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miesphere.py
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miesphere.py
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#/usr/bin/env python
import scipy as sp
from scipy.special import jv, yv
from scipy.special import sph_jn, sph_yn
from scipy.special import eval_legendre
from mesh import Mesh, Cartesian
from mesh import myrange, stdoutw, stdoutf
def _print_progress(ii, N, what='done', mod=10):
per = int(100*(ii+1)/N)
if per%mod == 0:
stdoutw('\rInfo: {0}% {3}. [{1}/{2}]'.format(
per, ii+1, N, what))
stdoutf()
def fun_cart2sph(F):
def f(n, z):
return sp.sqrt(sp.pi/(2*z))* F(n+1/2.0, z)
#return sp.sqrt(1/z)* F(n+1/2.0, z)
return f
def fun_derivative(F):
def f(n, z):
return (n/z)*F(n, z) - F(n+1, z)
return f
J = fun_cart2sph(jv)
Jp = fun_derivative(J)
Y = fun_cart2sph(yv)
Yp = fun_derivative(Y)
H1 = lambda n, z: J(n, z) + 1j*Y(n, z)
H1p = lambda n, z: Jp(n, z) + 1j*Yp(n, z)
def coeff_ext(n, params, k):
R, ks, jumps = params
ce, ci = ks
jumpe, jumpi = jumps
ke, ki = ce*k, ci*k
ae, be = jumpe
ai, bi = jumpi
a = ke*J(n, ki*R)*Jp(n, ke*R) * ae*ai
b = ki*Jp(n, ki*R)*J(n, ke*R) * ae*bi
c = ki*H1(n, ke*R)*Jp(n, ki*R) * ae*bi
d = ke*H1p(n, ke*R)*J(n, ki*R) * ai*be
return (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
def coeff_int(n, params, k):
R, ks, jumps = params
ce, ci = ks
jumpe, jumpi = jumps
ke, ki = ce*k, ci*k
ae, be = jumpe
ai, bi = jumpi
a = ke*H1(n, ke*R)*Jp(n, ke*R) * be*ae
b = ke*J(n, ke*R)*H1p(n, ke*R) * be*be
c = ki*H1(n, ke*R)*Jp(n, ki*R) * ae*bi
d = ke*H1p(n, ke*R)*J(n, ki*R) * ai*be
return (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
def ref_inc(mesh, Params, name='ref-inc.pos', ext=True):
count = 0
N, params, kk = Params
R, (ce, ci), jumps = params
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
vals = [0+0j] * len(mesh.points)
for ii, point in enumerate(mesh.points):
_print_progress(ii, len(mesh.points), 'computed', mod=1)
p = Cartesian(point)
x, y, z = point
count += 1
if ins:
val = sp.exp(1j * ci * k * kk.dot(p))
else:
val = sp.exp(1j * ce * k * kk.dot(p))
vals[ii] = val
print(' --> {0} computations.'.format(count))
mesh.write(vals, name)
def mie_sphere(mesh, Params, name='mie-sphere.pos', field='sca'):
count = 0
N, params, kk = Params
R, (ce, ci), jumps = params
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
vals = [0+0j] * len(mesh.points)
for ii, point in enumerate(mesh.points):
_print_progress(ii, len(mesh.points), 'computed', mod=1)
p = Cartesian(point)
pnorm = p.norm()
pn = p.normalized()
costheta = pn.dot(kk)
for n in myrange(N):
if field == 'sca':
cn = coeff_ext(n, params, k) * H1(n, k*pnorm)
elif field == 'int':
cn = coeff_int(n, params, k) * J(n, ci*k*pnorm)
else:
cn = ((1j)**n)*(2*n+1)*J(n, k*pnorm)
c = eval_legendre(n, costheta)
count += 1
vals[ii] += cn * c
print(' --> {1} computations i.e. N={0}.'.format(N, count))
mesh.write(vals, name)
return vals
def mie_D4grid_slow(field, kk, R, C, ce, ci, jumpe, jumpi, N, point):
"""
Requires:
kk : numpy.array([kx, ky, kz])
R : radius of the sphere
C : center of the sphere
ce, ci : contrast sqrt(epsExt), sqrt*espInt)
jumpe: coeff jump exterior (alpha_Dir, beta_Neu)
jumpi: coeff jump interior (alpha_Dir, beta_Neu)
N : Number of modes
"""
pt = point[:]
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
# be careful with this test !!
if sp.linalg.norm(sp.linalg.norm(pt - C) - R) > 0.3:
return 0. + 0j
else:
jumps = (jumpe, jumpi)
params = (R, (ce, ci), jumps)
p = Cartesian((pt[0], pt[1], pt[2]))
pnorm = p.norm()
pn = p.normalized()
costheta = pn.dot(kk)
val = 0
for n in myrange(N):
if field == 'sca':
cn = coeff_ext(n, params, k) * H1(n, k*pnorm)
elif field == 'int':
cn = coeff_int(n, params, k) * J(n, ci*k*pnorm)
else:
cn = ((1j)**n)*(2*n+1)*J(n, k*pnorm)
c = eval_legendre(n, costheta)
val += cn * c
return val
def mie_N4grid_slow(field, kk, R, C, ce, ci, jumpe, jumpi, N, point):
"""
Requires:
kk : numpy.array([kx, ky, kz])
R : radius of the sphere
C : center of the sphere
ce, ci : contrast sqrt(epsExt), sqrt*espInt)
jumpe: coeff jump exterior (alpha_Dir, beta_Neu)
jumpi: coeff jump interior (alpha_Dir, beta_Neu)
N : Number of modes
"""
pt = point[:]
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
# be careful with this test !!
if sp.linalg.norm(sp.linalg.norm(pt - C) - R) > 0.3:
return 0. + 0j
else:
jumps = (jumpe, jumpi)
params = (R, (ce, ci), jumps)
p = Cartesian((pt[0], pt[1], pt[2]))
pnorm = p.norm()
pn = p.normalized()
costheta = pn.dot(kk)
val = 0
for n in myrange(N):
if field == 'sca':
cn = k * coeff_ext(n, params, k) * H1p(n, k*pnorm)
elif field == 'int':
cn = ci * k * coeff_int(n, params, k) * Jp(n, ci*k*pnorm)
else:
cn = k * ((1j)**n)*(2*n+1)*Jp(n, k*pnorm)
c = eval_legendre(n, costheta)
val += cn * c
return val
##########################################################################
##########################################################################
##########################################################################
##########################################################################
def mie_D4grid(field, kk, R, C, ce, ci, jumpe, jumpi, N, point):
"""
Requires:
kk : numpy.array([kx, ky, kz])
R : radius of the sphere
C : center of the sphere
ce, ci : contrast sqrt(epsExt), sqrt*espInt)
jumpe: coeff jump exterior (alpha_Dir, beta_Neu)
jumpi: coeff jump interior (alpha_Dir, beta_Neu)
N : Number of modes
"""
pt = point[:]
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
# be careful with this test !!
if sp.linalg.norm(sp.linalg.norm(pt - C) - R) > 0.3:
return 0. + 0j
else:
p = Cartesian((pt[0], pt[1], pt[2]))
pnorm = p.norm()
pn = p.normalized()
costheta = pn.dot(kk)
kpnorm = k * pnorm
ke, ki = ce * k, ci * k
keR, kiR = ke * R, ki * R
ae, be = jumpe
ai, bi = jumpi
ke_aeai = ke * ae * ai
ki_aebi = ki * ae * bi
ke_aibe = ke * ai * be
ke_beae = ke * be * ae
ke_bebe = ke * be * be
ki_bebe = ke * ae * bi
ke_aibe = ke * ai * be
sqrt_e = sp.sqrt(sp.pi / (2*keR))
sqrt_i = sp.sqrt(sp.pi / (2*kiR))
sqrt_n = sp.sqrt(sp.pi / (2*kpnorm))
sqrt_m = sp.sqrt(sp.pi / (2*ci*kpnorm))
val = 0
for n in myrange(N):
Je = sqrt_e * jv(n + 0.5, keR)
Ji = sqrt_i * jv(n + 0.5, kiR)
Jpe = (n / keR) * Je - sqrt_e * jv(n + 1.5, keR)
Jpi = (n / kiR) * Ji - sqrt_i * jv(n + 1.5, kiR)
Ye = sqrt_e * yv(n + 0.5, keR)
Ype = (n / keR) * Ye - sqrt_e * yv(n + 1.5, keR)
locH1 = Je + 1j * Ye
locH1p = Jpe + 1j * Ype
if field == 'sca':
a = ke_aeai * Ji * Jpe
b = ki_aebi * Jpi * Je
c = ki_aebi * locH1 * Jpi
d = ke_aibe * locH1p * Ji
v = (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
Jn = sqrt_n * jv(n + 0.5, kpnorm)
Yn = sqrt_n * yv(n + 0.5, kpnorm)
locH1 = Jn + 1j * Yn
cn = v * locH1
elif field == 'int':
a = ke_beae * locH1 * Jpe
b = ke_bebe * Je * locH1p
c = ki_aebi * locH1 * Jpi
d = ke_aibe * locH1p * Ji
v = (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
Jn = sqrt_m * jv(n + 0.5, ci*kpnorm)
cn = v * Jn
else:
cn = ((1j)**n)*(2*n+1)*J(n, k*pnorm)
c = eval_legendre(n, costheta)
val += cn * c
return val
def mie_N4grid(field, kk, R, C, ce, ci, jumpe, jumpi, N, point):
"""
Requires:
kk : numpy.array([kx, ky, kz])
R : radius of the sphere
C : center of the sphere
ce, ci : contrast sqrt(epsExt), sqrt*espInt)
jumpe: coeff jump exterior (alpha_Dir, beta_Neu)
jumpi: coeff jump interior (alpha_Dir, beta_Neu)
N : Number of modes
"""
pt = point[:]
kk = Cartesian(kk)
k = kk.norm()
kk = kk.normalized()
# be careful with this test !!
if sp.linalg.norm(sp.linalg.norm(pt - C) - R) > 0.3:
return 0. + 0j
else:
p = Cartesian((pt[0], pt[1], pt[2]))
pnorm = p.norm()
pn = p.normalized()
costheta = pn.dot(kk)
kpnorm = k * pnorm
ke, ki = ce * k, ci * k
keR, kiR = ke * R, ki * R
ae, be = jumpe
ai, bi = jumpi
ke_aeai = ke * ae * ai
ki_aebi = ki * ae * bi
ke_aibe = ke * ai * be
ke_beae = ke * be * ae
ke_bebe = ke * be * be
ki_bebe = ke * ae * bi
ke_aibe = ke * ai * be
sqrt_e = sp.sqrt(sp.pi / (2*keR))
sqrt_i = sp.sqrt(sp.pi / (2*kiR))
sqrt_n = sp.sqrt(sp.pi / (2*kpnorm))
sqrt_m = sp.sqrt(sp.pi / (2*ci*kpnorm))
val = 0
for n in myrange(N):
Je = sqrt_e * jv(n + 0.5, keR)
Ji = sqrt_i * jv(n + 0.5, kiR)
Jpe = (n / keR) * Je - sqrt_e * jv(n + 1.5, keR)
Jpi = (n / kiR) * Ji - sqrt_i * jv(n + 1.5, kiR)
Ye = sqrt_e * yv(n + 0.5, keR)
Ype = (n / keR) * Ye - sqrt_e * yv(n + 1.5, keR)
locH1 = Je + 1j * Ye
locH1p = Jpe + 1j * Ype
if field == 'sca':
a = ke_aeai * Ji * Jpe
b = ki_aebi * Jpi * Je
c = ki_aebi * locH1 * Jpi
d = ke_aibe * locH1p * Ji
v = (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
Jn = sqrt_n * jv(n + 0.5, kpnorm)
Jpn = (n / kpnorm) * Jn - sqrt_n * jv(n + 1.5, kpnorm)
Yn = sqrt_n * yv(n + 0.5, kpnorm)
Ypn = (n / kpnorm) * Yn - sqrt_n * yv(n + 1.5, kpnorm)
locH1p = Jpn + 1j * Ypn
cn = k * v * locH1p
elif field == 'int':
a = ke_beae * locH1 * Jpe
b = ke_bebe * Je * locH1p
c = ki_aebi * locH1 * Jpi
d = ke_aibe * locH1p * Ji
v = (2*n+1)*( (1j)**n ) * (a - b) / (c - d)
Jn = sqrt_m * jv(n + 0.5, ci*kpnorm)
Jpn = (n / (ci*kpnorm)) * Jn - sqrt_m * jv(n + 1.5, ci*kpnorm)
cn = ci * k * v * Jpn
else:
cn = k * ((1j)**n)*(2*n+1)*Jp(n, k*pnorm)
c = eval_legendre(n, costheta)
val += cn * c
return val
##########################################################################
##########################################################################
##########################################################################
##########################################################################
if __name__ == "__main__":
epsExt, epsInt = 1, 2
ll = 9.5
R = 1.0
N = 10
# k = 2*sp.pi / ll
k = 0.3 * sp.pi # 3.1
kk = (0., k, 0.)
params = R, (sp.sqrt(epsExt), sp.sqrt(epsInt)), ((1., 1.), (1., 1.))
Params = N, params, kk
m = Mesh('geo/sphere-disjoint.msh', 1)
sca = mie_sphere(m, Params, 'mie{}-sca.pos'.format(N), field='sca')
ins = mie_sphere(m, Params, 'mie{}-int.pos'.format(N), field='int')
inc = mie_sphere(m, Params, 'mie{}-inc.pos'.format(N), field='inc')
ref_inc(m, Params)
ref_inc(m, Params, name='ref-inc-int.pos', ext=False)
ext = [ v for ii, v in enumerate(sca) ]
m.write(ext, 'mie{}-ext.pos'.format(N))
diff = [ v - ins[ii] -inc[ii] for ii, v in enumerate(ext) ]
m.write(diff, 'mie{}-diff.pos'.format(N))