def pwe_to_ff_conversion(vacuum_wavelength, plane_wave_expansion):
"""Compute the far field of a plane wave expansion object.
Args:
vacuum_wavelength (float): Vacuum wavelength in length units.
plane_wave_expansion (PlaneWaveExpansion): Plane wave expansion to convert into far field object.
Returns:
A FarField object containing the far field intensity.
"""
omega = flds.angular_frequency(vacuum_wavelength)
k = plane_wave_expansion.k
kp = plane_wave_expansion.k_parallel
if plane_wave_expansion.kind == 'upgoing':
polar_angles = np.arcsin(kp / k)
elif plane_wave_expansion.kind == 'downgoing':
polar_angles = np.pi - np.arcsin(kp / k)
else:
raise ValueError('PWE type not specified')
if any(polar_angles.imag):
raise ValueError('complex angles are not allowed')
azimuthal_angles = plane_wave_expansion.azimuthal_angles
kkz2 = flds.k_z(k_parallel=kp, k=k)**2 * k
intens = (2 * np.pi**2 / omega * kkz2[np.newaxis, :, np.newaxis] *
abs(plane_wave_expansion.coefficients)**2).real
srt_idcs = np.argsort(polar_angles) # reversing order in case of downgoing
ff = FarField(polar_angles=polar_angles[srt_idcs],
azimuthal_angles=azimuthal_angles)
ff.signal = intens[:, srt_idcs, :]
return ff
def wavenumber(self, layer_number, vacuum_wavelength):
"""
Args:
layer_number (int): number of layer in question
vacuum_wavelength (float): vacuum wavelength
Returns:
wavenumber in that layer as float
"""
return self.refractive_indices[layer_number] * flds.angular_frequency(
vacuum_wavelength=vacuum_wavelength)
def internal_field_piecewise_expansion(vacuum_wavelength, particle_list, layer_system):
"""Compute a piecewise field expansion of the internal field of spheres.
Args:
vacuum_wavelength (float): vacuum wavelength
particle_list (list): list of smuthi.particles.Particle objects
layer_system (smuthi.layers.LayerSystem): stratified medium
Returns:
internal field as smuthi.field_expansion.PiecewiseFieldExpansion object
"""
intfld = fldex.PiecewiseFieldExpansion()
for particle in particle_list:
if type(particle).__name__ == 'Sphere':
i_part = layer_system.layer_number(particle.position[2])
k_medium = flds.angular_frequency(vacuum_wavelength) * layer_system.refractive_indices[i_part]
k_particle = flds.angular_frequency(vacuum_wavelength) * particle.refractive_index
internal_field = fldex.SphericalWaveExpansion(
k_particle,
l_max=particle.l_max,
m_max=particle.m_max,
kind='regular',
reference_point=particle.position)
internal_field.validity_conditions.append(particle.is_inside)
for tau in range(2):
for l in range(1, particle.l_max+1):
for m in range(-l, l+1):
n = flds.multi_to_single_index(tau, l, m, particle.l_max, particle.m_max)
b_to_c = (tmt.internal_mie_coefficient(tau, l, k_medium, k_particle, particle.radius)
/ tmt.mie_coefficient(tau, l, k_medium, k_particle, particle.radius))
internal_field.coefficients[n] = particle.scattered_field.coefficients[n] * b_to_c
intfld.expansion_list.append(internal_field)
particle.internal_field = internal_field
return intfld
def scattering_cross_section(initial_field,
particle_list,
layer_system,
polar_angles='default',
azimuthal_angles='default'):
"""Evaluate and display the differential scattering cross section as a function of solid angle.
Args:
initial_field (smuthi.initial.PlaneWave): Initial Plane wave
particle_list (list): scattering particles
layer_system (smuthi.layers.LayerSystem): stratified medium
polar_angles (numpy.ndarray or str): polar angles values (radian).
if 'default', use smuthi.fields.default_polar_angles
azimuthal_angles (numpy.ndarray or str): azimuthal angle values (radian)
if 'default', use smuthi.fields.default_azimuthal_angles
Returns:
A tuple of smuthi.field_expansion.FarField objects, one for forward scattering (i.e., into the top hemisphere) and one for backward
scattering (bottom hemisphere).
"""
if not type(initial_field).__name__ == 'PlaneWave':
raise ValueError(
'Cross section only defined for plane wave excitation.')
i_top = layer_system.number_of_layers() - 1
vacuum_wavelength = initial_field.vacuum_wavelength
omega = flds.angular_frequency(vacuum_wavelength)
k_bot = omega * layer_system.refractive_indices[0]
k_top = omega * layer_system.refractive_indices[-1]
# read plane wave parameters
A_P = initial_field.amplitude
beta_P = initial_field.polar_angle
if np.cos(beta_P) > 0:
i_P = 0
n_P = layer_system.refractive_indices[i_P]
else:
i_P = i_top
n_P = layer_system.refractive_indices[i_P]
if n_P.imag:
raise ValueError(
'plane wave from absorbing layer: cross section undefined')
else:
n_P = n_P.real
initial_intensity = abs(A_P)**2 * abs(np.cos(beta_P)) * n_P / 2
dscs = scattered_far_field(vacuum_wavelength, particle_list, layer_system,
polar_angles, azimuthal_angles)
dscs.signal_type = 'differential scattering cross section'
dscs.signal = dscs.signal / initial_intensity
return dscs
def testGMRES(self):
# Parameter input ----------------------------
vacuum_wavelength = 550
beam_polar_angle = np.pi * 7 / 8
beam_azimuthal_angle = np.pi * 1 / 3
beam_polarization = 0
beam_amplitude = 1
beam_neff_array = np.linspace(0, 2, 501, endpoint=False)
beam_waist = 1000
beam_focal_point = [200, 200, 200]
#neff_waypoints = [0, 0.5, 0.8 - 0.01j, 2 - 0.01j, 2.5, 5]
#neff_discr = 1e-2
# --------------------------------------------
#coord.set_default_k_parallel(vacuum_wavelength, neff_waypoints, neff_discr)
# initialize particle object
sphere1 = part.Sphere(position=[100, 100, 150], refractive_index=2.4 + 0.0j, radius=110, l_max=4, m_max=4)
sphere2 = part.Sphere(position=[-100, -100, 250], refractive_index=1.9 + 0.0j, radius=120, l_max=3, m_max=3)
sphere3 = part.Sphere(position=[-200, 100, 300], 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], [2, 1.4, 2])
# 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, reference_point=beam_focal_point, beam_waist=beam_waist,
k_parallel_array=beam_neff_array * flds.angular_frequency(vacuum_wavelength))
# initialize simulation object
simulation_lu = simul.Simulation(layer_system=lay_sys, particle_list=particle_list, initial_field=init_fld,
solver_type='LU', log_to_terminal='nose2' not in sys.modules.keys()) # suppress output if called by nose
simulation_lu.run()
coefficients_lu = particle_list[0].scattered_field.coefficients
simulation_gmres = simul.Simulation(layer_system=lay_sys, particle_list=particle_list, initial_field=init_fld,
solver_type='gmres', solver_tolerance=1e-5,
log_to_terminal=(
not sys.argv[0].endswith('nose2'))) # suppress output if called by nose
simulation_gmres.run()
coefficients_gmres = particle_list[0].scattered_field.coefficients
np.testing.assert_allclose(np.linalg.norm(coefficients_lu), np.linalg.norm(coefficients_gmres), rtol=1e-5)
def solve(self):
"""Compute scattered field coefficients and store them
in the particles' spherical wave expansion objects."""
if len(self.particle_list) > 0:
if self.solver_type == 'LU':
sys.stdout.write('Solve (LU decomposition) : ...')
if not hasattr(self.master_matrix.linear_operator, 'A'):
raise ValueError(
'LU factorization only possible '
'with the option "store coupling matrix".')
if not hasattr(self.master_matrix, 'LU_piv'):
lu, piv = scipy.linalg.lu_factor(
self.master_matrix.linear_operator.A,
overwrite_a=False)
self.master_matrix.LU_piv = (lu, piv)
b = scipy.linalg.lu_solve(self.master_matrix.LU_piv,
self.t_matrix.right_hand_side())
sys.stdout.write(' done\n')
sys.stdout.flush()
elif self.solver_type == 'gmres':
rhs = self.t_matrix.right_hand_side()
start_time = time.time()
def status_msg(rk):
global iter_num
iter_msg = ('Solve (GMRES) : Iter ' +
str(iter_num) + ' | Rel. residual: ' +
"{:.2e}".format(np.linalg.norm(rk)) +
' | elapsed: ' +
str(int(time.time() - start_time)) + 's')
sys.stdout.write('\r' + iter_msg)
iter_num += 1
global iter_num
iter_num = 0
b, info = scipy.sparse.linalg.gmres(
self.master_matrix.linear_operator,
rhs,
rhs,
tol=self.solver_tolerance,
callback=status_msg)
# sys.stdout.write('\n')
else:
raise ValueError(
'This solver type is currently not implemented.')
for iS, particle in enumerate(self.particle_list):
i_iS = self.layer_system.layer_number(particle.position[2])
n_iS = self.layer_system.refractive_indices[i_iS]
k = flds.angular_frequency(
self.initial_field.vacuum_wavelength) * n_iS
loz, upz = self.layer_system.lower_zlimit(
i_iS), self.layer_system.upper_zlimit(i_iS)
particle.scattered_field = fldex.SphericalWaveExpansion(
k=k,
l_max=particle.l_max,
m_max=particle.m_max,
kind='outgoing',
reference_point=particle.position,
lower_z=loz,
upper_z=upz)
particle.scattered_field.coefficients = b[
self.master_matrix.index_block(iS)]
particle.scattered_field.validity_conditions.append(
particle.is_outside)
self.initial_field.validity_conditions.append(particle.is_outside)
def extinction_cross_section(initial_field, particle_list, layer_system):
"""Evaluate the extinction cross section.
Args:
initial_field (smuthi.initial_field.PlaneWave): Plane wave object
particle_list (list): List of smuthi.particles.Particle objects
layer_system (smuthi.layers.LayerSystem): Representing the stratified medium
Returns:
Dictionary with following entries
- 'top': Extinction in the positinve z-direction (top layer)
- 'bottom': Extinction in the negative z-direction (bottom layer)
"""
if not type(initial_field).__name__ == 'PlaneWave':
raise ValueError(
'Cross section only defined for plane wave excitation.')
i_top = layer_system.number_of_layers() - 1
vacuum_wavelength = initial_field.vacuum_wavelength
omega = flds.angular_frequency(vacuum_wavelength)
k_bot = omega * layer_system.refractive_indices[0]
k_top = omega * layer_system.refractive_indices[-1]
# read plane wave parameters
pol_P = initial_field.polarization
beta_P = initial_field.polar_angle
alpha_P = initial_field.azimuthal_angle
if np.cos(beta_P) > 0:
i_P = 0
n_P = layer_system.refractive_indices[i_P]
k_P = k_bot
else:
i_P = i_top
n_P = layer_system.refractive_indices[i_P]
k_P = k_top
if n_P.imag:
raise ValueError(
'plane wave from absorbing layer: cross section undefined')
else:
n_P = n_P.real
# complex amplitude of initial wave (including phase factor for reference point)
kappa_P = np.sin(beta_P) * k_P
kx = np.cos(alpha_P) * kappa_P
ky = np.sin(alpha_P) * kappa_P
pm_kz_P = k_P * np.cos(beta_P)
kvec_P = np.array([kx, ky, pm_kz_P])
rvec_iP = np.array([0, 0, layer_system.reference_z(i_P)])
rvec_0 = np.array(initial_field.reference_point)
ejkriP = np.exp(1j * np.dot(kvec_P, rvec_iP - rvec_0))
A_P = initial_field.amplitude * ejkriP
initial_intensity = abs(A_P)**2 * abs(np.cos(beta_P)) * n_P / 2
pwe_scat_top, _ = sf.scattered_field_pwe(vacuum_wavelength, particle_list,
layer_system, i_top, kappa_P,
alpha_P)
_, pwe_scat_bottom = sf.scattered_field_pwe(vacuum_wavelength,
particle_list, layer_system, 0,
kappa_P, alpha_P)
# bottom extinction
_, pwe_init_bottom = initial_field.plane_wave_expansion(layer_system, 0)
kz_bot = flds.k_z(k_parallel=kappa_P, k=k_bot)
gRPbot = np.squeeze(pwe_init_bottom.coefficients[pol_P])
g_scat_bottom = np.squeeze(pwe_scat_bottom.coefficients[pol_P])
P_bot_ext = 4 * np.pi**2 * kz_bot / omega * (gRPbot *
np.conj(g_scat_bottom)).real
bottom_extinction_cs = -P_bot_ext / initial_intensity
# top extinction
pwe_init_top, _ = initial_field.plane_wave_expansion(layer_system, i_top)
gRPtop = np.squeeze(pwe_init_top.coefficients[pol_P])
kz_top = flds.k_z(k_parallel=kappa_P, k=k_top)
g_scat_top = np.squeeze(pwe_scat_top.coefficients[pol_P])
P_top_ext = 4 * np.pi**2 * kz_top / omega * (gRPtop *
np.conj(g_scat_top)).real
top_extinction_cs = -P_top_ext / initial_intensity
extinction_cs = {'top': top_extinction_cs, 'bottom': bottom_extinction_cs}
return extinction_cs
def scattered_far_field(vacuum_wavelength,
particle_list,
layer_system,
polar_angles='default',
azimuthal_angles='default'):
"""
Evaluate the scattered far field.
Args:
vacuum_wavelength (float): in length units
particle_list (list): list of smuthi.Particle objects
layer_system (smuthi.layers.LayerSystem): represents the stratified medium
polar_angles (numpy.ndarray or str): polar angles values (radian).
if 'default', use smuthi.fields.default_polar_angles
azimuthal_angles (numpy.ndarray or str): azimuthal angle values (radian)
if 'default', use smuthi.fields.default_azimuthal_angles
Returns:
A smuthi.field_expansion.FarField object of the scattered field.
"""
omega = flds.angular_frequency(vacuum_wavelength)
if type(polar_angles) == str and polar_angles == 'default':
polar_angles = flds.default_polar_angles
if type(azimuthal_angles) == str and azimuthal_angles == 'default':
azimuthal_angles = flds.default_azimuthal_angles
if any(polar_angles.imag):
raise ValueError("complex angles not allowed in far field")
i_top = layer_system.number_of_layers() - 1
top_polar_angles = polar_angles[polar_angles < (np.pi / 2)]
bottom_polar_angles = polar_angles[polar_angles > (np.pi / 2)]
neff_top = np.sort(
np.sin(top_polar_angles) * layer_system.refractive_indices[i_top])
neff_bottom = np.sort(
np.sin(bottom_polar_angles) * layer_system.refractive_indices[0])
if len(top_polar_angles
) > 1 and layer_system.refractive_indices[i_top].imag == 0:
pwe_top, _ = sf.scattered_field_pwe(vacuum_wavelength,
particle_list,
layer_system,
i_top,
k_parallel=neff_top * omega,
azimuthal_angles=azimuthal_angles,
include_direct=True,
include_layer_response=True)
top_far_field = pwe_to_ff_conversion(
vacuum_wavelength=vacuum_wavelength, plane_wave_expansion=pwe_top)
else:
top_far_field = None
if len(bottom_polar_angles
) > 1 and layer_system.refractive_indices[0].imag == 0:
_, pwe_bottom = sf.scattered_field_pwe(
vacuum_wavelength,
particle_list,
layer_system,
0,
k_parallel=neff_bottom * omega,
azimuthal_angles=azimuthal_angles,
include_direct=True,
include_layer_response=True)
bottom_far_field = pwe_to_ff_conversion(
vacuum_wavelength=vacuum_wavelength,
plane_wave_expansion=pwe_bottom)
else:
bottom_far_field = None
if top_far_field is not None:
far_field = top_far_field
if bottom_far_field is not None:
far_field.append(bottom_far_field)
else:
far_field = bottom_far_field
far_field.polar_angles = far_field.polar_angles.real
return far_field
def direct_coupling_block_pvwf_mediated(vacuum_wavelength, receiving_particle,
emitting_particle, layer_system,
k_parallel):
"""Direct particle coupling matrix :math:`W` for two particles (via plane vector wave functions).
For details, see:
Dominik Theobald et al., Phys. Rev. A 96, 033822, DOI: 10.1103/PhysRevA.96.033822 or arXiv:1708.04808
Args:
vacuum_wavelength (float): Vacuum wavelength :math:`\lambda` (length unit)
receiving_particle (smuthi.particles.Particle): Particle that receives the scattered field
emitting_particle (smuthi.particles.Particle): Particle that emits the scattered field
layer_system (smuthi.layers.LayerSystem): Stratified medium in which the coupling takes place
k_parallel (numpy.array): In-plane wavenumber for plane wave expansion
Returns:
Direct coupling matrix block (numpy array).
"""
if type(receiving_particle).__name__ != 'Spheroid' or type(
emitting_particle).__name__ != 'Spheroid':
raise NotImplementedError(
'plane wave coupling currently implemented only for spheroids')
lmax1 = receiving_particle.l_max
mmax1 = receiving_particle.m_max
assert lmax1 == mmax1, 'PVWF coupling requires lmax == mmax for each particle.'
lmax2 = emitting_particle.l_max
mmax2 = emitting_particle.m_max
assert lmax2 == mmax2, 'PVWF coupling requires lmax == mmax for each particle.'
lmax = max([lmax1, lmax2])
m_max = max([mmax1, mmax2])
blocksize1 = flds.blocksize(lmax1, mmax1)
blocksize2 = flds.blocksize(lmax2, mmax2)
n_medium = layer_system.refractive_indices[layer_system.layer_number(
receiving_particle.position[2])]
# finding the orientation of a plane separating the spheroids
_, _, alpha, beta = spheroids_closest_points(
emitting_particle.semi_axis_a, emitting_particle.semi_axis_c,
emitting_particle.position, emitting_particle.euler_angles,
receiving_particle.semi_axis_a, receiving_particle.semi_axis_c,
receiving_particle.position, receiving_particle.euler_angles)
# positions
r1 = np.array(receiving_particle.position)
r2 = np.array(emitting_particle.position)
r21_lab = r1 - r2 # laboratory coordinate system
# distance vector in rotated coordinate system
r21_rot = np.dot(
np.dot([[np.cos(beta), 0, np.sin(beta)], [0, 1, 0],
[-np.sin(beta), 0, np.cos(beta)]],
[[np.cos(alpha), -np.sin(alpha), 0],
[np.sin(alpha), np.cos(alpha), 0], [0, 0, 1]]), r21_lab)
rho21 = (r21_rot[0]**2 + r21_rot[1]**2)**0.5
phi21 = np.arctan2(r21_rot[1], r21_rot[0])
z21 = r21_rot[2]
# wavenumbers
omega = flds.angular_frequency(vacuum_wavelength)
k = omega * n_medium
kz = flds.k_z(k_parallel=k_parallel,
vacuum_wavelength=vacuum_wavelength,
refractive_index=n_medium)
if z21 < 0:
kz_var = -kz
else:
kz_var = kz
# Bessel lookup
bessel_list = []
for dm in range(mmax1 + mmax2 + 1):
bessel_list.append(scipy.special.jn(dm, k_parallel * rho21))
# legendre function lookups
ct = kz_var / k
st = k_parallel / k
_, pilm_list, taulm_list = sf.legendre_normalized(ct, st, lmax)
# initialize result
w = np.zeros((blocksize1, blocksize2), dtype=complex)
# prefactor
const_arr = k_parallel / (kz * k) * np.exp(1j * (kz_var * z21))
for m1 in range(-mmax1, mmax1 + 1):
for m2 in range(-mmax2, mmax2 + 1):
jmm_eimphi_bessel = 4 * 1j**abs(m2 - m1) * np.exp(
1j * phi21 * (m2 - m1)) * bessel_list[abs(m2 - m1)]
prefactor = const_arr * jmm_eimphi_bessel
for l1 in range(max(1, abs(m1)), lmax1 + 1):
for l2 in range(max(1, abs(m2)), lmax2 + 1):
for tau1 in range(2):
n1 = flds.multi_to_single_index(
tau1, l1, m1, lmax1, mmax1)
for tau2 in range(2):
n2 = flds.multi_to_single_index(
tau2, l2, m2, lmax2, mmax2)
for pol in range(2):
B_dag = trf.transformation_coefficients_vwf(
tau1,
l1,
m1,
pol,
pilm_list=pilm_list,
taulm_list=taulm_list,
dagger=True)
B = trf.transformation_coefficients_vwf(
tau2,
l2,
m2,
pol,
pilm_list=pilm_list,
taulm_list=taulm_list,
dagger=False)
integrand = prefactor * B * B_dag
w[n1, n2] += np.trapz(integrand, k_parallel)
rot_mat_1 = trf.block_rotation_matrix_D_svwf(lmax1, mmax1, 0, beta, alpha)
rot_mat_2 = trf.block_rotation_matrix_D_svwf(lmax2, mmax2, -alpha, -beta,
0)
return np.dot(np.dot(np.transpose(rot_mat_1), w), np.transpose(rot_mat_2))
def direct_coupling_block(vacuum_wavelength, receiving_particle,
emitting_particle, layer_system):
"""Direct particle coupling matrix :math:`W` for two particles. This routine is explicit, but slow.
Args:
vacuum_wavelength (float): Vacuum wavelength :math:`\lambda` (length unit)
receiving_particle (smuthi.particles.Particle): Particle that receives the scattered field
emitting_particle (smuthi.particles.Particle): Particle that emits the scattered field
layer_system (smuthi.layers.LayerSystem): Stratified medium in which the coupling takes place
Returns:
Direct coupling matrix block as numpy array.
"""
omega = flds.angular_frequency(vacuum_wavelength)
# index specs
lmax1 = receiving_particle.l_max
mmax1 = receiving_particle.m_max
lmax2 = emitting_particle.l_max
mmax2 = emitting_particle.m_max
blocksize1 = flds.blocksize(lmax1, mmax1)
blocksize2 = flds.blocksize(lmax2, mmax2)
# initialize result
w = np.zeros((blocksize1, blocksize2), dtype=complex)
# check if particles are in same layer
rS1 = receiving_particle.position
rS2 = emitting_particle.position
iS1 = layer_system.layer_number(rS1[2])
iS2 = layer_system.layer_number(rS2[2])
if iS1 == iS2 and not emitting_particle == receiving_particle:
k = omega * layer_system.refractive_indices[iS1]
dx = rS1[0] - rS2[0]
dy = rS1[1] - rS2[1]
dz = rS1[2] - rS2[2]
d = np.sqrt(dx**2 + dy**2 + dz**2)
cos_theta = dz / d
sin_theta = np.sqrt(dx**2 + dy**2) / d
phi = np.arctan2(dy, dx)
# spherical functions
bessel_h = [
sf.spherical_hankel(n, k * d) for n in range(lmax1 + lmax2 + 1)
]
legendre, _, _ = sf.legendre_normalized(cos_theta, sin_theta,
lmax1 + lmax2)
# the particle coupling operator is the transpose of the SVWF translation operator
# therefore, (l1,m1) and (l2,m2) are interchanged:
for m1 in range(-mmax1, mmax1 + 1):
for m2 in range(-mmax2, mmax2 + 1):
eimph = np.exp(1j * (m2 - m1) * phi)
for l1 in range(max(1, abs(m1)), lmax1 + 1):
for l2 in range(max(1, abs(m2)), lmax2 + 1):
A, B = complex(0), complex(0)
for ld in range(max(abs(l1 - l2), abs(m1 - m2)), l1 +
l2 + 1): # if ld<abs(m1-m2) then P=0
a5, b5 = trf.ab5_coefficients(l2, m2, l1, m1, ld)
A += a5 * bessel_h[ld] * legendre[ld][abs(m1 - m2)]
B += b5 * bessel_h[ld] * legendre[ld][abs(m1 - m2)]
A, B = eimph * A, eimph * B
for tau1 in range(2):
n1 = flds.multi_to_single_index(
tau1, l1, m1, lmax1, mmax1)
for tau2 in range(2):
n2 = flds.multi_to_single_index(
tau2, l2, m2, lmax2, mmax2)
if tau1 == tau2:
w[n1, n2] = A
else:
w[n1, n2] = B
return w
rho13 = np.sqrt(
sum([(sphere1.position[i] - sphere3.position[i])**2 for i in range(3)]))
wr13 = layer_mediated_coupling_block(vacuum_wavelength, sphere1, sphere3,
lay_sys)
w13 = 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,
reference_point=beam_focal_point,
beam_waist=beam_waist,
k_parallel_array=beam_neff_array *
flds.angular_frequency(vacuum_wavelength))
# initialize simulation object
simulation_direct = simul.Simulation(
layer_system=lay_sys,
particle_list=particle_list,
initial_field=init_fld,
solver_type='LU',
store_coupling_matrix=True,
log_to_terminal=(not sys.argv[0].endswith('nose2')
)) # suppress output if called by nose
simulation_direct.run()
coefficients_direct = particle_list[0].scattered_field.coefficients
cu.enable_gpu()
simulation_lookup_linear_gpu = simul.Simulation(
def select_numerical_parameters(simulation,
detector="extinction cross section",
tolerance=1e-3,
max_iter=20,
neff_imag=1e-2,
neff_step=1e-2,
select_neff_max=True,
neff_max_increment=0.5,
neff_max=None,
select_neff_step=True,
select_multipole_cutoff=True,
relative_convergence=True,
suppress_simulation_output=True):
"""Trigger automatic selection routines for various numerical parameters.
Args:
simulation (smuthi.simulation.Simulation): Simulation object from which parameters are read and into which
results are stored.
detector (function or string): Function that accepts a simulation object and returns a detector
value the change of which is used to define convergence.
Alternatively, use "extinction cross section" (default) to have
the extinction cross section as the detector value.
tolerance (float): Relative tolerance for the detector value change.
max_iter (int): Break convergence loops after that number of iterations, even if
no convergence has been achieved.
neff_imag (float): Extent of the contour into the negative imaginary direction
(in terms of effective refractive index, n_eff=kappa/omega).
neff_step (float): Discretization of the contour (in terms of eff. refractive
index) - if `select_neff_step` is true, this value will be
eventually overwritten. However, it is required in any case.
Default: 1e-2
select_neff_max (logical): If set to true (default), the Sommerfeld integral truncation parameter
`neff_max` is determined automatically with the help of a
Cauchy convergence criterion.
neff_max_increment (float): Only needed if `select_neff_max` is true.
Step size with which `neff_max` is incremented.
neff_max (float): Only needed if `select_neff_max` is false.
Truncation value of contour (in terms of effective refractive
index).
select_neff_step (logical): If set to true (default), the Sommerfeld integral discretization
parameter `neff_step` is determined automatically with the help of
a Cauchy convergence criterion.
select_multipole_cutoff (logical): If set to true (default), the multipole expansion cutoff
parameters `l_max` and `m_max` are determined automatically with
the help of a Cauchy convergence criterion.
relative_convergence (logical): If set to true (default), the `neff_max` convergence and the
`l_max` and `m_max` convergence routine are performed in the
spirit of relative convergence, i.e., the multipole expansion
convergence is checked again for each value of the Sommerfeld
integral truncation. This takes more time, but is required at
least in the case of flat particles near interfaces.
suppress_simulation_output (logical): If set to false (default), suppress any output from simulations
and only display convergence progress
"""
print("")
print("----------------------------------------")
print("Starting automatic paramateter selection")
print("----------------------------------------")
if select_neff_max:
converge_neff_max(simulation=simulation,
detector=detector,
tolerance=tolerance,
max_iter=max_iter,
neff_imag=neff_imag,
neff_step=neff_step,
neff_max_increment=neff_max_increment,
converge_lm=relative_convergence)
neff_max = simulation.k_parallel[-1] / angular_frequency(
simulation.initial_field.vacuum_wavelength)
if select_multipole_cutoff:
converge_multipole_cutoff(simulation=simulation,
detector=detector,
tolerance=tolerance,
max_iter=max_iter)
if select_neff_step:
converge_neff_step(simulation=simulation,
detector=detector,
tolerance=tolerance,
max_iter=max_iter,
neff_imag=neff_imag,
neff_max=neff_max)
def converge_neff_max(simulation,
detector="extinction cross section",
tolerance=1e-3,
max_iter=20,
neff_imag=1e-2,
neff_step=2e-3,
neff_max_increment=0.5,
converge_lm=True):
"""Find a suitable truncation value for the multiple scattering Sommerfeld integral contour and update the
simulation object accordingly.
Args:
simulation (smuthi.simulation.Simulation): Simulation object
detector (function or string): Function that accepts a simulation object and returns a detector
value the change of which is used to define convergence.
Alternatively, use "extinction cross section" (default) to have
the extinction cross section as the detector value.
tolerance (float): Relative tolerance for the detector value change.
max_iter (int): Break convergence loops after that number of iterations, even if
no convergence has been achieved.
neff_imag (float): Extent of the contour into the negative imaginary direction
(in terms of effective refractive index, n_eff=kappa/omega).
neff_step (float): Discretization of the contour (in terms of eff. refractive
index).
neff_max_increment (float): Increment the neff_max parameter with that step size
converge_lm (logical): If set to true, update multipole truncation during each step
(this takes longer time, but is necessary for critical use cases
like flat particles on a substrate)
Returns:
Detector value for converged settings.
"""
print("")
print("---------------------------")
log.write_blue("Searching suitable neff_max")
update_contour(simulation=simulation,
neff_imag=neff_imag,
neff_max_offset=0,
neff_step=neff_step)
simulation.k_parallel = flds.reasonable_Sommerfeld_kpar_contour(
vacuum_wavelength=simulation.initial_field.vacuum_wavelength,
layer_refractive_indices=simulation.layer_system.refractive_indices,
neff_imag=neff_imag,
neff_max_offset=0,
neff_resolution=neff_step)
neff_max = simulation.k_parallel[-1] / angular_frequency(
simulation.initial_field.vacuum_wavelength)
print("Starting value: neff_max=%f" % neff_max.real)
if converge_lm:
with log.LoggerIndented():
current_value = converge_multipole_cutoff(
simulation=simulation,
detector=detector,
tolerance=tolerance /
2, # otherwise, results flucutate by tolerance and convergence check is compromised
max_iter=max_iter)
else:
current_value = evaluate(simulation, detector)
for _ in range(max_iter):
old_neff_max = neff_max
neff_max = neff_max + neff_max_increment
update_contour(simulation=simulation,
neff_imag=neff_imag,
neff_max=neff_max,
neff_step=neff_step)
print("---------------------------------------")
print("Try neff_max = %f" % neff_max.real)
if converge_lm:
with log.LoggerIndented():
new_value = converge_multipole_cutoff(
simulation=simulation,
detector=detector,
tolerance=tolerance,
max_iter=max_iter,
current_value=current_value)
else:
new_value = evaluate(simulation, detector)
rel_diff = abs(new_value - current_value) / abs(current_value)
print("Old detector value:", current_value)
print("New detector value:", new_value)
print("Relative difference:", rel_diff)
if rel_diff < tolerance: # in this case: discard l_max increment
neff_max = old_neff_max
update_contour(simulation=simulation,
neff_imag=neff_imag,
neff_max=neff_max,
neff_step=neff_step)
log.write_green(
"Relative difference smaller than tolerance. Keep neff_max = %f"
% neff_max.real)
return current_value
else:
current_value = new_value
log.write_red("No convergence achieved. Keep neff_max = %i" % neff_max)
return None
lmax = 10
rx = 100
ry = -100
rz = 100
dx = 400
dy = 800
dz = -500
tau = 0
l = 2
m = -1
# --------------------------------------------
k = flds.angular_frequency(vacuum_wavelength) * surrounding_medium_refractive_index
# outgoing wave
Ex, Ey, Ez = vwf.spherical_vector_wave_function(rx + dx, ry + dy, rz + dz, k, 3, tau, l, m)
# series of incoming waves
Ex2, Ey2, Ez2 = complex(0), complex(0), complex(0)
for tau2 in range(2):
for l2 in range(1, lmax + 1):
for m2 in range(-l2, l2 + 1):
Mx, My, Mz = vwf.spherical_vector_wave_function(rx, ry, rz, k, 1, tau2, l2, m2)
A = trf.translation_coefficients_svwf(tau, l, m, tau2, l2, m2, k, [dx, dy, dz])
Ex2 += Mx * A
Ey2 += My * A
Ez2 += Mz * A
