diff --git a/kwave/kmedium.py b/kwave/kmedium.py
index 2886299d..89353088 100644
--- a/kwave/kmedium.py
+++ b/kwave/kmedium.py
@@ -1,6 +1,6 @@
 import logging
 from dataclasses import dataclass
-from typing import List
+from typing import List, Optional, Sequence, Union
 
 import numpy as np
 
@@ -9,42 +9,43 @@
 
 @dataclass
 class kWaveMedium(object):
+    """
+    Medium properties for k-Wave simulations.
+    
+    Note: For heterogeneous medium parameters, medium.sound_speed and medium.density
+    must be given in matrix form with the same dimensions as kgrid. For homogeneous
+    medium parameters, these can be given as single numeric values. If the medium is
+    homogeneous and velocity inputs or outputs are not required, it is not necessary
+    to specify medium.density.
+    """
     # sound speed distribution within the acoustic medium [m/s] | required to be defined
-    sound_speed: np.array
+    sound_speed: Union[float, int, np.ndarray]
     # reference sound speed used within the k-space operator (phase correction term) [m/s]
-    sound_speed_ref: np.array = None
+    sound_speed_ref: Optional[Union[float, int, np.ndarray]] = None
     # density distribution within the acoustic medium [kg/m^3]
-    density: np.array = None
+    density: Optional[Union[float, int, np.ndarray]] = None
     # power law absorption coefficient [dB/(MHz^y cm)]
-    alpha_coeff: np.array = None
+    alpha_coeff: Optional[Union[float, int, np.ndarray]] = None
     # power law absorption exponent
-    alpha_power: np.array = None
+    alpha_power: Optional[Union[float, int, np.ndarray]] = None
     # optional input to force either the absorption or dispersion terms in the equation of state to be excluded;
     # valid inputs are 'no_absorption' or 'no_dispersion'
-    alpha_mode: np.array = None
+    alpha_mode: Optional[str] = None
     # frequency domain filter applied to the absorption and dispersion terms in the equation of state
-    alpha_filter: np.array = None
+    alpha_filter: Optional[np.ndarray] = None
     # two element array used to control the sign of absorption and dispersion terms in the equation of state
-    alpha_sign: np.array = None
+    alpha_sign: Optional[np.ndarray] = None
     # parameter of nonlinearity
-    BonA: np.array = None
+    BonA: Optional[Union[float, int, np.ndarray]] = None
     # is the medium absorbing?
     absorbing: bool = False
     # is the medium absorbing stokes?
     stokes: bool = False
 
-    #  """
-    #     Note: For heterogeneous medium parameters, medium.sound_speed and
-    #     medium.density must be given in matrix form with the same dimensions as
-    #     kgrid. For homogeneous medium parameters, these can be given as single
-    #     numeric values. If the medium is homogeneous and velocity inputs or
-    #     outputs are not required, it is not necessary to specify medium.density.
-    # """
-
     def __post_init__(self):
         self.sound_speed = np.atleast_1d(self.sound_speed)
 
-    def check_fields(self, kgrid_shape: np.ndarray) -> None:
+    def check_fields(self, kgrid_shape: Sequence[int]) -> None:
         """
         Check whether the given properties are valid
 
@@ -63,17 +64,19 @@ def check_fields(self, kgrid_shape: np.ndarray) -> None:
             ], "medium.alpha_mode must be set to 'no_absorption', 'no_dispersion', or 'stokes'."
 
         # check the absorption filter input is valid
-        if self.alpha_filter is not None and not (self.alpha_filter.shape == kgrid_shape).all():
+        if self.alpha_filter is not None and self.alpha_filter.shape != tuple(kgrid_shape):
             raise ValueError("medium.alpha_filter must be the same size as the computational grid.")
 
         # check the absorption sign input is valid
-        if self.alpha_sign is not None and (not kwave.utils.checkutils.is_number(self.alpha_sign) or (self.alpha_sign.size != 2)):
-            raise ValueError(
-                "medium.alpha_sign must be given as a " "2 element numerical array controlling absorption and dispersion, respectively."
-            )
+        if self.alpha_sign is not None:
+            alpha_sign_arr = np.atleast_1d(self.alpha_sign)
+            if alpha_sign_arr.size != 2 or not np.issubdtype(alpha_sign_arr.dtype, np.number):
+                raise ValueError(
+                    "medium.alpha_sign must be a 2 element numeric array controlling absorption and dispersion, respectively."
+                )
 
         # check alpha_coeff is non-negative and real
-        if not np.all(np.isreal(self.alpha_coeff)) or np.any(self.alpha_coeff < 0):
+        if self.alpha_coeff is not None and (not np.all(np.isreal(self.alpha_coeff)) or np.any(self.alpha_coeff < 0)):
             raise ValueError("medium.alpha_coeff must be non-negative and real.")
 
     def is_defined(self, *fields) -> List[bool]:
@@ -102,7 +105,7 @@ def ensure_defined(self, *fields) -> None:
             None
         """
         for f in fields:
-            assert getattr(self, f) is not None, f"The field {f} must be not be None"
+            assert getattr(self, f) is not None, f"The field {f} must not be None"
 
     def is_nonlinear(self) -> bool:
         """
@@ -167,8 +170,10 @@ def _check_absorbing_with_stokes(self):
         self.ensure_defined("alpha_coeff")
 
         # give warning if y is specified
-        if self.alpha_power is not None and (self.alpha_power.size != 1 or self.alpha_power != 2):
-            logging.log(logging.WARN, "the axisymmetric code and stokes absorption assume alpha_power = 2, user value ignored.")
+        if self.alpha_power is not None:
+            ap = np.asarray(self.alpha_power)
+            if ap.size != 1 or not np.isclose(ap.item(), 2.0):
+                logging.warning("the axisymmetric code and stokes absorption assume alpha_power = 2, user value ignored.")
 
         # overwrite y value
         self.alpha_power = 2
diff --git a/tests/test_kmedium.py b/tests/test_kmedium.py
new file mode 100644
index 00000000..5908c5ab
--- /dev/null
+++ b/tests/test_kmedium.py
@@ -0,0 +1,247 @@
+"""
+kWaveMedium comprehensive test suite
+
+Tests for code paths not covered by existing tests to improve code coverage.
+"""
+
+from unittest.mock import patch
+
+import numpy as np
+import pytest
+
+from kwave.data import Vector
+from kwave.kgrid import kWaveGrid
+from kwave.kmedium import kWaveMedium
+
+
+def test_elastic_properties_access():
+    """Test access to elastic code related properties (should raise NotImplementedError)"""
+    medium = kWaveMedium(sound_speed=1500)
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.sound_speed_shear
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.sound_speed_ref_shear
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.sound_speed_compression
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.sound_speed_ref_compression
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.alpha_coeff_compression
+
+    with pytest.raises(NotImplementedError, match="Elastic simulation"):
+        _ = medium.alpha_coeff_shear
+
+
+def test_is_defined_method():
+    """Test is_defined method with various scenarios"""
+    medium = kWaveMedium(
+        sound_speed=1500,
+        density=1000,
+        alpha_coeff=0.75
+    )
+
+    # Test single field
+    assert medium.is_defined('sound_speed') == [True]
+    assert medium.is_defined('density') == [True]
+    assert medium.is_defined('alpha_coeff') == [True]
+    assert medium.is_defined('alpha_power') == [False]
+    assert medium.is_defined('BonA') == [False]
+
+    # Test multiple fields
+    result = medium.is_defined('sound_speed', 'density', 'alpha_power', 'BonA')
+    assert result == [True, True, False, False]
+
+
+def test_ensure_defined_method():
+    """Test ensure_defined method"""
+    medium = kWaveMedium(sound_speed=1500, density=1000)
+
+    # Test defined fields
+    medium.ensure_defined('sound_speed', 'density')  # Should not raise exception
+
+    # Test undefined fields
+    with pytest.raises(AssertionError, match="alpha_coeff must not be None"):
+        medium.ensure_defined('alpha_coeff')
+
+    with pytest.raises(AssertionError, match="alpha_power must not be None"):
+        medium.ensure_defined('alpha_power')
+
+
+def test_is_nonlinear_method():
+    """Test is_nonlinear method"""
+    # Linear medium
+    medium1 = kWaveMedium(sound_speed=1500)
+    assert not medium1.is_nonlinear()
+
+    # Nonlinear medium
+    medium2 = kWaveMedium(sound_speed=1500, BonA=6.0)
+    assert medium2.is_nonlinear()
+
+
+def test_stokes_mode_alpha_power_none():
+    """Test Stokes mode when alpha_power is None"""
+    medium = kWaveMedium(sound_speed=1500, alpha_coeff=0.75)
+
+    # When alpha_power is None, setting Stokes mode should set it to 2
+    medium.set_absorbing(is_absorbing=True, is_stokes=True)
+    assert medium.alpha_power == 2
+
+
+def test_stokes_mode_alpha_power_array():
+    """Test Stokes mode when alpha_power is an array"""
+    # Test multi-element array
+    medium1 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_power=np.array([1.5, 1.8]))
+
+    with patch('logging.warning') as mock_warning:
+        medium1.set_absorbing(is_absorbing=True, is_stokes=True)
+        mock_warning.assert_called_once()
+        assert "alpha_power = 2" in mock_warning.call_args[0][0]
+
+    assert medium1.alpha_power == 2
+
+
+def test_absorbing_without_stokes_alpha_power_validation():
+    """Test alpha_power validation in non-Stokes absorbing mode"""
+    # Test alpha_power must be scalar
+    medium1 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_power=np.array([1.5, 1.8]))
+
+    with pytest.raises(AssertionError, match="must be scalar"):
+        medium1.set_absorbing(is_absorbing=True, is_stokes=False)
+
+    # Test alpha_power must be in range 0-3
+    medium2 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_power=-0.5)
+
+    with pytest.raises(AssertionError, match="between 0 and 3"):
+        medium2.set_absorbing(is_absorbing=True, is_stokes=False)
+
+    medium3 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_power=3.5)
+
+    with pytest.raises(AssertionError, match="between 0 and 3"):
+        medium3.set_absorbing(is_absorbing=True, is_stokes=False)
+
+
+def test_alpha_mode_validation_edge_cases():
+    """Test alpha_mode validation edge cases"""
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+
+    # Test None value (should pass)
+    medium1 = kWaveMedium(sound_speed=1500, alpha_mode=None)
+    medium1.check_fields(kgrid.N)  # Should not raise exception
+
+    # Test empty string (should fail)
+    medium2 = kWaveMedium(sound_speed=1500, alpha_mode="")
+    with pytest.raises(AssertionError):
+        medium2.check_fields(kgrid.N)
+
+
+def test_alpha_filter_none():
+    """Test when alpha_filter is None"""
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+
+    medium = kWaveMedium(sound_speed=1500, alpha_filter=None)
+    medium.check_fields(kgrid.N)  # Should not raise exception
+
+
+def test_alpha_sign_none():
+    """Test when alpha_sign is None"""
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+
+    medium = kWaveMedium(sound_speed=1500, alpha_sign=None)
+    medium.check_fields(kgrid.N)  # Should not raise exception
+
+def test_alpha_sign_wrong_size_raises():
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+    medium = kWaveMedium(sound_speed=1500, alpha_sign=np.array([1.0]))
+    with pytest.raises(ValueError, match="2 element numeric array"):
+        medium.check_fields(kgrid.N)
+
+def test_alpha_sign_non_numeric_raises():
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+    medium = kWaveMedium(sound_speed=1500, alpha_sign=np.array(["a", "b"], dtype=object))
+    with pytest.raises(ValueError, match="2 element numeric array"):
+        medium.check_fields(kgrid.N)
+
+def test_alpha_coeff_none():
+    """Test when alpha_coeff is None"""
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+
+    medium = kWaveMedium(sound_speed=1500, alpha_coeff=None)
+    medium.check_fields(kgrid.N)  # Should not raise exception
+
+
+def test_alpha_coeff_array_validation():
+    """Test alpha_coeff array validation"""
+    kgrid = kWaveGrid(Vector([64, 64]), Vector([0.1e-3, 0.1e-3]))
+
+    # Valid array
+    medium1 = kWaveMedium(sound_speed=1500, alpha_coeff=np.array([0.5, 0.6, 0.7]))
+    medium1.check_fields(kgrid.N)  # Should not raise exception
+
+    # Array with negative values
+    medium2 = kWaveMedium(sound_speed=1500, alpha_coeff=np.array([0.5, -0.1, 0.7]))
+    with pytest.raises(ValueError, match="non-negative and real"):
+        medium2.check_fields(kgrid.N)
+
+    # Array with complex values
+    medium3 = kWaveMedium(sound_speed=1500, alpha_coeff=np.array([0.5, 0.6 + 0.1j, 0.7]))
+    with pytest.raises(ValueError, match="non-negative and real"):
+        medium3.check_fields(kgrid.N)
+
+
+def test_post_init_sound_speed_conversion():
+    """Test sound_speed conversion in __post_init__"""
+    # Scalar input
+    medium1 = kWaveMedium(sound_speed=1500)
+    assert isinstance(medium1.sound_speed, np.ndarray)
+    assert medium1.sound_speed.shape == (1,)
+
+    # Array input
+    medium2 = kWaveMedium(sound_speed=np.array([1500, 1600]))
+    assert isinstance(medium2.sound_speed, np.ndarray)
+    assert medium2.sound_speed.shape == (2,)
+
+
+def test_stokes_mode_alpha_mode_restrictions():
+    """Test alpha_mode restrictions in Stokes mode"""
+    # Test no_absorption mode
+    medium1 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_mode='no_absorption')
+    with pytest.raises(NotImplementedError, match="not supported with the axisymmetric code"):
+        medium1.set_absorbing(is_absorbing=True, is_stokes=True)
+
+    # Test no_dispersion mode
+    medium2 = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_mode='no_dispersion')
+    with pytest.raises(NotImplementedError, match="not supported with the axisymmetric code"):
+        medium2.set_absorbing(is_absorbing=True, is_stokes=True)
+
+
+def test_absorbing_flags():
+    """Test setting of absorbing and stokes flags"""
+    medium = kWaveMedium(sound_speed=1500, alpha_coeff=0.75, alpha_power=1.5)
+
+    # Initial state
+    assert not medium.absorbing
+    assert not medium.stokes
+
+    # Set to non-Stokes absorbing
+    medium.set_absorbing(is_absorbing=True, is_stokes=False)
+    assert medium.absorbing
+    assert not medium.stokes
+
+    # Reset
+    medium.absorbing = False
+    medium.stokes = False
+
+    # Set to Stokes absorbing
+    medium.set_absorbing(is_absorbing=True, is_stokes=True)
+    assert medium.absorbing
+    assert medium.stokes
+
+    # Set to non-absorbing
+    medium.set_absorbing(is_absorbing=False, is_stokes=False)
+    assert not medium.absorbing
+    assert not medium.stokes