diff --git a/docs/analytic_beam_tutorial.rst b/docs/analytic_beam_tutorial.rst
index 46badb37ec..f168f36098 100644
--- a/docs/analytic_beam_tutorial.rst
+++ b/docs/analytic_beam_tutorial.rst
@@ -19,6 +19,11 @@ or :meth:`pyuvdata.analytic_beam.AnalyticBeam.power_eval` methods as appropriate
 Evaluating an Airy Beam power response
 **************************************
 
+This code evaluates and plots an Airy beam power response. Note that we exclude
+the cross polarizations, since this is an unpolarized the cross polarizations
+are identical to the auto polarization power beams. If the cross polarizations
+are included the array returned from the ``power_eval`` method will be complex.
+
 .. code-block:: python
 
   >>> import matplotlib.pyplot as plt
@@ -85,6 +90,12 @@ Evaluating an Airy Beam power response
 Evaluating a Short Dipole Beam E-Field response
 ***********************************************
 
+This code evaluates and plots a short (Herzian) dipole beam E-field response
+(also called the Jones matrix). Since it is the E-Field response, we have 4
+effective maps because we have the response to each polarization basis vector
+for each feed. In the case of a short dipole, these maps do not have an imaginary
+part, but in general E-Field beams can be complex, so a complex array is returned.
+
 .. code-block:: python
 
   >>> import matplotlib.pyplot as plt
@@ -239,10 +250,13 @@ actually calculate the response of the new beam:
       - ``freq_array``: an array of frequencies in Hz at which to evaluate the beam.
         Must be a 1D array.
 
-    and it must return a complex array of beam responses with the shape:
-    (1, ``Npols``, ``freq_array.size``, ``az_array.size``).
-    ``Npols`` is equal to either ``Nfeeds`` squared if ``include_cross_pols``
-    is True (the default) or ``Nfeeds`` if ``include_cross_pols`` is False.
+    and it must return an array of beam responses with the shape:
+    (1, ``Npols``, ``freq_array.size``, ``az_array.size``). The array can be complex
+    if cross polarizations are included (if it is not complex it will be made
+    complex if the cross polarizations are included when it is called via the
+    ``power_eval`` method on the base class). ``Npols`` is equal to either
+    ``Nfeeds`` squared if ``include_cross_pols`` is True (the default) or
+    ``Nfeeds`` if ``include_cross_pols`` is False.
 
 Note that if you need to do some manipulation or validation of the fields after
 they are specified by the user, you can use the dataclass's ``__post_init__``