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Fix Lorentz model and harmonic convention #125

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Merged
merged 1 commit into from
Jan 20, 2022
Merged

Fix Lorentz model and harmonic convention #125

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13 changes: 10 additions & 3 deletions tests/test_components.py
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Original file line number Diff line number Diff line change
Expand Up @@ -221,24 +221,30 @@ def test_medium_dispersion():
m_PR = PoleResidue(eps_inf=1.0, poles=[(1 + 2j, 1 + 3j), (2 + 4j, 1 + 5j)])
m_SM = Sellmeier(coeffs=[(2, 3), (2, 4)])
m_LZ = Lorentz(eps_inf=1.0, coeffs=[(1, 3, 2), (2, 4, 1)])
m_LZ2 = Lorentz(eps_inf=1.0, coeffs=[(1, 2, 3), (2, 1, 4)])
m_DR = Drude(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])
m_DB = Debye(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])

freqs = np.linspace(0.01, 1, 1001)
for medium in [m_PR, m_SM, m_LZ, m_DR, m_DB]:
for medium in [m_PR, m_SM, m_LZ, m_LZ2, m_DR, m_DB]:
eps_c = medium.eps_model(freqs)

for medium in [m_SM, m_LZ, m_LZ2, m_DR, m_DB]:
eps_c = medium.eps_model(freqs)
assert np.all(eps_c.imag >= 0)


def test_medium_dispersion_conversion():

m_PR = PoleResidue(eps_inf=1.0, poles=[((1 + 2j), (1 + 3j)), ((2 + 4j), (1 + 5j))])
m_SM = Sellmeier(coeffs=[(2, 3), (2, 4)])
m_LZ = Lorentz(eps_inf=1.0, coeffs=[(1, 3, 2), (2, 4, 1)])
m_LZ2 = Lorentz(eps_inf=1.0, coeffs=[(1, 2, 3), (2, 1, 4)])
m_DR = Drude(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])
m_DB = Debye(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])

freqs = np.linspace(0.01, 1, 1001)
for medium in [m_PR, m_SM, m_DB, m_LZ, m_DR]: # , m_DB]:
for medium in [m_PR, m_SM, m_DB, m_LZ, m_DR, m_LZ2]: # , m_DB]:
eps_model = medium.eps_model(freqs)
eps_pr = medium.pole_residue.eps_model(freqs)
np.testing.assert_allclose(eps_model, eps_pr)
Expand All @@ -249,10 +255,11 @@ def test_medium_dispersion_create():
m_PR = PoleResidue(eps_inf=1.0, poles=[((1 + 2j), (1 + 3j)), ((2 + 4j), (1 + 5j))])
m_SM = Sellmeier(coeffs=[(2, 3), (2, 4)])
m_LZ = Lorentz(eps_inf=1.0, coeffs=[(1, 3, 2), (2, 4, 1)])
m_LZ2 = Lorentz(eps_inf=1.0, coeffs=[(1, 2, 3), (2, 1, 4)])
m_DR = Drude(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])
m_DB = Debye(eps_inf=1.0, coeffs=[(1, 3), (2, 4)])

for medium in [m_PR, m_SM, m_DB, m_LZ, m_DR]:
for medium in [m_PR, m_SM, m_DB, m_LZ, m_DR, m_LZ2]:
struct = Structure(geometry=Box(size=(1, 1, 1)), medium=medium)


Expand Down
36 changes: 20 additions & 16 deletions tidy3d/components/medium.py
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Original file line number Diff line number Diff line change
Expand Up @@ -597,7 +597,7 @@ class Lorentz(DispersiveMedium):

.. math::
\\epsilon(f) = \\epsilon_\\infty + \\sum_i
\\frac{\\Delta\\epsilon_i f_i^2}{f_i^2 + 2jf\\delta_i - f^2}
\\frac{\\Delta\\epsilon_i f_i^2}{f_i^2 - 2jf\\delta_i - f^2}

where :math:`f, f_i, \\delta_i` are in Hz.

Expand Down Expand Up @@ -639,7 +639,7 @@ def eps_model(self, frequency: float) -> complex:
"""
eps = self.eps_inf + 0.0j
for (de, f, delta) in self.coeffs:
eps += (de * f ** 2) / (f ** 2 + 2j * frequency * delta - frequency ** 2)
eps += (de * f ** 2) / (f ** 2 - 2j * frequency * delta - frequency ** 2)
return eps

@property
Expand All @@ -653,14 +653,18 @@ def pole_residue(self):
d = 2 * np.pi * delta

if d > w:
r = 1j * np.sqrt(d * d - w * w)
r = np.sqrt(d * d - w * w) + 0j
a0 = -d + r
c0 = de * w ** 2 / 4 / r
a1 = -d - r
c1 = -c0
poles.append((a0, c0))
poles.append((a1, c1))
else:
r = np.sqrt(w * w - d * d)

a = d - 1j * r
c = 1j * de * w ** 2 / 2 / r

poles.append((a, c))
a = -d - 1j * r
c = 1j * de * w ** 2 / 2 / r
poles.append((a, c))

return PoleResidue(
eps_inf=self.eps_inf,
Expand All @@ -676,7 +680,7 @@ class Drude(DispersiveMedium):

.. math::
\\epsilon(f) = \\epsilon_\\infty - \\sum_i
\\frac{ f_i^2}{f^2 - jf\\delta_i}
\\frac{ f_i^2}{f^2 + jf\\delta_i}

where :math:`f, f_i, \\delta_i` are in Hz.

Expand Down Expand Up @@ -718,7 +722,7 @@ def eps_model(self, frequency: float) -> complex:
"""
eps = self.eps_inf + 0.0j
for (f, delta) in self.coeffs:
eps -= (f ** 2) / (frequency ** 2 - 1j * frequency * delta)
eps -= (f ** 2) / (frequency ** 2 + 1j * frequency * delta)
return eps

@property
Expand All @@ -731,11 +735,11 @@ def pole_residue(self):
w = 2 * np.pi * f
d = 2 * np.pi * delta

c0 = -(w ** 2) / 2 / d + 0j
c0 = (w ** 2) / 2 / d + 0j
a0 = 0j

c1 = w ** 2 / 2 / d + 0j
a1 = d + 0j
c1 = -c0
a1 = -d + 0j

poles.append((a0, c0))
poles.append((a1, c1))
Expand All @@ -754,7 +758,7 @@ class Debye(DispersiveMedium):

.. math::
\\epsilon(f) = \\epsilon_\\infty + \\sum_i
\\frac{\\Delta\\epsilon_i}{1 + jf\\tau_i}
\\frac{\\Delta\\epsilon_i}{1 - jf\\tau_i}

where :math:`f` is in Hz, and :math:`\\tau_i` is in seconds.

Expand Down Expand Up @@ -796,7 +800,7 @@ def eps_model(self, frequency: float) -> complex:
"""
eps = self.eps_inf + 0.0j
for (de, tau) in self.coeffs:
eps += de / (1 + 1j * frequency * tau)
eps += de / (1 - 1j * frequency * tau)
return eps

@property
Expand All @@ -805,7 +809,7 @@ def pole_residue(self):

poles = []
for (de, tau) in self.coeffs:
a = 2 * np.pi / tau + 0j
a = -2 * np.pi / tau + 0j
c = -0.5 * de * a
poles.append((a, c))

Expand Down