def __compute_superstrate(self, structure, harmonics, S_global):
Nharm = harmonics.Nharm
kx_mat = self.kx_mat
ky_mat = self.ky_mat
# reflection region
Q_ref_mat = np.zeros((2 * Nharm, 2 * Nharm), dtype=complex)
Q_ref_mat[0:Nharm, 0:Nharm] = matmul(kx_mat, ky_mat)
Q_ref_mat[0:Nharm, Nharm:2*Nharm] = structure.UR2*structure.ER2*self.I_mat -\
matmul(kx_mat, kx_mat)
Q_ref_mat[Nharm:2*Nharm, 0:Nharm] = matmul(ky_mat, ky_mat) -\
structure.UR2*structure.ER2*self.I_mat
Q_ref_mat[Nharm:2 * Nharm, Nharm:2 * Nharm] = -matmul(ky_mat, kx_mat)
Q_ref_mat /= structure.UR2
self.W_ref_mat = np.diag(np.ones(2 * Nharm))
lambda_ref_mat = np.concatenate(
(np.concatenate((-1j * self.kz_ref_mat, self.zeros_mat), axis=1),
np.concatenate((self.zeros_mat, -1j * self.kz_ref_mat), axis=1)))
V_ref_mat = matmul(Q_ref_mat, np.linalg.inv(lambda_ref_mat))
A_ref_mat = matmul(np.linalg.inv(self.W0_mat), self.W_ref_mat) +\
matmul(np.linalg.inv(self.V0_mat), V_ref_mat)
B_ref_mat = matmul(np.linalg.inv(self.W0_mat), self.W_ref_mat) -\
matmul(np.linalg.inv(self.V0_mat), V_ref_mat)
S_ref_11 = -matmul(np.linalg.inv(A_ref_mat), B_ref_mat)
S_ref_12 = 2 * np.linalg.inv(A_ref_mat)
S_ref_21 = 0.5 * (
A_ref_mat - matmul(B_ref_mat, np.linalg.inv(A_ref_mat), B_ref_mat))
S_ref_22 = matmul(B_ref_mat, np.linalg.inv(A_ref_mat))
S_ref = np.concatenate((np.concatenate((S_ref_11, S_ref_12), axis=1),
np.concatenate((S_ref_21, S_ref_22), axis=1)))
S_global = redheffer_star_prod(S_ref, S_global, self.I_big_mat)
return S_global
def __compute_substrate(self, structure, harmonics, S_global):
Nharm = harmonics.Nharm
kx_mat = self.kx_mat
ky_mat = self.ky_mat
# transmission region
Q_trn_mat = np.zeros((2 * Nharm, 2 * Nharm), dtype=complex)
Q_trn_mat[0:Nharm, 0:Nharm] = matmul(kx_mat, ky_mat)
Q_trn_mat[0:Nharm, Nharm:2*Nharm] = structure.UR1*structure.ER1*self.I_mat -\
matmul(kx_mat, kx_mat)
Q_trn_mat[Nharm:2*Nharm, 0:Nharm] = matmul(ky_mat, ky_mat) -\
structure.UR1*structure.ER1*self.I_mat
Q_trn_mat[Nharm:2 * Nharm, Nharm:2 * Nharm] = -matmul(ky_mat, kx_mat)
Q_trn_mat /= structure.UR1
self.W_trn_mat = np.diag(np.ones(2 * Nharm))
lambda_trn_mat = np.concatenate(
(np.concatenate((1j * self.kz_trn_mat, self.zeros_mat), axis=1),
np.concatenate((self.zeros_mat, 1j * self.kz_trn_mat), axis=1)))
V_trn_mat = matmul(Q_trn_mat, np.linalg.inv(lambda_trn_mat))
A_trn_mat = matmul(np.linalg.inv(self.W0_mat), self.W_trn_mat) +\
matmul(np.linalg.inv(self.V0_mat), V_trn_mat)
B_trn_mat = matmul(np.linalg.inv(self.W0_mat), self.W_trn_mat) -\
matmul(np.linalg.inv(self.V0_mat), V_trn_mat)
S_trn_11 = matmul(B_trn_mat, np.linalg.inv(A_trn_mat))
S_trn_12 = 0.5 * (
A_trn_mat - matmul(B_trn_mat, np.linalg.inv(A_trn_mat), B_trn_mat))
S_trn_21 = 2 * np.linalg.inv(A_trn_mat)
S_trn_22 = -matmul(np.linalg.inv(A_trn_mat), B_trn_mat)
S_trn = np.concatenate((np.concatenate((S_trn_11, S_trn_12), axis=1),
np.concatenate((S_trn_21, S_trn_22), axis=1)))
S_global = redheffer_star_prod(S_global, S_trn, self.I_big_mat)
return S_global
def __compute_layers(self, structure, source, S_global):
kx, ky = self.k_inc[0], self.k_inc[1]
# take layers into account
for i in range(0, structure.num_layers):
ur = structure.ur_vec[i]
er = structure.er_vec[i]
l = structure.layer_thicknesses_vec[i]
s_layer_mat = self.__calc_s_mat(l, ur, er, kx, ky, source.K0)
S_global = redheffer_star_prod(S_global, s_layer_mat, UNIT_MAT_2D)
return S_global
def __compute_layers(self, structure, source, harmonics, S_global):
Nharm = harmonics.Nharm
kx_mat = self.kx_mat
ky_mat = self.ky_mat
# iterating through layers
for i in range(0, structure.num_layers):
ERC = structure.erc_vec[i]
URC = structure.urc_vec[i]
thickness = structure.L[i]
P_mat = np.zeros((2 * Nharm, 2 * Nharm), dtype=complex)
P_mat[0:Nharm, 0:Nharm] = matmul(kx_mat, np.linalg.inv(ERC),
ky_mat)
P_mat[0:Nharm, Nharm:2 *
Nharm] = URC - matmul(kx_mat, np.linalg.inv(ERC), kx_mat)
P_mat[Nharm:2 * Nharm,
0:Nharm] = matmul(ky_mat, np.linalg.inv(ERC), ky_mat) - URC
P_mat[Nharm:2 * Nharm, Nharm:2 *
Nharm] = -matmul(ky_mat, np.linalg.inv(ERC), kx_mat)
Q_mat = np.zeros((2 * Nharm, 2 * Nharm), dtype=complex)
Q_mat[0:Nharm, 0:Nharm] = matmul(kx_mat, np.linalg.inv(URC),
ky_mat)
Q_mat[0:Nharm, Nharm:2 *
Nharm] = ERC - matmul(kx_mat, np.linalg.inv(URC), kx_mat)
Q_mat[Nharm:2 * Nharm,
0:Nharm] = matmul(ky_mat, np.linalg.inv(URC), ky_mat) - ERC
Q_mat[Nharm:2 * Nharm, Nharm:2 *
Nharm] = -matmul(ky_mat, np.linalg.inv(URC), kx_mat)
Omega_sq_mat = matmul(P_mat, Q_mat)
v_vec, W_mat = np.linalg.eig(Omega_sq_mat)
lambda_mat = np.diag(np.conj(np.sqrt(v_vec)))
V_mat = matmul(Q_mat, W_mat, np.linalg.inv(lambda_mat))
A_mat = matmul(np.linalg.inv(W_mat), self.W0_mat) +\
matmul(np.linalg.inv(V_mat), self.V0_mat)
B_mat = matmul(np.linalg.inv(W_mat), self.W0_mat) -\
matmul(np.linalg.inv(V_mat), self.V0_mat)
X_mat = np.diag(
np.exp(-np.diag(lambda_mat) * source.K0 * thickness))
S_11 = matmul(np.linalg.inv(A_mat -\
matmul(X_mat, B_mat, np.linalg.inv(A_mat), X_mat, B_mat)),
(matmul(X_mat, B_mat, np.linalg.inv(A_mat), X_mat, A_mat) - B_mat))
S_12 = matmul(np.linalg.inv(A_mat -\
matmul(X_mat, B_mat, np.linalg.inv(A_mat), X_mat, B_mat)),
X_mat, (A_mat - matmul(B_mat, np.linalg.inv(A_mat), B_mat)))
S = np.concatenate((np.concatenate(
(S_11, S_12), axis=1), np.concatenate((S_12, S_11), axis=1)))
S_global = redheffer_star_prod(S_global, S, self.I_big_mat)
return S_global
def __compute_substrate(self, structure, S_global):
kx, ky = self.k_inc[0], self.k_inc[1]
# take substrate into account
_, v_trn_mat = self.__calc_layer_params(structure.UR2, structure.ER2, kx, ky)
vg_mat = self.__calc_gap_layer_params(kx, ky)
a_trn_mat = UNIT_MAT_2D + matmul(np.linalg.inv(vg_mat), v_trn_mat)
b_trn_mat = UNIT_MAT_2D - matmul(np.linalg.inv(vg_mat), v_trn_mat)
s_trn_11_mat = matmul(b_trn_mat, np.linalg.inv(a_trn_mat))
s_trn_12_mat = 0.5*(a_trn_mat - matmul(b_trn_mat,
np.linalg.inv(a_trn_mat), b_trn_mat))
s_trn_21_mat = 2*np.linalg.inv(a_trn_mat)
s_trn_22_mat = -matmul(np.linalg.inv(a_trn_mat), b_trn_mat)
s_trn_mat = np.concatenate((np.concatenate((s_trn_11_mat, s_trn_12_mat), axis=1),
np.concatenate((s_trn_21_mat, s_trn_22_mat), axis=1)))
S_global = redheffer_star_prod(S_global, s_trn_mat, UNIT_MAT_2D)
return S_global