Add note regarding singular contributions and radiative LDOS to tutorial on Brillouin-zone integration in 1D

doc/docs/Python_Tutorials/Custom_Source.md

@@ -636,22 +636,8 @@ The simulation script is in [examples/dipole_in_1D_vacuum_1D.py](https://github.
 
 ![](../images/dipole_radiation_pattern_phi0_ey.png#center)
 
-As a final note, computing the [extraction efficiency of an LED](Local_Density_of_States.md#extraction-efficiency-of-a-light-emitting-diode-led) (not covered in this tutorial) requires the calculation of the total power emitted by the dipole. This can be done in the 1D approach outlined in this tutorial using the local density of states (LDOS) by summing the power from each point source (i.e. planewave) in the Brillouin-zone integration obtained using:
+As a final note, computing the [extraction efficiency of an LED](Local_Density_of_States.md#extraction-efficiency-of-a-light-emitting-diode-led) (not covered in this tutorial) requires the calculation of the total power emitted by the dipole. Generally, this *cannot* be done in the 1D approach outlined in this tutorial using the local density of states (LDOS) by summing the power from each point source (i.e. planewave) in the Brillouin-zone integration. This is because coupling into *lossless* guided modes of the slab only occurs at discrete $k$ values which contribute delta-function terms to the Brillouin-zone integrand. Singular contributions such as this cannot be directly handled by numerical quadrature. A workaround is to use a **lossy system**, for example a system where PML attenuates the waveguide modes (analogous to cylindrical-coordinates system in the LED tutorial linked above), or perhaps one adds a small imaginary part to $\varepsilon$ or $\omega$. Nevertheless, Brillouin-zone integration can still be used to compute the power *radiated* into air (i.e., the "radiative LDOS") which depends on the dipole position.
 
-```py
-    sim.run(
-        mp.dft_ldos(frequency, 0, 1),
-        until_after_sources=mp.stop_when_fields_decayed(
-            25, src_cmpt, mon_pt, FIELD_DECAY_THRESHOLD
-        )
-    )
-
-    delta_length = 1 / RESOLUTION_UM
-    flux_planewave = (
-        -np.real(sim.ldos_Fdata[0] * np.conj(sim.ldos_Jdata[0])) *
-        delta_length
-    )
-```
 
 Dipole Emission of a Cleaved Multilayer Stack
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