def solve_interior(self):
"""solve for the interior of the sphere, the cn and dn coefficients"""
#TODO shouldn't this be multiplied by self.radius?
xvals = self.material_data['k'] * self.radius
m = (self.material_data['eps'] / self.material_data['eps_b'])**.5
mt = m * self.material_data['mu_b'] / self.material_data['mu']
jn = riccati_1(self.lmax, xvals)
yn = riccati_2(self.lmax, xvals)
if self.material.name == 'metal':
f = self.material_data['mu_b'] / self.material_data['mu']
c = (jn[0] * yn[1] - yn[0] * jn[1]) / (f * yn[0] * jnm[1])
d = (jn[0] * yn[1] - yn[0] * jn[1]) / (f * jnm[0] * yn[1])
else:
jnm = riccati_1(self.lmax, m * xvals)
c = (m * jn[0] * yn[1] - m * yn[0] * jn[1]) / (jnm[0] * yn[1] -
mt * yn[0] * jnm[1])
d = (m * jn[0] * yn[1] -
m * yn[0] * jn[1]) / (mt * jnm[0] * yn[1] - yn[0] * jnm[1])
self.cn[...] = np.nan_to_num(c.T)
self.dn[...] = np.nan_to_num(d.T)
self.interior_computed = True
return self.cn, self.dn
def sphere(nmax, mat, r, eps_b=1, mu_b=1):
"""Determine an, bn coefficients for a sphere
nmax = maximum number of orders to use
mat = material object
r = radius
eps_b = background permittivity
mu_b = background permeability
Returns multipoles object"""
n_b = (eps_b)**.5
xvals = mat.k*r*n_b
an = np.zeros((nmax,mat.Nfreq), dtype=np.complex)
bn = np.zeros((nmax,mat.Nfreq), dtype=np.complex)
for i,x in enumerate(xvals):
m = (mat.eps[i]/eps_b)**.5
mt = m*mu_b/mat.mu[i]
jn,jn_p = riccati_1(nmax,x)
jnm,jnm_p = riccati_1(nmax,m*x)
yn,yn_p = riccati_2(nmax,x)
a = (mt*jnm*jn_p - jn*jnm_p)/(mt*jnm*yn_p - yn*jnm_p)
b = (jnm*jn_p - mt*jn*jnm_p)/(jnm*yn_p - mt*yn*jnm_p)
an[:,i] = a[1:]
bn[:,i] = b[1:]
an = np.nan_to_num(an)
bn = np.nan_to_num(bn)
return multipoles(mat.wav,an,bn)
def solve_exterior(self):
"""solve for the exterior of the sphere, the an and bn coefficients"""
xvals = self.material_data['k']*self.radius
m = (self.material_data['eps']/self.material_data['eps_b'])**.5
mt = m*self.material_data['mu_b']/self.material_data['mu']
jn = riccati_1(self.lmax,xvals)
yn = riccati_2(self.lmax,xvals)
if self.material.name == 'metal':
a = jn[1]/yn[1]
b = jn[0]/yn[0]
else:
jnm = riccati_1(self.lmax,m*xvals)
a = (mt*jnm[0]*jn[1] - jn[0]*jnm[1])/(mt*jnm[0]*yn[1] - yn[0]*jnm[1])
b = (jnm[0]*jn[1] - mt*jn[0]*jnm[1])/(jnm[0]*yn[1] - mt*yn[0]*jnm[1])
self.an[...] = np.nan_to_num(a.T)
self.bn[...] = np.nan_to_num(b.T)
self.exterior_computed = True
return self.an, self.bn