def spherical_wave_expansion(self, particle, layer_system):
"""Regular spherical wave expansion of the wave including layer system response, at the locations of the
particles.
Args:
particle (smuthi.particles.Particle): particle relative to which the swe is computed
layer_system (smuthi.layer.LayerSystem): stratified medium
Returns:
regular smuthi.field_expansion.SphericalWaveExpansion object
"""
virtual_particle = part.Particle(position=self.position,
l_max=1,
m_max=1)
wd = pc.direct_coupling_block(vacuum_wavelength=self.vacuum_wavelength,
receiving_particle=particle,
emitting_particle=virtual_particle,
layer_system=layer_system)
wr = pc.layer_mediated_coupling_block(
vacuum_wavelength=self.vacuum_wavelength,
receiving_particle=particle,
emitting_particle=virtual_particle,
layer_system=layer_system,
k_parallel=self.k_parallel)
k = self.angular_frequency() * layer_system.refractive_indices[
layer_system.layer_number(particle.position[2])]
swe = fldex.SphericalWaveExpansion(k=k,
l_max=particle.l_max,
m_max=particle.m_max,
kind='regular',
reference_point=particle.position)
swe.coefficients = np.dot(
wd + wr,
self.outgoing_spherical_wave_expansion(layer_system).coefficients)
return swe
def test_w_against_wr():
coord.set_default_k_parallel(wl, [0, 0.8, 0.8 - 0.1j, 2.1 - 0.1j, 2.1, 7],
2e-3)
laysys_air_1 = lay.LayerSystem(thicknesses=[0, 0],
refractive_indices=[1, 1])
laysys_air_2 = lay.LayerSystem(thicknesses=[0, 250, 0],
refractive_indices=[1, 1, 1])
part1 = part.Sphere(position=[100, -100, 200],
refractive_index=1.7,
radius=100,
l_max=2,
m_max=2)
part2 = part.Sphere(position=[-100, 200, 400],
refractive_index=1.7,
radius=100,
l_max=2,
m_max=2)
w_air_1 = coup.direct_coupling_block(wl, part1, part2, laysys_air_1)
wr_air_2 = coup.layer_mediated_coupling_block(wl, part1, part2,
laysys_air_2)
error = wr_air_2 - w_air_1
np.testing.assert_almost_equal(wr_air_2, w_air_1, decimal=4)
def __init__(self,
vacuum_wavelength,
particle_list,
layer_system,
k_parallel='default'):
SystemMatrix.__init__(self, particle_list)
coup_mat = np.zeros(self.shape, dtype=complex)
sys.stdout.write('Coupling matrix memory footprint: ' +
coup.size_format(coup_mat.nbytes) + '\n')
sys.stdout.flush()
for s1, particle1 in enumerate(
tqdm(particle_list,
desc='Particle coupling matrix ',
file=sys.stdout,
bar_format='{l_bar}{bar}| elapsed: {elapsed} '
'remaining: {remaining}')):
idx1 = np.array(self.index_block(s1))[:, None]
for s2, particle2 in enumerate(particle_list):
idx2 = self.index_block(s2)
coup_mat[idx1, idx2] = (coup.layer_mediated_coupling_block(
vacuum_wavelength, particle1, particle2, layer_system,
k_parallel) + coup.direct_coupling_block(
vacuum_wavelength, particle1, particle2, layer_system))
self.linear_operator = scipy.sparse.linalg.aslinearoperator(coup_mat)
def test_w_against_prototype():
part1 = part.Sphere(position=[100, -100, 200],
refractive_index=1.7,
radius=100,
l_max=2,
m_max=2)
part2 = part.Sphere(position=[-100, 200, 300],
refractive_index=1.7,
radius=100,
l_max=2,
m_max=2)
part3 = part.Sphere(position=[200, 200, -300],
refractive_index=1.7,
radius=100,
l_max=2,
m_max=2)
laysys_waveguide = lay.LayerSystem(thicknesses=[0, 500, 0],
refractive_indices=[1, 2, 1])
w_wg11 = coup.direct_coupling_block(wl, part1, part1, laysys_waveguide)
w_wg12 = coup.direct_coupling_block(wl, part1, part2, laysys_waveguide)
w_wg13 = coup.direct_coupling_block(wl, part1, part3, laysys_waveguide)
w_wg_0010 = 0.078085976865533 + 0.054600388160436j
assert abs((w_wg12[0, 0] - w_wg_0010) / w_wg_0010) < 1e-5
w_wg_0110 = -0.014419231182754 + 0.029269376752105j
assert abs((w_wg12[1, 0] - w_wg_0110) / w_wg_0110) < 1e-5
w_wg_0912 = -0.118607476554146 + 0.020532217124574j
assert abs((w_wg12[9, 2] - w_wg_0912) / w_wg_0912) < 1e-5
assert np.linalg.norm(w_wg11) == 0 # no direct self interaction
assert np.linalg.norm(
w_wg13
) == 0 # no direct interaction between particles in different layers
def dissipated_power(self,
particle_list,
layer_system,
show_progress=True):
r"""Compute the power that the dipole feeds into the system.
It is computed according to
.. math::
P = P_0 + \frac{\omega}{2} \mathrm{Im} (\mathbf{\mu}^* \cdot \mathbf{E}(\mathbf{r}_D))
where :math:`P_0` is the power that the dipole would feed into an infinte homogeneous medium with the same
refractive index as the layer that contains the dipole, :math:`\mathbf{r}_D` is the location of the dipole,
:math:`\omega` is the angular frequency, :math:`\mathbf{\mu}` is the dipole moment and :math:`\mathbf{E}`
includes the reflections of the dipole field from the layer interfaces, as well as the scattered field from all
particles.
Args:
particle_list (list of smuthi.particles.Particle objects): scattering particles
layer_system (smuthi.layers.LayerSystem): stratified medium
show_progress (bool): if true, display progress
Returns:
dissipated power as float
"""
k = layer_system.wavenumber(
layer_system.layer_number(self.position[2]),
self.vacuum_wavelength)
virtual_particle = part.Particle(position=self.position,
l_max=1,
m_max=1)
scattered_field_swe = fldex.SphericalWaveExpansion(
k=k,
l_max=1,
m_max=1,
kind='regular',
reference_point=self.position)
if show_progress:
iterator = tqdm(
particle_list,
desc='Dipole dissipated power ',
file=sys.stdout,
bar_format=
'{l_bar}{bar}| elapsed: {elapsed} remaining: {remaining}')
else:
iterator = particle_list
for particle in iterator:
wd = pc.direct_coupling_block(
vacuum_wavelength=self.vacuum_wavelength,
receiving_particle=virtual_particle,
emitting_particle=particle,
layer_system=layer_system)
wr = pc.layer_mediated_coupling_block(
vacuum_wavelength=self.vacuum_wavelength,
receiving_particle=virtual_particle,
emitting_particle=particle,
layer_system=layer_system,
k_parallel=self.k_parallel)
scattered_field_swe.coefficients += np.dot(
wd + wr, particle.scattered_field.coefficients)
e_x_scat, e_y_scat, e_z_scat = scattered_field_swe.electric_field(
x=self.position[0], y=self.position[1], z=self.position[2])
e_x_in, e_y_in, e_z_in = self.electric_field(
x=self.position[0],
y=self.position[1],
z=self.position[2],
layer_system=layer_system,
include_direct_field=False)
power = self.angular_frequency() / 2 * (
np.conjugate(self.dipole_moment[0]) *
(e_x_scat + e_x_in) + np.conjugate(self.dipole_moment[1]) *
(e_y_scat + e_y_in) + np.conjugate(self.dipole_moment[2]) *
(e_z_scat + e_z_in)).imag
return self.dissipated_power_homogeneous_background(
layer_system) + power
# Test fails for mmax != lmax,
# Computation of matrix elements in the laboratory coordinate system of degree l
# require the knowledge of all orders m of same degree l: m = (-l, -l + 1, ..., l - 1, l)
# see e.g.: Mishchenko et al., Scattering, Absorption, and Emission of Light by Small Particles,
# Cambridge University Press, 2002. Eq. (5.29) p. 120
#spheroid1 = part.Spheroid(position=[0, 0, 400],euler_angles=[0, 0, 0],
# refractive_index=2.4 + 0.0j, semi_axis_c=50, semi_axis_a=100, l_max=2, m_max=1)
#
#spheroid2 = part.Spheroid(position=[0,0,0],euler_angles=[0, 0, 0],
# refractive_index=2.4 + 0.0j, semi_axis_c=100, semi_axis_a=50, l_max=2, m_max=2)
# conventional coupling using svwf addition theorem
W = pacou.direct_coupling_block(vacuum_wavelength=wl,
receiving_particle=spheroid2,
emitting_particle=spheroid1,
layer_system=lay_sys)
# plane wave coupling
k_parallel = coord.complex_contour(
vacuum_wavelength=wl,
neff_waypoints=[0, 0.9, 0.9 - 0.1j, 1.1 - 0.1j, 1.1, 7],
neff_resolution=1e-3)
W_pvwf = pacou.direct_coupling_block_pvwf_mediated(
vacuum_wavelength=wl,
receiving_particle=spheroid2,
emitting_particle=spheroid1,
layer_system=lay_sys,
k_parallel=k_parallel)
refractive_index=1.7 + 0.0j,
radius=90,
l_max=3,
m_max=3)
particle_list = [sphere1, sphere2, sphere3]
# initialize layer system object
lay_sys = lay.LayerSystem([0, 400, 0], [1.5, 2 + 0.01j, 1])
phi12 = np.arctan2(sphere1.position[1] - sphere2.position[1],
sphere1.position[0] - sphere2.position[0])
rho12 = np.sqrt(
sum([(sphere1.position[i] - sphere2.position[i])**2 for i in range(3)]))
wr12 = coup.layer_mediated_coupling_block(vacuum_wavelength, sphere1, sphere2,
lay_sys)
w12 = coup.direct_coupling_block(vacuum_wavelength, sphere1, sphere2, lay_sys)
phi13 = np.arctan2(sphere1.position[1] - sphere3.position[1],
sphere1.position[0] - sphere3.position[0])
rho13 = np.sqrt(
sum([(sphere1.position[i] - sphere3.position[i])**2 for i in range(3)]))
wr13 = coup.layer_mediated_coupling_block(vacuum_wavelength, sphere1, sphere3,
lay_sys)
w13 = coup.direct_coupling_block(vacuum_wavelength, sphere1, sphere3, lay_sys)
# initialize initial field object
init_fld = init.GaussianBeam(vacuum_wavelength=vacuum_wavelength,
polar_angle=beam_polar_angle,
azimuthal_angle=beam_azimuthal_angle,
polarization=beam_polarization,
amplitude=beam_amplitude,