coexist with visibly
+larger raw-snapshot error because the latter includes weak nonguided tails on
+the monitor plane.
 """
 
 import numpy
@@ -104,7 +107,7 @@ def main() -> None:
         epsilon=epsilon,
     )
     # A small global phase aligns the real-valued source with the late-cycle
-    # monitor comparison. The underlying phasor problem is unchanged.
+    # raw-snapshot diagnostic. The underlying phasor problem is unchanged.
     j_mode *= numpy.exp(1j * SOURCE_PHASE)
     monitor_mode = waveguide_3d.solve_mode(
         0,

meanas/fdtd/__init__.py

@@ -165,6 +165,11 @@ with caller-provided sample times and weights. In this codebase the matching
 electric-current convention is typically `E -= dt * J / epsilon` in FDTD and
 `-i \omega J` on the right-hand side of the FDFD wave equation.
 
+For FDTD/FDFD equivalence, this phasor path is the primary comparison workflow.
+It isolates the guided `+\omega` response that the frequency-domain solver
+targets directly, regardless of whether the underlying FDTD run used real- or
+complex-valued fields.
+
 For exact pulsed FDTD/FDFD equivalence it is often simplest to keep the
 injected source, fields, and CPML auxiliary state complex-valued. The
 `real_injection_scale(...)` helper is instead for the more ordinary one-run
@@ -172,6 +177,17 @@ real-valued source path, where the intended positive-frequency waveform is
 injected through `numpy.real(scale * waveform)` and any remaining negative-
 frequency leakage is controlled by the pulse bandwidth and run length.
 
+`reconstruct_real(...)` is for a different question: given a phasor, what late
+real-valued field snapshot should it produce? That raw-snapshot comparison is
+stricter and noisier because a monitor plane generally contains both the guided
+field and the remaining orthogonal content,
+
+$$ E_{\text{monitor}} = E_{\text{guided}} + E_{\text{residual}} . $$
+
+Phasor/modal comparisons mostly validate the guided `+\omega` term. Raw
+real-field comparisons expose both terms at once, so they should be treated as
+secondary diagnostics rather than the main solver-equivalence benchmark.
+
 The Ricker wavelet (normalized second derivative of a Gaussian) is commonly used for the pulse
 shape. It can be written
 

meanas/test/test_waveguide_fdtd_fdfd.py

@@ -711,7 +711,11 @@ def test_straight_waveguide_fdtd_fdfd_overlap_and_flux_agree() -> None:
     assert result.overlap_phase_deg < 0.5
 
 
-def test_straight_waveguide_real_monitor_fields_match_reconstructed_real_fields() -> None:
+def test_straight_waveguide_real_snapshot_diagnostic_tracks_guided_content_and_bounded_residual() -> None:
+    # The phasor-based waveguide tests above are the primary FDTD/FDFD
+    # equivalence benchmark. This raw real-field check is intentionally stricter:
+    # it validates that late monitor snapshots keep the guided content close to
+    # the reconstructed FDFD field while the orthogonal residual stays bounded.
     result = _run_real_field_straight_waveguide_case()
     ranked_snapshots = sorted(
         result.snapshots,