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from __future__ import division
import unittest
import numpy as np
import meep as mp
## Farady rotation rate for gyrotropic Lorentzian medium
def kgyro_lorentzian(freq, epsn, f0, gamma, sigma, b0):
dfsq = (f0**2 - 1j*freq*gamma - freq**2)
eperp = epsn + sigma * f0**2 * dfsq / (dfsq**2 - (freq*b0)**2)
eta = sigma * f0**2 * freq * b0 / (dfsq**2 - (freq*b0)**2)
return 2*np.pi*freq * np.sqrt(0.5*(eperp - np.sqrt(eperp**2 - eta**2)))
## Farady rotation rate for gyrotropic Drude medium
def kgyro_drude(freq, epsn, f0, gamma, sigma, b0):
dfsq = - 1j*freq*gamma - freq**2
eperp = epsn + sigma * f0**2 * dfsq / (dfsq**2 - (freq*b0)**2)
eta = sigma * f0**2 * freq * b0 / (dfsq**2 - (freq*b0)**2)
return 2*np.pi*freq * np.sqrt(0.5*(eperp - np.sqrt(eperp**2 - eta**2)))
## Farady rotation rate for Landau-Lifshitz-Gilbert medium
def kgyro_llg(freq, epsn, f0, gamma, sigma, alpha):
df1 = f0 - 1j*freq*alpha
df2 = freq + 1j*gamma
eperp = epsn + sigma * df1/(df1**2 - df2**2)
eta = sigma * df2 / (df1**2 - df2**2)
return 2*np.pi*freq * np.sqrt(0.5*(eperp - np.sqrt(eperp**2 - eta**2)))
class TestFaradayRotation(unittest.TestCase):
## Simulate a linearly polarized plane wave traveling along the gyrotropy axis.
## Extract Faraday rotation angle by comparing the Ex and Ey amplitudes, and
## compare to a theoretical result corresponding to rotation rate KPRED.
## The default acceptable tolerance TOL is 1.5 degrees.
def check_rotation(self, mat, L, fsrc, zsrc, resolution, tmax, zout, kpred, tol=1.5):
cell = mp.Vector3(0, 0, L)
pml_layers = [mp.PML(thickness=1.0, direction=mp.Z)]
sources = [mp.Source(mp.ContinuousSource(frequency=fsrc),
component=mp.Ex, center=mp.Vector3(0, 0, zsrc))]
self.sim = mp.Simulation(cell_size=cell, geometry=[], sources=sources,
boundary_layers=pml_layers,
default_material=mat, resolution=resolution)
record_Ex, record_Ey, record_t = [], [], []
def record_ex_ey(sim):
record_Ex.append(sim.get_field_point(mp.Ex, mp.Vector3(0, 0, zout)))
record_Ey.append(sim.get_field_point(mp.Ey, mp.Vector3(0, 0, zout)))
record_t.append(sim.meep_time())
self.sim.run(mp.after_time(0.5*tmax, mp.at_every(1e-6, record_ex_ey)), until=tmax)
ex_rel = np.amax(abs(np.fft.fft(record_Ex)))
ey_rel = np.amax(abs(np.fft.fft(record_Ey)))
result = np.arctan2(ey_rel, ex_rel) * 180/np.pi
Ex_theory = np.abs(np.cos(kpred * (zout - zsrc)).real)
Ey_theory = np.abs(np.sin(kpred * (zout - zsrc)).real)
expected = np.arctan2(Ey_theory, Ex_theory) * 180/np.pi
print("Rotation angle (in degrees): {}, expected {}\n".format(result, expected))
np.testing.assert_allclose(expected, result, atol=tol)
def test_faraday_rotation(self):
L, zsrc, zout = 12.0, -4.5, 4.0
freq, tmax = 0.8, 100.0
resolution = 24
## Test gyrotropic Lorentzian medium
epsn, f0, gamma, sn, b0 = 1.5, 1.0, 1e-3, 0.1, 0.15
susc = [mp.GyrotropicLorentzianSusceptibility(frequency=f0, gamma=gamma, sigma=sn,
bias=mp.Vector3(0, 0, b0))]
mat = mp.Medium(epsilon=epsn, mu=1, E_susceptibilities=susc)
k = kgyro_lorentzian(freq, epsn, f0, gamma, sn, b0)
print('=' * 24)
print("Testing Faraday rotation for gyrotropic Lorentzian model...")
self.check_rotation(mat, L, freq, zsrc, resolution, tmax, zout, k)
## Test gyrotropic Drude medium
susc = [mp.GyrotropicDrudeSusceptibility(frequency=f0, gamma=gamma, sigma=sn,
bias=mp.Vector3(0, 0, b0))]
mat = mp.Medium(epsilon=epsn, mu=1, E_susceptibilities=susc)
k = kgyro_drude(freq, epsn, f0, gamma, sn, b0)
print('=' * 24)
print("Testing Faraday rotation for gyrotropic Drude model...")
self.check_rotation(mat, L, freq, zsrc, resolution, tmax, zout, k)
## Test Landau-Lifshitz-Gilbert medium
alpha = 1e-5
susc = [mp.GyrotropicSaturatedSusceptibility(frequency=f0, gamma=gamma, sigma=sn,
alpha=alpha,
bias=mp.Vector3(0, 0, 1.0))]
mat = mp.Medium(epsilon=epsn, mu=1, E_susceptibilities=susc)
k = kgyro_llg(freq, epsn, f0, gamma, sn, alpha)
print('=' * 24)
print("Testing Faraday rotation for Landau-Lifshitz-Gilbert model...")
self.check_rotation(mat, L, freq, zsrc, resolution, tmax, zout, k)
if __name__ == '__main__':
unittest.main()
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