Added KerrMedium

CHANGELOG.md

@@ -6,6 +6,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ## [Unreleased]
 
 ### Added
+- `KerrMedium` with chi3 nonlinear susceptibility.
 - Source with arbitrary user-specified time dependence through `CustomSourceTime`.
 
 ### Changed

tests/sims/simulation_2_3_0.json

@@ -591,6 +591,33 @@
                 "subpixel": false
             }
         },
+        {
+            "geometry": {
+                "type": "Box",
+                "center": [
+                    -1.0,
+                    0.5,
+                    0.5
+                ],
+                "size": [
+                    1.0,
+                    1.0,
+                    1.0
+                ]
+            },
+            "name": null,
+            "type": "Structure",
+            "medium": {
+                "name": null,
+                "frequency_range": null,
+                "allow_gain": false,
+                "type": "KerrMedium",
+                "permittivity": 1.0,
+                "conductivity": 0.0,
+                "numiters": 20,
+                "chi3": 0.1
+            }
+        },
         {
             "geometry": {
                 "type": "PolySlab",

tests/test_components/test_medium.py

@@ -410,3 +410,7 @@ def test_fully_anisotropic_media():
 
     assert all(np.isin(np.round(perm_d), np.round(np.diag(perm_diag))))
     assert all(np.isin(np.round(cond_d), np.round(np.diag(cond_diag))))
+
+
+def test_nonlinear_medium():
+    med = td.KerrMedium(chi3=1.5, numiters=20)

tests/utils.py

@@ -223,6 +223,13 @@ def prepend_tmp(path):
             ),
             medium=custom_sellmeier,
         ),
+        Structure(
+            geometry=Box(
+                size=(1, 1, 1),
+                center=(-1.0, 0.5, 0.5),
+            ),
+            medium=KerrMedium(chi3=0.1, numiters=20),
+        ),
         Structure(
             geometry=PolySlab(
                 vertices=[(-1.5, -1.5), (-0.5, -1.5), (-0.5, -0.5)], slab_bounds=[-1, 1]

tidy3d/__init__.py

@@ -14,6 +14,7 @@
 from .components.medium import CustomMedium, CustomPoleResidue
 from .components.medium import CustomSellmeier, FullyAnisotropicMedium
 from .components.medium import CustomLorentz, CustomDrude, CustomDebye, CustomAnisotropicMedium
+from .components.medium import KerrMedium
 from .components.transformation import RotationAroundAxis
 
 # structures
@@ -82,7 +83,7 @@
 from .material_library.parametric_materials import Graphene
 
 # for docs
-from .components.medium import AbstractMedium
+from .components.medium import AbstractMedium, AbstractNonlinearMedium
 from .components.geometry import Geometry
 from .components.source import Source, SourceTime
 from .components.monitor import Monitor

tidy3d/components/medium.py

@@ -2927,6 +2927,61 @@ class CustomAnisotropicMediumInternal(CustomAnisotropicMedium):
     )
 
 
+class AbstractNonlinearMedium(AbstractMedium, ABC):
+    """Abstract nonlinear medium.
+
+    Note
+    ----
+    The nonlinear constitutive relation is solved iteratively; it may not converge
+    for large nonlinearities. Increasing `numiters` can help with convergence.
+
+    """
+
+    numiters: pd.PositiveInt = pd.Field(
+        1,
+        title="Number of iterations",
+        description="Number of iterations for solving nonlinear constitutive relation.",
+    )
+
+
+class KerrMedium(AbstractNonlinearMedium, Medium):
+    """Kerr medium described by an instantaneous chi3 nonlinear susceptibility, as in the 
+    expression below for the nonlinear polarization.
+
+    Note
+    ----
+    .. math::
+
+        P_{NL} = \\epsilon_0 \\chi_3 |E|^2 E
+
+    Note
+    ----
+    The nonlinear constitutive relation is solved iteratively; it may not converge
+    for large nonlinearities. Increasing `numiters` can help with convergence.
+
+    Note
+    ----
+    For complex fields (e.g. when using Bloch boundary conditions), the nonlinearity
+    is applied separately to the real and imaginary parts, so that the above equation
+    holds when both E and :math:`P_{NL}` are replaced by their real or imaginary parts.
+    Since the physical fields are real, it wouldn't make sense to apply the instantaneous
+    nonlinearity directly to the complex fields.
+
+    Note
+    ----
+    Different field components do not interact nonlinearly. For example,
+    when calculating :math:`P_{NL, x}`, we approximate :math:`|E|^2 \\approx |E_x|^2`.
+    This approximation is valid when the E field is predominantly polarized along one
+    of the x, y, or z axes.
+
+    Example
+    -------
+    >>> medium = KerrMedium(chi3=1)
+    """
+
+    chi3: float = pd.Field(..., title="Chi3", description="Chi3 nonlinear susceptibility.")
+
+
 # types of mediums that can be used in Simulation and Structures
 
 MediumType3D = Union[
@@ -2946,6 +3001,7 @@ class CustomAnisotropicMediumInternal(CustomAnisotropicMedium):
     CustomDebye,
     CustomDrude,
     CustomAnisotropicMedium,
+    KerrMedium,
 ]