def H_field_from_particle(self, i, x, y, z, source=True):
"""Compute the magnetic field around particle i
Arguments:
i particle number
x x position (array-like)
y y position (array-like)
z z position (array-like)
source Include the source field (bool, default=True)
Returns: H[3,...]
"""
rad, theta, phi = miepy.coordinates.cart_to_sph(
x, y, z, origin=self.position[i])
H_sph = miepy.expand_H(self.p_scat[i],
self.material_data.k_b,
mode=miepy.vsh_mode.outgoing,
eps=self.material_data.eps_b,
mu=self.material_data.mu_b)(rad, theta, phi)
Hscat = miepy.coordinates.vec_sph_to_cart(H_sph, theta, phi)
p = self.p_inc[i]
if not source:
p -= self.p_src[i]
H_sph = miepy.expand_H(p,
self.material_data.k_b,
mode=miepy.vsh_mode.incident,
eps=self.material_data.eps_b,
mu=self.material_data.mu_b)(rad, theta, phi)
Hinc = miepy.coordinates.vec_sph_to_cart(H_sph, theta, phi)
return Hscat + Hinc
def test_power_2d_integration(self):
"""power by integrating Poynting vector in 2D plane"""
lmax = 6
p_src = self.source.structure([0, 0, 0], k, lmax)
a = 3000 * nm
x = np.linspace(-a, a, 20)
y = np.linspace(-a, a, 20)
X, Y = np.meshgrid(x, y)
R, THETA, PHI = miepy.coordinates.cart_to_sph(X, Y, 0)
Efunc = miepy.expand_E(p_src, k, miepy.vsh_mode.incident)
Hfunc = miepy.expand_H(p_src, k, miepy.vsh_mode.incident, 1, 1)
E = Efunc(R, THETA, PHI)
H = Hfunc(R, THETA, PHI)
E = miepy.coordinates.vec_sph_to_cart(E, THETA, PHI)
H = miepy.coordinates.vec_sph_to_cart(H, THETA, PHI) / Z0
S = 0.5 * np.linalg.norm(np.cross(E, np.conjugate(H), axis=0), axis=0)
S = 0.5 * np.cross(E, np.conjugate(H), axis=0)[2]
# S = 0.5*np.sum(np.abs(E)**2, axis=0)
P = trapz_2d(x, y, S).real
assert np.allclose(P, self.power, rtol=.04)
def H_field(self,
x1,
x2,
x3,
interior=True,
source=True,
mask=False,
far=False,
spherical=False):
"""Compute the magnetic field due to all particles
Arguments:
x1 x/r position (array-like)
x2 y/theta position (array-like)
x3 z/phi position (array-like)
interior (optional) compute interior fields (bool, default=True)
source (optional) include the source field (bool, default=True)
mask (optional) set interior fields to 0 (bool, default=False)
far (optional) use expressions valid only for far-field (bool, default=False)
spherical (optional) input/output in spherical coordinates (bool, default=False)
Returns: H[3,...]
"""
x1, x2, x3 = (np.asarray(x) for x in (x1, x2, x3))
shape = max(*[x.shape for x in (x1, x2, x3)], key=len)
H = np.zeros((3, ) + shape, dtype=complex)
if spherical:
(x, y, z) = miepy.coordinates.sph_to_cart(x1,
x2,
x3,
origin=self.origin)
else:
(x, y, z) = (x1, x2, x3)
if far:
expand = miepy.expand_H_far
else:
expand = partial(miepy.expand_H, mode=miepy.vsh_mode.outgoing)
for i in range(self.Nparticles):
rad, theta, phi = miepy.coordinates.cart_to_sph(
x, y, z, origin=self.position[i])
H_sph = expand(self.p_scat[i],
self.material_data.k_b,
eps=self.material_data.eps_b,
mu=self.material_data.mu_b)(rad, theta, phi)
H += miepy.coordinates.vec_sph_to_cart(H_sph, theta, phi)
if source:
H += self.H_source(x, y, z, far=far, spherical=False)
#TODO: what if x is scalar...
if interior and not mask and not far:
for i in range(self.Nparticles):
x0, y0, z0 = self.position[i]
idx = ((x - x0)**2 + (y - y0)**2 +
(z - z0)**2 < self.particles[i].enclosed_radius()**2)
k_int = 2 * np.pi * self.material_data.n[i] / self.wavelength
rad, theta, phi = miepy.coordinates.cart_to_sph(
x, y, z, origin=self.position[i])
H_sph = miepy.expand_H(self.p_int[i],
k_int,
eps=self.material_data.eps[i],
mu=self.material_data.mu[i],
mode=miepy.vsh_mode.interior)(
rad[idx], theta[idx], phi[idx])
H[:, idx] = miepy.coordinates.vec_sph_to_cart(
H_sph, theta[idx], phi[idx])
if mask and not far:
for i in range(self.Nparticles):
x0, y0, z0 = self.position[i]
idx = ((x - x0)**2 + (y - y0)**2 +
(z - z0)**2 < self.particles[i].enclosed_radius()**2)
H[:, idx] = 0
#TODO: does this depend on the origin?
if spherical:
H = miepy.coordinates.vec_cart_to_sph(H, theta=x2, phi=x3)
return H