def mat_tm_tm(eps_array, d_array, eps_inv_mat, gk, indmode1, oms1, As1, Bs1,
chis1, indmode2, oms2, As2, Bs2, chis2, pp):
"""
Matrix block for TM-TM mode coupling
"""
# Index matrix selecting the participating modes
indmat = np.ix_(indmode1, indmode2)
# Number of layers
Nl = eps_array.size
# Build the matrix layer by layer
mat = bd.zeros((indmode1.size, indmode2.size))
for il in range(0, Nl):
mat = mat + eps_inv_mat[il][indmat]*(
(pp[indmat] * bd.outer(bd.conj(chis1[il, :]), chis2[il, :]) + \
bd.outer(gk[indmode1], gk[indmode2])) * (
bd.outer(bd.conj(As1[il, :]), As2[il, :]) *
IJ_layer(il, Nl, chis2[il, :] - bd.conj(chis1[il, :][:, bd.newaxis]),
d_array) +
bd.outer(bd.conj(Bs1[il, :]), Bs2[il, :]) *
IJ_layer(il, Nl, -chis2[il, :] + bd.conj(chis1[il, :][:, bd.newaxis]),
d_array)) - \
(pp[indmat] * bd.outer(bd.conj(chis1[il, :]), chis2[il, :]) - \
bd.outer(gk[indmode1], gk[indmode2])) * (
bd.outer(bd.conj(As1[il, :]), Bs2[il, :]) *
IJ_layer(il, Nl, -chis2[il, :] - bd.conj(chis1[il, :][:, bd.newaxis]),
d_array) +
bd.outer(bd.conj(Bs1[il, :]), As2[il, :]) *
IJ_layer(il, Nl, chis2[il, :] + bd.conj(chis1[il, :][:, bd.newaxis]),
d_array)) )
return mat
def mat_tm_te(eps_array, d_array, eps_inv_mat, indmode1, oms1, As1, Bs1, chis1,
indmode2, oms2, As2, Bs2, chis2, pq):
"""
Matrix block for TM-TE mode coupling
"""
# Index matrix selecting the participating modes
indmat = np.ix_(indmode1, indmode2)
# Number of layers
Nl = eps_array.size
# Build the matrix layer by layer
mat = bd.zeros((indmode1.size, indmode2.size))
for il in range(0, Nl):
mat = mat + 1j * eps_inv_mat[il][indmat] * \
eps_array[il] * bd.conj(chis1[il, :])[:, bd.newaxis] * (
bd.outer(bd.conj(As1[il, :]), As2[il, :]) *
IJ_layer(il, Nl, chis2[il, :] - bd.conj(chis1[il, :][:, bd.newaxis]),
d_array)
-bd.outer(bd.conj(Bs1[il, :]), Bs2[il, :]) *
IJ_layer(il, Nl, -chis2[il, :] + bd.conj(chis1[il, :][:, bd.newaxis]),
d_array)
+bd.outer(bd.conj(As1[il, :]), Bs2[il, :]) *
IJ_layer(il, Nl, -chis2[il, :] - bd.conj(chis1[il, :][:, bd.newaxis]),
d_array)
-bd.outer(bd.conj(Bs1[il, :]), As2[il, :]) *
IJ_layer(il, Nl, chis2[il, :] + bd.conj(chis1[il, :][:, bd.newaxis]),
d_array) )
# Final pre-factor
mat = mat * (oms2**2)[bd.newaxis, :] * pq[indmat]
return mat
def normalization_coeff(omega, g, eps_array, d_array, chi_array, ABref,
pol='TE'):
"""
Normalization of the guided modes (i.e. the A and B coeffs)
"""
assert len(d_array)==len(eps_array)-2, \
'd_array should have length = num_layers'
if chi_array is None:
chi_array = chi(omega, g, eps_array)
As = ABref[:, 0].ravel()
Bs = ABref[:, 1].ravel()
if pol == 'TM':
term1 = (bd.abs(Bs[0])**2) * J_alpha(chi_array[0]-bd.conj(chi_array[0]))
term2 = (bd.abs(As[-1])**2) * \
J_alpha(chi_array[-1]-bd.conj(chi_array[-1]))
term3 = (
(bd.abs(As[1:-1])**2 + bd.abs(Bs[1:-1])**2) * \
I_alpha(chi_array[1:-1]-bd.conj(chi_array[1:-1]),d_array) +
(bd.conj(As[1:-1]) * Bs[1:-1] + As[1:-1] * bd.conj(Bs[1:-1])) *
I_alpha(-chi_array[1:-1]-bd.conj(chi_array[1:-1]),d_array) )
return term1 + term2 + bd.sum(term3)
elif pol == 'TE':
term1 = (bd.abs(chi_array[0])**2 + g**2) * \
(bd.abs(Bs[0])**2) * J_alpha(chi_array[0]-bd.conj(chi_array[0]))
term2 = (bd.abs(chi_array[-1])**2 + g**2) * \
(bd.abs(As[-1])**2) * J_alpha(chi_array[-1]-bd.conj(chi_array[-1]))
term3 = (bd.abs(chi_array[1:-1])**2 + g**2) * (
(bd.abs(As[1:-1])**2 + bd.abs(Bs[1:-1])**2) * \
I_alpha(chi_array[1:-1]-bd.conj(chi_array[1:-1]), d_array)) + \
(g**2 - bd.abs(chi_array[1:-1])**2) * (
(bd.conj(As[1:-1]) * Bs[1:-1] + As[1:-1] * bd.conj(Bs[1:-1])) *
I_alpha(-chi_array[1:-1]-bd.conj(chi_array[1:-1]), d_array) )
return term1 + term2 + bd.sum(term3)
else:
raise Exception('Polarization should be TE or TM.')