def test_index_matched_interface(source, rtol):
"""
An interface that is index-matched with the medium is identical to not having an interface (cross-section comparison)
"""
interface = miepy.interface(medium, z=zpos)
cluster = miepy.sphere_cluster(position=[0, 0, 0],
radius=radius,
material=material,
medium=medium,
lmax=2,
source=source,
interface=interface,
wavelength=wavelength)
C1 = np.array(cluster.cross_sections())
cluster = miepy.sphere_cluster(position=[0, 0, 0],
radius=radius,
material=material,
medium=medium,
lmax=2,
source=source,
wavelength=wavelength)
C2 = np.array(cluster.cross_sections())
assert np.allclose(C1, C2, atol=0, rtol=1e-15)
def test_interface_z_translation(s1, s2, rtol):
"""
Moving the source and particle is identical to moving the interface (cross-section comparison)
"""
interface = miepy.interface(miepy.constant_material(index=1.7))
cluster = miepy.sphere_cluster(position=[0, 0, -zpos],
radius=radius,
material=material,
medium=medium,
lmax=2,
source=s1,
interface=interface,
wavelength=wavelength)
C1 = np.array(cluster.cross_sections())
interface = miepy.interface(miepy.constant_material(index=1.7), z=zpos)
cluster = miepy.sphere_cluster(position=[0, 0, 0],
radius=radius,
material=material,
medium=medium,
lmax=2,
source=s2,
interface=interface,
wavelength=wavelength)
C2 = np.array(cluster.cross_sections())
assert np.allclose(C1, C2, atol=0, rtol=rtol)
def test_medium_scaling_force(plot=False):
"""ensure that the radiation pressure on a single sphere scales with
background index as n^5 for small, high-index sphere"""
n_b = np.linspace(1, 5, 10)
F = np.zeros_like(n_b)
for i, n in enumerate(n_b):
sphere = miepy.sphere_cluster(
position=[0, 0, 0],
radius=2 * nm,
material=miepy.constant_material(40**2),
medium=miepy.constant_material(n**2),
source=miepy.sources.plane_wave.from_string(polarization='x'),
wavelength=2800 * nm,
lmax=2)
F[i] = sphere.force_on_particle(0)[2]
F_fit = np.max(F) * (n_b / np.max(n_b))**5
if not plot:
L2 = np.linalg.norm(F - F_fit) / F.shape[0]
avg = np.average(F + F_fit) / 2
print(L2, avg)
assert L2 < 1e-2 * avg
else:
plt.figure()
plt.plot(n_b, F, label='exact force')
plt.plot(n_b, F_fit, 'o', label='$n_b^5$ scaling')
plt.xlabel('$n_b$')
plt.ylabel('force')
plt.legend()
plt.title(test_medium_scaling_force.__name__, weight='bold')
def test_sphere_cluster_tmatrix_particle():
"""sphere_cluster_particle in miepy.cluster yields the same results as miepy.sphere_cluster"""
L = 155*nm
lmax = 6
cluster = miepy.sphere_cluster(position=[[-L/2, 0,0], [L/2,0,0]],
material=Ag,
radius=75*nm,
source=source,
lmax=lmax,
medium=medium,
wavelength=800*nm)
C1 = cluster.cross_sections()
cluster.solve_cluster_coefficients()
p1 = cluster.p_cluster
particle = miepy.sphere_cluster_particle(cluster.position, cluster.radius, Ag, lmax=lmax)
cluster = miepy.cluster(particles=particle,
source=source,
lmax=lmax,
medium=medium,
wavelength=800*nm)
C2 = cluster.cross_sections()
p2 = cluster.p_scat
assert np.allclose(C1, C2, rtol=7e-4, atol=0), 'equal cross-sections'
assert np.allclose(p1, p2, rtol=1e-2, atol=1e-12), 'equal cluster scattering coefficients'
def test_cross_section_methods_monomer(plot=False):
"""test two cross-section methods for a single particle (monomer)"""
C1 = np.zeros_like(wavelengths)
C2 = np.zeros([len(wavelengths), 2, 2])
for i, wavelength in enumerate(tqdm(wavelengths)):
cluster = miepy.sphere_cluster(
position=[0, 0, 0],
radius=75 * nm,
material=miepy.constant_material(3.7**2),
source=miepy.sources.plane_wave.from_string(polarization='x'),
lmax=2,
wavelength=wavelength)
C1[i] = cluster.cross_sections().scattering
C2[i] = cluster.cross_sections_per_multipole().scattering
C2_sum = np.sum(C2, axis=(1, 2))
if not plot:
L2 = np.linalg.norm(C1 - C2_sum) / C1.shape[0]
avg = np.average(C1 + C2_sum) / 2
print(L2, avg)
assert L2 < 1e-4 * avg
else:
plt.figure()
plt.plot(wavelengths / nm, C1, label='total scattering')
plt.plot(wavelengths / nm, C2_sum, 'o', label='total scattering')
plt.plot(wavelengths / nm, C2[:, 0, 0], label='eD')
plt.plot(wavelengths / nm, C2[:, 1, 0], label='mD')
plt.plot(wavelengths / nm, C2[:, 0, 1], label='eQ')
plt.plot(wavelengths / nm, C2[:, 1, 1], label='mQ')
plt.legend()
def test_boundary_conditions():
"""verifies the continunity of tangential components of E and H at the surface of a particle"""
radius = 50 * nm
cluster = miepy.sphere_cluster(
position=[[0, 0, 0]],
radius=radius,
material=miepy.materials.Ag(),
lmax=2,
wavelength=600 * nm,
source=miepy.sources.plane_wave.from_string(polarization='y'),
medium=miepy.constant_material(1.2**2))
theta = 0.3
phi = 0.3
eps = .1 * nm
E_out = cluster.E_field(radius + eps, theta, phi, spherical=True)
E_in = cluster.E_field(radius - eps, theta, phi, spherical=True)
H_out = cluster.H_field(radius + eps, theta, phi, spherical=True)
H_in = cluster.H_field(radius - eps, theta, phi, spherical=True)
assert np.allclose(E_out[1:], E_in[1:], atol=4e-2, rtol=0)
assert np.allclose(H_out[1:], H_in[1:], atol=4e-2, rtol=0)
def fields():
pos = lattice[:]*600*nm
# pos -= np.average(pos, axis=0)[np.newaxis]
xmax = 100*nm
pos = [[-xmax,-xmax,0], [xmax,xmax,0]]
cluster = miepy.sphere_cluster(position=pos,
radius=75*nm,
material=Ag,
source=source,
wavelength=800*nm,
lmax=lmax,
medium=water)
xmax = 500*nm
x = np.linspace(-xmax, xmax, 250)
y = np.linspace(-xmax, xmax, 250)
X, Y = np.meshgrid(x, y)
Z = np.zeros_like(X)
E = cluster.E_field(X, Y, Z)
Esrc = cluster.E_source(X, Y, Z)
# enhance = np.linalg.norm(E, axis=0)/np.linalg.norm(Esrc, axis=0)
enhance = np.linalg.norm(E, axis=0)**2
return dict(enhance=enhance, X=X, Y=Y, E=E)
def test_cluster_field_near_to_far():
"""
Compare scattered E/H-field of a cluster in far field using near and far field expressions
Expressions are expected to converge in the limit r -> infinity
"""
x = np.linspace(-600 * nm, 600 * nm, 3)
y = np.linspace(-600 * nm, 600 * nm, 3)
cluster = miepy.sphere_cluster(position=[[xv, yv, 0] for xv in x
for yv in y],
radius=100 * nm,
material=miepy.constant_material(index=2),
wavelength=wav,
source=miepy.sources.plane_wave([1, 1]),
lmax=3)
theta = np.linspace(0, np.pi, 5)
phi = np.linspace(0, 2 * np.pi, 5)
THETA, PHI = np.meshgrid(theta, phi)
radius = np.ones_like(THETA)
E1 = cluster.E_field(radius, THETA, PHI, spherical=True, source=False)
E2 = cluster.E_angular(THETA, PHI, radius=radius, source=False)
H1 = cluster.H_field(radius, THETA, PHI, spherical=True, source=False)
H2 = cluster.H_angular(THETA, PHI, radius=radius, source=False)
assert np.allclose(E1[0], 0, atol=1e-10), 'radial component of E goes to 0'
assert np.allclose(E1[1:], E2, atol=0, rtol=1e-6), 'E converges'
assert np.allclose(H1[0], 0, atol=1e-10), 'radial component of H goes to 0'
assert np.allclose(H1[1:], H2, atol=0, rtol=1e-6), 'H converges'
def test_maxwells_equations_cluster_near_field(source):
"""
Verify Maxwell's equations for a cluster at a point in the near field
"""
cluster = miepy.sphere_cluster(position=[[-400 * nm, -200 * nm, 0],
[200 * nm, 200 * nm, 100 * nm]],
radius=100 * nm,
material=miepy.constant_material(index=3.7),
source=source,
wavelength=wav,
lmax=2)
x0, y0, z0 = 0, 0, 0
eps = .1 * nm
x = np.linspace(x0, x0 + eps, 2)
y = np.linspace(y0, y0 + eps, 2)
z = np.linspace(z0, z0 + eps, 2)
X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
E_grid = cluster.E_field(X, Y, Z)
E = np.average(E_grid, axis=(1, 2, 3))
divE = div(E_grid, eps)
curlE = curl(E_grid, eps)
H_grid = cluster.H_field(X, Y, Z, k)
H = np.average(H_grid, axis=(1, 2, 3))
divH = div(H_grid, eps)
curlH = curl(H_grid, eps)
assert np.abs(divE / (k * np.linalg.norm(E))) < 1e-6, 'div(E) = 0'
assert np.abs(divH / (k * np.linalg.norm(H))) < 1e-6, 'div(H) = 0'
assert np.allclose(curlE, 1j * k * H, atol=0, rtol=1e-6), 'curl(E) = ikH'
assert np.allclose(curlH, -1j * k * E, atol=0, rtol=1e-6), 'curl(H) = -ikE'
def test_interactions_off(plot=False):
"""compare extinction of cluster to single Mie extinction with interactions disabled
expect: E(cluster) = N*E(single)
"""
sep = 200 * nm
C1, A1, E1 = [np.zeros_like(wavelengths, dtype=float) for i in range(3)]
for i, wavelength in enumerate(wavelengths):
sol = miepy.sphere_cluster(position=[[sep / 2, 0, 0], [-sep / 2, 0,
0]],
radius=radius,
material=Ag,
source=source,
wavelength=wavelength,
lmax=lmax,
interactions=False)
C1[i], A1[i], E1[i] = sol.cross_sections()
# single
sphere = miepy.single_mie_sphere(radius, Ag, wavelengths, lmax)
Cs, As, Es = sphere.cross_sections()
if not plot:
for a, b, tol in [(E1, 2 * Es, 1e-15)]:
L2 = np.linalg.norm(a - b) / a.shape[0]
avg = np.average(a + b) / 2
print(L2, avg)
assert L2 < tol * avg
else:
fig, ax = plt.subplots()
ax.plot(wavelengths / nm, C1, color='C0', label='scattering (cluster)')
ax.plot(wavelengths / nm, A1, color='C1', label='absorption (cluster)')
ax.plot(wavelengths / nm, E1, color='C2', label='extinction (cluster)')
ax.plot(wavelengths / nm,
2 * Cs,
'o',
color='C0',
label='scattering (N x single)')
ax.plot(wavelengths / nm,
2 * As,
'o',
color='C1',
label='absorption (N x single)')
ax.plot(wavelengths / nm,
2 * Es,
'o',
color='C2',
label='extinction (N x single)')
ax.set(xlabel='wavelength (nm)',
ylabel='cross-section',
title='test_interactions_off')
ax.legend()
def test_off_center_particle(plot=False):
"""make sure scattering by a sphere away from the origin is equal to scattering of a particle at the origin"""
# at the origin
C1, A1, E1, C2, A2, E2 = [
np.zeros_like(wavelengths, dtype=float) for i in range(6)
]
for i, wavelength in enumerate(wavelengths):
sol = miepy.sphere_cluster(position=[0, 0, 0],
radius=radius,
material=Ag,
source=source,
wavelength=wavelength,
lmax=lmax)
C1[i], A1[i], E1[i] = sol.cross_sections()
# displace sphere
sol.update_position([40 * nm, 50 * nm, 60 * nm])
C2[i], A2[i], E2[i] = sol.cross_sections()
if not plot:
for a, b, tol in [(C1, C2, 1e-15), (A1, A2, 1e-14), (E1, E2, 1e-15)]:
L2 = np.linalg.norm(a - b) / a.shape[0]
avg = np.average(a + b) / 2
print(L2, avg)
assert L2 < tol * avg
else:
fig, ax = plt.subplots()
ax.plot(wavelengths / nm, C1, color='C0', label='scattering (origin)')
ax.plot(wavelengths / nm, A1, color='C1', label='absorption (origin)')
ax.plot(wavelengths / nm, E1, color='C2', label='extinction (origin)')
ax.plot(wavelengths / nm,
C2,
'o',
color='C0',
label='scattering (displaced)')
ax.plot(wavelengths / nm,
A2,
'o',
color='C1',
label='absorption (displaced)')
ax.plot(wavelengths / nm,
E2,
'o',
color='C2',
label='extinction (displaced)')
ax.set(xlabel='wavelength (nm)',
ylabel='cross-section',
title='test_off_center_particle')
ax.legend()
def sim():
cluster = miepy.sphere_cluster(position=initial,
radius=radius,
material=Ag,
source=source,
wavelength=wavelength,
medium=water,
lmax=2)
bd = stoked_from_cluster_2d(cluster, dt=dt, temperature=300)
for i in pbar(range(Nsteps)):
if i % 10 == 0:
yield dict(pos=bd.position)
bd.step()
def tests(Nmax, step=1):
Nparticles = np.arange(1, Nmax + 1, step)
t_force, t_flux, t_build, t_solve, t_source = [
np.zeros_like(Nparticles, dtype=float) for i in range(5)
]
for i, N in enumerate(Nparticles):
print(N, Nmax)
# positions = [[n*separation, 0, 0] for n in range(N)]
positions = hexagonal_lattice_particles(N) * separation
mie = miepy.sphere_cluster(position=positions,
radius=radius,
material=Ag,
source=source,
wavelength=600 * nm,
lmax=2)
t_force[i] = time_function(mie.force)
t_flux[i] = time_function(mie.cross_sections)
t_build[i] = time_function(
partial(miepy.interactions.sphere_aggregate_tmatrix, mie.position,
mie.mie_scat, mie.material_data.k_b))
A = miepy.interactions.sphere_aggregate_tmatrix(
mie.position, mie.mie_scat, k=mie.material_data.k_b)
t_solve[i] = time_function(
partial(solve_linear_system,
A,
mie.p_src,
method=miepy.solver.bicgstab))
x = np.linspace(0, N * separation, 1)
y = 2 * radius * np.ones_like(x)
z = np.zeros_like(x)
t_source[i] = time_function(mie._solve_source_decomposition)
fig, ax = plt.subplots()
ax.plot(Nparticles, t_force * 1e3, '-o', label='force')
ax.plot(Nparticles, t_flux * 1e3, '-o', label='flux')
ax.plot(Nparticles, t_build * 1e3, '-o', label='build')
ax.plot(Nparticles, t_solve * 1e3, '-o', label='solve')
ax.plot(Nparticles, t_source * 1e3, '-o', label='source')
ax.legend()
ax.set(xlabel='number of particles', ylabel='runtime (ms)')
plt.show()
def test_maxwells_equations_cluster_far_field(source):
"""
Verify Maxwell's equations for a cluster at a point in the far field
"""
cluster = miepy.sphere_cluster(position=[[-400 * nm, -200 * nm, 0],
[200 * nm, 200 * nm, 100 * nm]],
radius=100 * nm,
material=miepy.constant_material(index=3.7),
source=source,
wavelength=wav,
lmax=2)
x0, y0, z0 = 0, 0, 1
eps = 1 * nm
x = np.linspace(x0, x0 + eps, 2)
y = np.linspace(y0, y0 + eps, 2)
z = np.linspace(z0, z0 + eps, 2)
X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
R, THETA, PHI = miepy.coordinates.cart_to_sph(X, Y, Z)
E_grid = cluster.E_angular(THETA, PHI, radius=R)
E_grid = np.insert(E_grid, 0, 0, axis=0)
E_grid = miepy.coordinates.vec_sph_to_cart(E_grid, THETA, PHI)
E = np.average(E_grid, axis=(1, 2, 3))
divE = div(E_grid, eps)
curlE = curl(E_grid, eps)
H_grid = cluster.H_angular(THETA, PHI, radius=R)
H_grid = np.insert(H_grid, 0, 0, axis=0)
H_grid = miepy.coordinates.vec_sph_to_cart(H_grid, THETA, PHI)
H = np.average(H_grid, axis=(1, 2, 3))
divH = div(H_grid, eps)
curlH = curl(H_grid, eps)
assert np.abs(divE / (k * np.linalg.norm(E))) < 1e-6, 'div(E) = 0'
assert np.abs(divH / (k * np.linalg.norm(H))) < 1e-6, 'div(H) = 0'
assert np.allclose(curlE[:2], 1j * k * H[:2], atol=0,
rtol=1e-5), 'curl(E) = ikH'
assert np.allclose(curlH[:2], -1j * k * E[:2], atol=0,
rtol=1e-5), 'curl(H) = -ikE'
def tests(Nmax, step=1):
Nparticles = np.arange(1, Nmax+1, step)
names = ['build', 'solve', 'flux', 'force']
ftimer = {name: np.zeros_like(Nparticles, dtype=float) for name in names}
for i,N in enumerate(Nparticles):
print(N, Nmax)
positions = [[n*separation, 0, 0] for n in range(N)]
mie = miepy.sphere_cluster(position=positions,
radius=radius,
material=Ag,
source=source,
wavelength=600*nm,
lmax=2)
ftimer['force'][i] = time_function(mie.force)
ftimer['flux'][i] = time_function(mie.cross_sections)
ftimer['build'][i] = time_function(partial(miepy.interactions.sphere_aggregate_tmatrix,
mie.position, mie.mie_scat, mie.material_data.k_b))
A = miepy.interactions.sphere_aggregate_tmatrix(mie.position, mie.mie_scat, k=mie.material_data.k_b)
ftimer['solve'][i] = time_function(partial(solve_linear_system, A, mie.p_src, method=miepy.solver.bicgstab))
return ftimer, Nparticles
def test_tmatrix_sphere_is_sphere(material, atol):
"""tmatrix method with spheres should be equivalent to sphere cluster"""
position = [[-300*nm, 0, 0], [300*nm, 0, 0]]
spheres = miepy.sphere_cluster(position=position,
radius=radius,
material=material,
source=source,
wavelength=wavelength,
lmax=lmax,
medium=medium)
particles = [miepy.sphere(pos, radius, material) for pos in position]
cluster = miepy.cluster(particles=particles,
source=source,
wavelength=wavelength,
lmax=lmax,
medium=medium)
print(np.max(np.abs(spheres.p_inc - cluster.p_inc)))
assert np.allclose(spheres.p_inc, cluster.p_inc, rtol=0, atol=atol)
S, A, E = sphere.cross_sections()
Fz = sphere.radiation_force()
# Generalized Mie Theory (GMT)
source = miepy.sources.plane_wave.from_string(polarization='x')
scat = np.zeros_like(wavelengths)
absorb = np.zeros_like(wavelengths)
extinct = np.zeros_like(wavelengths)
force = np.zeros((3, ) + wavelengths.shape)
for i, wavelength in enumerate(wavelengths):
system = miepy.sphere_cluster(position=[0, 0, 0],
radius=radius,
material=dielectric,
source=source,
wavelength=wavelength,
lmax=lmax,
medium=medium)
scat[i], absorb[i], extinct[i] = system.cross_sections()
force[:, i] = system.force_on_particle(0)
def test_scattering():
"""compare scattering cross-section of GMT and single Mie theory"""
L2 = np.linalg.norm(scat - S) / scat.shape[0]
avg = np.average(np.abs(S) + np.abs(scat)) / 2
assert np.all(L2 < 1e-15 * avg)
Ag = miepy.materials.Ag()
radius = 75*nm
source = miepy.sources.plane_wave.from_string(polarization='rhc', direction='-z')
lmax = 2
water = miepy.materials.water()
wavelength = 800*nm
separation = 600*nm
L = 1
lattice = hexagonal_lattice_layers(L)
cluster = miepy.sphere_cluster(position=separation*lattice,
radius=radius,
material=Ag,
source=source,
wavelength=wavelength,
lmax=lmax,
medium=water)
xmax = L*separation + 8*radius
x = np.linspace(-xmax, xmax, 100)
y = np.linspace(-xmax, xmax, 100)
X, Y = np.meshgrid(x, y)
Z = np.zeros_like(X)
E = cluster.E_field(X, Y, Z)
I = np.sum(np.abs(E)**2, axis=0)
fig, axes = plt.subplots(ncols=3, figsize=(15,6))
ax = axes[0]
# save_opts=[{'format':'png'},
# {'format':'raw'}],
# outputdir=(projects_directory_location + "/smuthi_output_" + str( comparison + job_idx ) + "/"),
# xmin=-1000,
# xmax=1000,
# ymin=-1000,
# ymax=1000,
# zmin=focal_length_nm,
# zmax=focal_length_nm,
# resolution_step=50,
# simulation=simulation,
# show_internal_field=False)
mie_cluster = miepy.sphere_cluster(
medium=background_dielectric,
position=random_centers, radius=random_radii, material=random_materials,
source=plane_wave, wavelength=(probe_wavelength_nm*nm), lmax=lmax )#, interface=air_interface )
gmmt_data[ comparison + job_idx, 0 ] = np.sum(
np.abs( mie_cluster.E_field( 0.25 * device_size_x_nm * nm, 0.25 * device_size_y_nm * nm, focal_z_nm * nm ) )**2 )
gmmt_data[ comparison + job_idx, 1 ] = np.sum(
np.abs( mie_cluster.E_field( -0.25 * device_size_x_nm * nm, 0.25 * device_size_y_nm * nm, focal_z_nm * nm ) )**2 )
gmmt_data[ comparison + job_idx, 2 ] = np.sum(
np.abs( mie_cluster.E_field( -0.25 * device_size_x_nm * nm, -0.25 * device_size_y_nm * nm, focal_z_nm * nm ) )**2 )
gmmt_data[ comparison + job_idx, 3 ] = np.sum(
np.abs( mie_cluster.E_field( 0.25 * device_size_x_nm * nm, -0.25 * device_size_y_nm * nm, focal_z_nm * nm ) )**2 )
gmmt_focal_intensity[ comparison + job_idx ] = np.sum(
np.abs( mie_cluster.E_field( focal_lateral_search_mesh_x_nm, focal_lateral_search_mesh_y_nm, focal_lateral_search_mesh_z_nm ) )**2,
axis=0 )
gmmt_focal_E[ comparison + job_idx ] = mie_cluster.E_field( focal_lateral_search_mesh_x_nm, focal_lateral_search_mesh_y_nm, focal_lateral_search_mesh_z_nm )
wavelengths = np.linspace(400 * nm, 1000 * nm, 40)
frequency = np.linspace(1, 1 / 0.4, 40)
separation = 400 * nm
radius = 75 * nm
Au = miepy.data_material(wavelengths, eps)
source = miepy.sources.plane_wave.from_string(polarization='rhc')
gmtF = np.zeros((3, ) + wavelengths.shape)
gmtC = np.zeros((3, ) + wavelengths.shape)
for i, wavelength in enumerate(wavelengths):
sol = miepy.sphere_cluster(position=[[-separation / 2, 0, 0],
[separation / 2, 0, 0]],
radius=radius,
material=Au,
source=source,
wavelength=wavelength,
lmax=2)
gmtF[:, i] = sol.force_on_particle(1)
gmtC[:, i] = sol.cross_sections()
def test_fdtd_cross_sections(plot=False):
"""compare cross-sections to fdtd"""
if not plot:
L2 = np.linalg.norm(scat - gmtC[0]) / scat.shape[0]
assert np.all(L2 < 8e-15)
L2 = np.linalg.norm(absorb - gmtC[1]) / absorb.shape[0]
"""
Far-field analysis with the GMT
"""
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib as mpl
import miepy
nm = 1e-9
sol = miepy.sphere_cluster(
position=[[-100 * nm, 0, 0], [100 * nm, 0, 0]],
radius=75 * nm,
material=miepy.constant_material(3.6**2),
source=miepy.sources.plane_wave.from_string(polarization='y'),
wavelength=600 * nm,
lmax=2)
### xy plane far-field
fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
r = 10000 * nm
phi = np.linspace(0, 2 * np.pi, 100)
theta = np.pi / 2
THETA, PHI = np.meshgrid(theta, phi, indexing='ij')
E = sol.E_angular(THETA, PHI).squeeze()
I = np.sum(np.abs(E)**2, axis=0)
Ag = miepy.materials.Ag()
radius = 75 * nm
source = miepy.sources.plane_wave.from_string(polarization='x')
separations = np.linspace(2 * radius + 10 * nm, 2 * radius + 200 * nm, 5)
analytic_scattering = np.zeros(separations.shape)
analytic_absorption = np.zeros(separations.shape)
poynting_scattering = np.zeros(separations.shape)
poynting_absorption = np.zeros(separations.shape)
for i, separation in enumerate(tqdm(separations)):
mie = miepy.sphere_cluster(position=[[separation / 2, 0, 0],
[-separation / 2, 0, 0]],
radius=radius,
material=Ag,
source=source,
wavelength=800 * nm,
lmax=1)
analytic_scattering[i], analytic_absorption[i], _ = mie.cross_sections()
poynting_scattering[i], poynting_absorption[
i], _ = miepy.flux._gmt_cross_sections_from_poynting(
mie, radius=separation + radius, sampling=60)
def test_scattering():
"""comapre analytic scattering to numerical Poynting vector approach"""
L2 = np.linalg.norm(analytic_scattering -
poynting_scattering) / poynting_scattering.shape[0]
def test_medium_cross_sections(plot=False):
"""verify cross-sections of an Au dimer in water by comparing with Poynting vector approach"""
Nwav = 5
Au = miepy.materials.Au()
radius = 50 * nm
lmax = 2
nb = 1.33
medium = miepy.constant_material(nb**2)
wavelengths = np.linspace(500 * nm, 1000 * nm, Nwav)
separation = 2 * radius + 40 * nm
source = miepy.sources.plane_wave.from_string(polarization='x')
THETA, PHI = miepy.coordinates.sphere_mesh(20)
R = (separation / 2 + radius + 20 * nm) * np.ones_like(THETA)
X, Y, Z = miepy.coordinates.sph_to_cart(R, THETA, PHI)
scat, absorb, extinct, C, A = (np.zeros_like(wavelengths)
for i in range(5))
for i, wavelength in enumerate(wavelengths):
sol = miepy.sphere_cluster(position=[[separation / 2, 0, 0],
[-separation / 2, 0, 0]],
radius=radius,
material=Au,
source=source,
medium=medium,
wavelength=wavelength,
lmax=lmax)
scat[i], absorb[i], extinct[i] = sol.cross_sections()
E = sol.E_field(X, Y, Z, source=False)
H = sol.H_field(X, Y, Z, source=False)
C[i] = miepy.flux.flux_from_poynting_sphere(E, H, R, eps=nb**2)
E = sol.E_field(X, Y, Z, source=True)
H = sol.H_field(X, Y, Z, source=True)
A[i] = -miepy.flux.flux_from_poynting_sphere(E, H, R, eps=nb**2)
if not plot:
for a, b, tol in [(C, scat, 1e-3), (A, absorb, 1e-3),
(C + A, extinct, 1e-3)]:
L2 = np.linalg.norm(a - b) / a.shape[0]
avg = np.average(a + b) / 2
print(L2, avg)
assert L2 < tol * avg
else:
plt.figure()
line, = plt.plot(wavelengths / nm,
C,
'o',
color='C0',
label='scattering (Poynting)')
line, = plt.plot(wavelengths / nm,
A,
'o',
color='C1',
label='absorbption (Poynting)')
line, = plt.plot(wavelengths / nm,
C + A,
'o',
color='C2',
label='extinction (Poynting)')
plt.axhline(color='black', linestyle='--')
line, = plt.plot(wavelengths / nm,
scat,
color='C0',
label='scattering (analytic)')
line, = plt.plot(wavelengths / nm,
absorb,
color='C1',
label='absorbption (analytic)')
line, = plt.plot(wavelengths / nm,
extinct,
color='C2',
label='extinction (analytic)')
plt.xlabel('wavelength (nm)')
plt.ylabel(r'cross-section ($\mu$m$^2$)')
plt.legend()
plt.title(test_medium_cross_sections.__name__, weight='bold')
