[waveguide_real / phasor] more work towards real-FDTD to FDFD equivalence

README.md

@@ -159,6 +159,10 @@ The tracked examples under `examples/` are the intended entry points for users:
   residual check against the matching FDFD operator.
 - `examples/waveguide.py`: waveguide mode solving, unidirectional mode-source
   construction, overlap readout, and FDTD/FDFD comparison on a guided structure.
+- `examples/waveguide_real.py`: real-valued continuous-wave FDTD on a straight
+  guide, with late-time monitor slices, guided-core windows, and mode-weighted
+  errors compared directly against real fields reconstructed from the matching
+  FDFD solution, plus a guided-mode / orthogonal-residual split.
 - `examples/fdfd.py`: direct frequency-domain waveguide excitation and overlap /
   Poynting analysis without a time-domain run.
 
@@ -189,3 +193,22 @@ For a broadband or continuous-wave FDTD run:
 4. Build the matching FDFD operator on the stretched `dxes` if CPML/SCPML is
    part of the simulation, and compare the extracted phasor to the FDFD field or
    residual.
+
+### Real-field reconstruction workflow
+
+For a continuous-wave real-valued FDTD run:
+
+1. Build the analytic source phasor for the structure, for example with
+   `waveguide_3d.compute_source(...)`.
+2. Run the real-valued FDTD simulation using the real part of that source.
+3. Solve the matching FDFD problem from the analytic source phasor on the
+   stretched `dxes`.
+4. Reconstruct late real `E/H/J` snapshots with
+   `reconstruct_real_e/h/j(...)` and compare those directly against the
+   real-valued FDTD fields, ideally on a monitor window or mode-weighted norm
+   centered on the guided field rather than on the full transverse plane. When
+   needed, split the monitor field into guided-mode and orthogonal residual
+   pieces to see whether the remaining mismatch is actually in the mode or in
+   weak nonguided tails.
+
+`examples/waveguide_real.py` is the reference implementation of this workflow.