diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3ca77b1c9..9e61f8ff8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -29,6 +29,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Inaccuracy in transforming gradients from edge to `PolySlab.vertices`.
 - Bug in `run_async` where an adjoint simulation would sometimes be assigned to the wrong forward simulation.
 - Validate against nonlinearity or modulation in `FullyAnisotropicMedium.from_diagonal`.
+- Add warning to complex-field nonlinearities, which may require more careful physical interpretation.
 
 
 ## [2.7.6] - 2024-10-30
diff --git a/tests/test_components/test_medium.py b/tests/test_components/test_medium.py
index 2b54ad76b..1dffefde6 100644
--- a/tests/test_components/test_medium.py
+++ b/tests/test_components/test_medium.py
@@ -562,15 +562,15 @@ def test_nonlinear_medium(log_capture):
     )
 
     # complex parameters
-    med = td.Medium(
-        nonlinear_spec=td.NonlinearSpec(
-            models=[
-                td.KerrNonlinearity(n2=-1 + 1j, n0=1),
-            ],
-            num_iters=20,
+    with AssertLogLevel(log_capture, "WARNING", contains_str="preferred"):
+        med = td.Medium(
+            nonlinear_spec=td.NonlinearSpec(
+                models=[
+                    td.KerrNonlinearity(n2=-1 + 1j, n0=1),
+                ],
+                num_iters=20,
+            )
         )
-    )
-    assert_log_level(log_capture, None)
 
     # warn about deprecated api
     med = td.Medium(nonlinear_spec=td.NonlinearSusceptibility(chi3=1.5))
@@ -621,10 +621,11 @@ def test_nonlinear_medium(log_capture):
     with pytest.raises(ValidationError):
         med = td.Medium(nonlinear_spec=td.NonlinearSpec(models=[td.KerrNonlinearity(n2=-1j, n0=1)]))
 
-    med = td.Medium(
-        nonlinear_spec=td.NonlinearSpec(models=[td.TwoPhotonAbsorption(beta=-1, n0=1)]),
-        allow_gain=True,
-    )
+    with AssertLogLevel(log_capture, "WARNING", contains_str="phenomenological"):
+        med = td.Medium(
+            nonlinear_spec=td.NonlinearSpec(models=[td.TwoPhotonAbsorption(beta=-1, n0=1)]),
+            allow_gain=True,
+        )
 
     # automatic detection of n0 and freq0
     n0 = 2
diff --git a/tests/test_plugins/test_adjoint.py b/tests/test_plugins/test_adjoint.py
index 8fd01fbb0..795412293 100644
--- a/tests/test_plugins/test_adjoint.py
+++ b/tests/test_plugins/test_adjoint.py
@@ -1858,7 +1858,7 @@ def test_nonlinear_warn(log_capture):
     )
 
     # make the nonlinear objects to add to the JaxSimulation one by one
-    nl_model = td.KerrNonlinearity(n2=1)
+    nl_model = td.NonlinearSusceptibility(chi3=1)
     nl_medium = td.Medium(nonlinear_spec=td.NonlinearSpec(models=[nl_model]))
     struct_static_nl = struct_static.updated_copy(medium=nl_medium)
     input_struct_nl = JaxStructureStaticMedium(geometry=struct.geometry, medium=nl_medium)
diff --git a/tidy3d/components/medium.py b/tidy3d/components/medium.py
index 6f25ca46d..4f5e8d760 100644
--- a/tidy3d/components/medium.py
+++ b/tidy3d/components/medium.py
@@ -442,6 +442,14 @@ def _hardcode_medium_freqs(
 
     def _validate_medium(self, medium: AbstractMedium):
         """Check that the model is compatible with the medium."""
+        log.warning(
+            "Found a medium with a 'TwoPhotonAbsorption' nonlinearity. "
+            "This uses a phenomenological model based on complex fields, "
+            "so care should be taken in interpreting the results. For more "
+            "information on the model, see the documentation at "
+            "'https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.TwoPhotonAbsorption.html' or the following reference: "
+            "'N. Suzuki, \"FDTD Analysis of Two-Photon Absorption and Free-Carrier Absorption in Si High-Index-Contrast Waveguides,\" J. Light. Technol. 25, 9 (2007).'."
+        )
         # if n0 is specified, we can go ahead and validate passivity
         if self.n0 is not None:
             self._validate_medium_freqs(medium, [])
@@ -481,7 +489,7 @@ class KerrNonlinearity(NonlinearModel):
     The fields in this equation are complex-valued, allowing a direct implementation of the Kerr
     nonlinearity. In contrast, the model :class:`.NonlinearSusceptibility` implements a
     chi3 nonlinear susceptibility using real-valued fields, giving rise to Kerr nonlinearity
-    as well as third-harmonic generation. The relationship between the parameters is given by
+    as well as third-harmonic generation and other effects. The relationship between the parameters is given by
     :math:`n_2 = \\frac{3}{4} \\frac{1}{\\varepsilon_0 c_0 n_0 \\operatorname{Re}(n_0)} \\chi_3`. The additional
     factor of :math:`\\frac{3}{4}` comes from the usage of complex-valued fields for the Kerr
     nonlinearity and real-valued fields for the nonlinear susceptibility.
@@ -538,6 +546,13 @@ def _hardcode_medium_freqs(
 
     def _validate_medium(self, medium: AbstractMedium):
         """Check that the model is compatible with the medium."""
+        log.warning(
+            "Found a medium with a 'KerrNonlinearity'. Usually, "
+            "'NonlinearSusceptibility' is preferred, as it captures "
+            "additional physical effects by acting on the underlying real fields. "
+            "The relation between the parameters is "
+            "'chi3 = (4/3) * eps_0 * c_0 * n0 * Re(n0) * n2'."
+        )
         # if n0 is specified, we can go ahead and validate passivity
         if self.n0 is not None:
             self._validate_medium_freqs(medium, [])