diff --git a/python/geom.py b/python/geom.py
index a129cf1a7..335b70a98 100755
--- a/python/geom.py
+++ b/python/geom.py
@@ -529,7 +529,7 @@ class MaterialGrid(object):
     the `default_material` argument of the [`Simulation`](#Simulation) constructor (similar to a
     [material function](#medium)).
     """
-    def __init__(self,grid_size,medium1,medium2,weights=None,grid_type="U_DEFAULT",do_averaging=False,beta=0,eta=0.5):
+    def __init__(self,grid_size,medium1,medium2,weights=None,grid_type="U_DEFAULT",do_averaging=False,beta=0,eta=0.5,damping=0):
         """
         Creates a `MaterialGrid` object.
 
@@ -563,11 +563,15 @@ def __init__(self,grid_size,medium1,medium2,weights=None,grid_type="U_DEFAULT",d
         grid values. Subpixel smoothing is fast and accurate because it exploits an analytic formulation
         for level-set functions.
 
+        A nonzero damping term creates an artificial conductivity σ = u(1-u)*damping, which acts as
+        dissipation loss that penalize intermediate pixel values of non-binarized structures. The value of
+        damping should be proportional to 2π times the typical frequency of the problem.
+
         It is possible to overlap any number of different `MaterialGrid`s. This can be useful for defining
         grids which are symmetric (e.g., mirror, rotation). One way to set this up is by overlapping a
         given `MaterialGrid` object with a symmetrized copy of itself. In the case of spatially overlapping
         `MaterialGrid` objects (with no intervening objects), any overlapping points are computed using the
-        method `grid_type` which is one of `"U_MIN"` (minimum of the overlapping grid values), `"U_PROD"` 
+        method `grid_type` which is one of `"U_MIN"` (minimum of the overlapping grid values), `"U_PROD"`
         (product), `"U_MEAN"` (mean), `"U_DEFAULT"` (topmost material grid). In general, these `"U_*"` options
         allow you to combine any material grids that overlap in space with no intervening objects.
         """
@@ -586,6 +590,7 @@ def isclose(a, b, rel_tol=1e-09, abs_tol=0.0):
         self.do_averaging = do_averaging
         self.beta = beta
         self.eta = eta
+        self.damping = damping
         if weights is None:
             self.weights = np.zeros((self.num_params,))
         elif weights.size != self.num_params:
diff --git a/python/typemap_utils.cpp b/python/typemap_utils.cpp
index 0602a72ff..e2182b3f8 100644
--- a/python/typemap_utils.cpp
+++ b/python/typemap_utils.cpp
@@ -581,11 +581,15 @@ static int pymaterial_to_material(PyObject *po, material_type *mt) {
     PyObject *py_eta = PyObject_GetAttrString(po, "eta");
     double eta = 0;
     if (py_eta) { eta = PyFloat_AsDouble(py_eta); }
-    md = make_material_grid(do_averaging,beta,eta);
+    PyObject *py_damping = PyObject_GetAttrString(po, "damping");
+    double damping = 0;
+    if (py_damping) { damping = PyFloat_AsDouble(py_damping); }
+    md = make_material_grid(do_averaging,beta,eta,damping);
     if (!pymaterial_grid_to_material_grid(po, md)) { return 0; }
     Py_XDECREF(py_do_averaging);
     Py_XDECREF(py_beta);
     Py_XDECREF(py_eta);
+    Py_XDECREF(py_damping);
   }
   else if (PyFunction_Check(po)) {
     PyObject *eps = PyObject_GetAttrString(po, "eps");
diff --git a/src/material_data.cpp b/src/material_data.cpp
index 74e46d0cc..323c72eb4 100644
--- a/src/material_data.cpp
+++ b/src/material_data.cpp
@@ -86,6 +86,7 @@ void material_data::copy_from(const material_data &from) {
   medium_2 = from.medium_2;
   beta = from.beta;
   eta = from.eta;
+  damping = from.damping;
 }
 
 material_type_list::material_type_list() : items(NULL), num_items(0) {}
diff --git a/src/material_data.hpp b/src/material_data.hpp
index b219112c6..2fcbae81d 100644
--- a/src/material_data.hpp
+++ b/src/material_data.hpp
@@ -135,6 +135,7 @@ struct material_data {
   medium_struct medium_2;
   double beta;
   double eta;
+  double damping;
   /*
   There are several possible scenarios when material grids overlap -- these
   different scenarios enable different applications.
@@ -180,7 +181,7 @@ extern material_type vacuum;
 material_type make_dielectric(double epsilon);
 material_type make_user_material(user_material_func user_func, void *user_data);
 material_type make_file_material(char *epsilon_input_file);
-material_type make_material_grid(bool do_averaging, double beta, double eta);
+material_type make_material_grid(bool do_averaging, double beta, double eta, double damping);
 void read_epsilon_file(const char *eps_input_file);
 void update_weights(material_type matgrid, double *weights);
 
diff --git a/src/meepgeom.cpp b/src/meepgeom.cpp
index f273ac55e..c914e8097 100644
--- a/src/meepgeom.cpp
+++ b/src/meepgeom.cpp
@@ -605,6 +605,10 @@ void epsilon_material_grid(material_data *md, double u) {
     // mm->D_conductivity_diag.x = mm->D_conductivity_diag.y = mm->D_conductivity_diag.z = u*(1-u) *
     // omega_mean;
   }
+  double fake_damping = u*(1-u)*(md->damping);
+  mm->D_conductivity_diag.x += fake_damping;
+  mm->D_conductivity_diag.y += fake_damping;
+  mm->D_conductivity_diag.z += fake_damping;
 }
 
 // return material of the point p from the file (assumed already read)
@@ -1507,20 +1511,26 @@ static double get_cnd(meep::component c, const medium_struct *m) {
   }
 }
 
+static bool has_conductivity(const material_type &md, meep::component c) {
+    medium_struct *mm;
+    if (is_medium(md, &mm) && get_cnd(c, mm)) return true;
+    if (md->which_subclass == material_data::MATERIAL_GRID &&
+        (get_cnd(c, &md->medium_1) || get_cnd(c, &md->medium_2) ||
+          md->damping != 0)) return true;
+    return false;
+}
+
 bool geom_epsilon::has_conductivity(meep::component c) {
   medium_struct *mm;
 
   FOR_DIRECTIONS(d) FOR_SIDES(b) {
     if (cond[d][b].prof) return true;
   }
-
   for (int i = 0; i < geometry.num_items; ++i)
-    if (is_medium(geometry.items[i].material, &mm) && get_cnd(c, mm)) return true;
-
+    if (meep_geom::has_conductivity((material_type) geometry.items[i].material, c)) return true;
   for (int i = 0; i < extra_materials.num_items; ++i)
-    if (is_medium(extra_materials.items[i], &mm) && get_cnd(c, mm)) return true;
-
-  return (is_medium(default_material, &mm) && get_cnd(c, mm) != 0);
+    if (meep_geom::has_conductivity((material_type) extra_materials.items[i], c)) return true;
+  return meep_geom::has_conductivity((material_type) default_material, c);
 }
 
 static meep::vec geometry_edge; // geometry_lattice.size / 2
@@ -2024,12 +2034,13 @@ material_type make_file_material(const char *eps_input_file) {
 /******************************************************************************/
 /* Material grid functions                                                    */
 /******************************************************************************/
-material_type make_material_grid(bool do_averaging, double beta, double eta) {
+material_type make_material_grid(bool do_averaging, double beta, double eta, double damping) {
   material_data *md = new material_data();
   md->which_subclass = material_data::MATERIAL_GRID;
   md->do_averaging = do_averaging;
   md->beta = beta;
   md->eta = eta;
+  md->damping = damping;
   return md;
 }
 
diff --git a/src/meepgeom.hpp b/src/meepgeom.hpp
index f7617686e..bd723866e 100644
--- a/src/meepgeom.hpp
+++ b/src/meepgeom.hpp
@@ -246,7 +246,7 @@ void set_materials_from_geom_epsilon(meep::structure *s, geom_epsilon *geps,
 material_type make_dielectric(double epsilon);
 material_type make_user_material(user_material_func user_func, void *user_data, bool do_averaging);
 material_type make_file_material(const char *eps_input_file);
-material_type make_material_grid(bool do_averaging, double beta, double eta);
+material_type make_material_grid(bool do_averaging, double beta, double eta, double damping);
 
 vector3 vec_to_vector3(const meep::vec &pt);
 meep::vec vector3_to_vec(const vector3 v3);