"""
Electric and magnetic field calculations.
Only e_far has been verified to work.
"""
import numpy as np
from miepython.vsh import M_odd_array, N_even_array
from miepython.util import cartesian_to_spherical, spherical_vector_to_cartesian
import miepython as mie
__all__ = ("e_near", "e_plane", "e_far")
[docs]
def e_far(lambda0, d_sphere, m_sphere, r, theta, phi):
"""
Calculate the electric field in the far field.
Args:
lambda0 (float): Wavelength the incident wave in vacuum.
d_sphere (float): Diameter of the sphere.
m_sphere (complex): Rrefractive index of the sphere
r (float): Radial distance at which the field is evaluated.
theta (float): Scattering angle (from z-axis) in radians.
phi (float): Azimuthal angle (from x-axis) in radians.
norm: type of normalization to use for scattering function
Returns:
tuple: Electric field components (E_r, E_theta, E_phi).
"""
x = np.pi * d_sphere / lambda0
jkr = 1j * 2 * np.pi * r / lambda0
amp = np.exp(jkr) / (-jkr)
S1, S2 = mie.S1_S2(m_sphere, x, np.cos(theta), norm="wiscombe")
E_r = np.zeros_like(S1, dtype=complex)
E_theta = S2 * amp * np.cos(phi)
E_phi = S1 * amp * np.sin(phi)
E_theta = np.conjugate(-E_theta)
E_phi = np.conjugate(-E_phi)
return np.array([E_r, E_theta, E_phi])
# def e_far_old(lambda0, d_sphere, m_sphere, r, theta, phi):
# """
# Calculate the electric field in the far field.
#
# Args:
# lambda0 (float): Wavelength the incident wave in vacuum.
# d_sphere (float): Diameter of the sphere.
# m_sphere (complex): Rrefractive index of the sphere
# r (float): Radial distance at which the field is evaluated.
# theta (float): Scattering angle (from z-axis) in radians.
# phi (float): Azimuthal angle (from x-axis) in radians.
# norm: type of normalization to use for scattering function
#
# Returns:
# tuple: Electric field components (E_r, E_theta, E_phi).
# """
# x = np.pi * d_sphere / lambda0
# jkr = 1j * 2 * np.pi * r / lambda0
# amp = np.exp(jkr) / (-jkr)
# mu = np.cos(theta)
#
# a, b = mie._an_bn(m_sphere, x, 0)
# N = len(a)
# pi = np.zeros(N)
# tau = np.zeros(N)
#
# n = np.arange(1, N + 1)
# scale = (2 * n + 1) / ((n + 1) * n)
#
# mie._pi_tau(mu, pi, tau)
#
# E_r = complex(0)
# E_theta = np.sum(scale * (tau * a + pi * b)) * amp * np.cos(phi)
# E_phi = np.sum(scale * (pi * a + tau * b)) * amp * np.sin(phi)
# return np.array([E_r, E_theta, E_phi])
#
#
# def e_near_old(abcd, lambda0, d_sphere, m_index, r, theta, phi):
# """
# Calculate the electric field in and around a sphere.
#
# Args:
# abcd (array): Mie coefficients [a, b, c, d]
# lambda0 (float): Wavelength of the incident wave in vacuum.
# d_sphere (float): Diameter of the sphere.
# m_index (complex): refractive index at r
# r (float): Radial distance at which the field is evaluated.
# theta (float): Polar angle in radians.
# phi (float): Azimuthal angle in radians.
#
# Returns:
# tuple: Electric field components (E_r, E_theta, E_phi).
# """
# a, b, c, d = abcd
# E_r = np.complex128(0)
# E_theta = np.complex128(0)
# E_phi = np.complex128(0)
#
# N = len(a)
# nn = np.arange(1, N + 1)
# scale = 1j**nn * (2 * nn + 1) / ((nn + 1) * nn)
#
# inside = r < d_sphere / 2
#
# for n in nn:
# Mn = M_odd(n, lambda0, d_sphere, m_index, r, theta, phi)
# Nn = N_even(n, lambda0, d_sphere, m_index, r, theta, phi)
#
# if inside:
# E_r += scale[n - 1] * (c[n - 1] * Mn[0] - 1j * d[n - 1] * Nn[0])
# E_theta += scale[n - 1] * (c[n - 1] * Mn[1] - 1j * d[n - 1] * Nn[1])
# E_phi += scale[n - 1] * (c[n - 1] * Mn[2] - 1j * d[n - 1] * Nn[2])
# else:
# E_r += scale[n - 1] * (1j * a[n - 1] * Nn[0] - b[n - 1] * Mn[0])
# th_part = scale[n - 1] * (1j * a[n - 1] * Nn[1] - b[n - 1] * Mn[1])
# E_theta += th_part
# E_phi += -scale[n - 1] * (1j * a[n - 1] * Nn[2] - b[n - 1] * Mn[2])
#
# return np.array([E_r, E_theta, E_phi])
[docs]
def e_near(abcd, lambda0, d_sphere, m_index, r, theta, phi):
"""
Calculate the electric field in and around a sphere.
Args:
abcd (array): Mie coefficients [a, b, c, d]
lambda0 (float): Wavelength of the incident wave in vacuum.
d_sphere (float): Diameter of the sphere.
m_index (complex): refractive index at r
r (float): Radial distance at which the field is evaluated.
theta (float): Polar angle in radians.
phi (float): Azimuthal angle in radians.
Returns:
tuple: Electric field components (E_r, E_theta, E_phi).
"""
a, b, c, d = abcd
N = len(a)
nn = np.arange(1, N + 1)
scale = 1j**nn * (2 * nn + 1) / ((nn + 1) * nn)
M_rad, M_the, M_phi = M_odd_array(N, lambda0, d_sphere, m_index, r, theta, phi)
N_rad, N_the, N_phi = N_even_array(N, lambda0, d_sphere, m_index, r, theta, phi)
if r < d_sphere / 2:
E_rad = np.sum(scale * (c * M_rad - 1j * d * N_rad))
E_the = np.sum(scale * (c * M_the - 1j * d * N_the))
E_phi = np.sum(scale * (c * M_phi - 1j * d * N_phi))
else:
E_rad = np.sum(scale * (1j * a * N_rad - b * M_rad))
E_the = np.sum(scale * (1j * a * N_the - b * M_the))
E_phi = np.sum(scale * (1j * a * N_phi - b * M_phi))
return np.array([E_rad, E_the, -E_phi])
[docs]
def e_plane(x, y, z, N=100):
"""
Calculate a plane wave using vector spherical harmonics.
Args:
x: position
y: position
z: position
N: number of points
Returns:
tuple: Electric field components (E_z, E_y, E_z).
"""
lambda0 = 1
m_index = 1
n = np.arange(1, N + 1)
scale = (1j) ** n * (2 * n + 1) / n / (n + 1)
r, theta, phi = cartesian_to_spherical(x, y, z)
d_sphere = 3 * r
M_r, M_theta, M_phi = M_odd_array(N, lambda0, d_sphere, m_index, r, theta, phi)
N_r, N_theta, N_phi = N_even_array(N, lambda0, d_sphere, m_index, r, theta, phi)
E_r = np.sum(scale * (M_r - 1j * N_r))
E_theta = np.sum(scale * (M_theta - 1j * N_theta))
E_phi = np.sum(scale * (M_phi - 1j * N_phi))
Ex, Ey, Ez = spherical_vector_to_cartesian(E_r, E_theta, E_phi, r, theta, phi)
return Ex, Ey, Ez