def compute_ft(self, gvec):
(gx, gy) = self._parse_ft_gvec(gvec)
gabs = np.sqrt(np.abs(np.square(gx)) + np.abs(np.square(gy)))
gabs += 1e-10 # To avoid numerical instability at zero
ft = bd.exp(-1j*gx*self.x_cent - 1j*gy*self.y_cent)*self.r* \
2*np.pi/gabs*bd.bessel1(gabs*self.r)
return ft
def S_T_matrices_TE(omega, g, eps_array, d_array):
"""
Function to get a list of S and T matrices for D22 calculation
"""
assert len(d_array)==len(eps_array)-2, \
'd_array should have length = num_layers'
chi_array = chi(omega, g, eps_array)
S11 = (chi_array[:-1] + chi_array[1:])
S12 = -chi_array[:-1] + chi_array[1:]
S22 = S11
S21 = S12
S_matrices = 0.5 / chi_array[1:].reshape(-1,1,1) * \
bd.array([[S11,S12],[S21,S22]]).transpose([2,0,1])
T11 = bd.exp(1j*chi_array[1:-1]*d_array/2)
T22 = bd.exp(-1j*chi_array[1:-1]*d_array/2)
T_matrices = bd.array([[T11,bd.zeros(T11.shape)],
[bd.zeros(T11.shape),T22]]).transpose([2,0,1])
return S_matrices, T_matrices
def compute_ft(self, gvec):
"""Compute Fourier transform of the polygon
The polygon is assumed to take a value of 1 inside and a value of 0
outside.
The Fourier transform calculation follows that of Lee, IEEE TAP (1984).
Parameters
----------
gvec : np.ndarray of shape (2, Ng)
g-vectors at which FT is evaluated
"""
(gx, gy) = self._parse_ft_gvec(gvec)
(xj, yj) = self.x_edges, self.y_edges
npts = xj.shape[0]
ng = gx.shape[0]
# Note: the paper uses +1j*g*x convention for FT while we use
# -1j*g*x everywhere in legume
gx = -gx[:, bd.newaxis]
gy = -gy[:, bd.newaxis]
xj = xj[bd.newaxis, :]
yj = yj[bd.newaxis, :]
ft = bd.zeros((ng), dtype=bd.complex);
aj = (bd.roll(xj, -1, axis=1) - xj + 1e-10) / \
(bd.roll(yj, -1, axis=1) - yj + 1e-20)
bj = xj - aj * yj
# We first handle the Gx = 0 case
ind_gx0 = np.abs(gx[:, 0]) < 1e-10
ind_gx = ~ind_gx0
if np.sum(ind_gx0) > 0:
# And first the Gy = 0 case
ind_gy0 = np.abs(gy[:, 0]) < 1e-10
if np.sum(ind_gy0*ind_gx0) > 0:
ft = ind_gx0*ind_gy0*bd.sum(xj * bd.roll(yj, -1, axis=1)-\
yj * bd.roll(xj, -1, axis=1))/2
# Remove the Gx = 0, Gy = 0 component
ind_gx0[ind_gy0] = False
# Compute the remaining Gx = 0 components
a2j = 1 / aj
b2j = yj - a2j * xj
bgtemp = gy * b2j
agtemp1 = bd.dot(gx, xj) + bd.dot(gy, a2j * xj)
agtemp2 = bd.dot(gx, bd.roll(xj, -1, axis=1)) + \
bd.dot(gy, a2j * bd.roll(xj, -1, axis=1))
denom = gy * (gx + bd.dot(gy, a2j))
ftemp = bd.sum(bd.exp(1j*bgtemp) * (bd.exp(1j*agtemp2) - \
bd.exp(1j*agtemp1)) * \
denom / (bd.square(denom) + 1e-50) , axis=1)
ft = bd.where(ind_gx0, ftemp, ft)
# Finally compute the general case for Gx != 0
if np.sum(ind_gx) > 0:
bgtemp = bd.dot(gx, bj)
agtemp1 = bd.dot(gy, yj) + bd.dot(gx, aj * yj)
agtemp2 = bd.dot(gy, bd.roll(yj, -1, axis=1)) + \
bd.dot(gx, aj * bd.roll(yj, -1, axis=1))
denom = gx * (gy + bd.dot(gx, aj))
ftemp = -bd.sum(bd.exp(1j*bgtemp) * (bd.exp(1j * agtemp2) - \
bd.exp(1j * agtemp1)) * \
denom / (bd.square(denom) + 1e-50) , axis=1)
ft = bd.where(ind_gx, ftemp, ft)
return ft
