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# From the Meep tutorial: plotting Faraday rotation of a linearly polarized plane wave
import meep as mp
## Parameters for a gyrotropic Lorentzian medium
epsn = 1.5 # background permittivity
f0 = 1.0 # natural frequency
gamma = 1e-6 # damping rate
sn = 0.1 # sigma parameter
b0 = 0.15 # magnitude of bias vector
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)
## Set up and run the Meep simulation:
tmax = 100
L = 20.0
cell = mp.Vector3(0, 0, L)
fsrc, src_z = 0.8, -8.5
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, src_z),
)
]
sim = mp.Simulation(
cell_size=cell,
geometry=[],
sources=sources,
boundary_layers=pml_layers,
default_material=mat,
resolution=50,
)
sim.run(until=tmax)
import matplotlib.pyplot as plt
## Plot results:
import numpy as np
ex_data = sim.get_efield_x().real
ey_data = sim.get_efield_y().real
z = np.linspace(-L / 2, L / 2, len(ex_data))
plt.figure(1)
plt.plot(z, ex_data, label="Ex")
plt.plot(z, ey_data, label="Ey")
plt.xlim(-L / 2, L / 2)
plt.xlabel("z")
plt.legend()
## Comparison with analytic result:
dfsq = f0**2 - 1j * fsrc * gamma - fsrc**2
eperp = epsn + sn * f0**2 * dfsq / (dfsq**2 - (fsrc * b0) ** 2)
eta = sn * f0**2 * fsrc * b0 / (dfsq**2 - (fsrc * b0) ** 2)
k_gyro = 2 * np.pi * fsrc * np.sqrt(0.5 * (eperp - np.sqrt(eperp**2 - eta**2)))
Ex_theory = 0.37 * np.cos(k_gyro * (z - src_z)).real
Ey_theory = 0.37 * np.sin(k_gyro * (z - src_z)).real
plt.figure(2)
plt.subplot(2, 1, 1)
plt.plot(z, ex_data, label="Ex (MEEP)")
plt.plot(z, Ex_theory, "k--")
plt.plot(z, -Ex_theory, "k--", label="Ex envelope (theory)")
plt.xlim(-L / 2, L / 2)
plt.xlabel("z")
plt.legend(loc="lower right")
plt.subplot(2, 1, 2)
plt.plot(z, ey_data, label="Ey (MEEP)")
plt.plot(z, Ey_theory, "k--")
plt.plot(z, -Ey_theory, "k--", label="Ey envelope (theory)")
plt.xlim(-L / 2, L / 2)
plt.xlabel("z")
plt.legend(loc="lower right")
plt.tight_layout()
plt.show()
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