def coupled_dip_mags_focused_beam(
mol_angle,
plas_angle,
d_col,
p0_position,
beam_x_positions,
E_d_angle=None,
drive_hbar_w=None,
alpha0_diag=None,
alpha1_diag=None,
n_b=None,
drive_amp=None,
return_polarizabilities=False,
):
""" Calculate dipole magnitudes with generalized dyadic
polarizabilities driven by a focused dipole PSF beam.
Returns dipole moment vecotrs as rows in array of shape
(# of seperations, # of beam positions, 3 cart. coords).
As with the rest of this module, 'd_col' is expected in shape
(number of seperations, 3)
'p0_positions' is expected in shape
(3)
beam_x_positions is currelty just assuming a 1d slice, so it
should be shape
(number of points) on the x axis.
To be consistent with super-res notation, 'mol' dipole is
placed at 'p0_position' and seperation vectrs point towards
this location from the 'plas' location,
p0_location - d_col = p1_location
so if we want p0 on the left, d has to be negative.
"""
# Initialize unit vector for molecule dipole in lab frame
phi_0 = mol_angle ## angle of bf_p0 in lab frame
# Initialize unit vecotr for molecule dipole in lab frame
phi_1 = plas_angle ## angle of bf_p1 in lab frame
k = (drive_hbar_w*n_b/hbar) / c
## Define positions with shape (num_seperations, 3)
if p0_position.ndim is 1:
p0_position = p0_position[None, :]
p1_position = p0_position - d_col
## Buld focused beam profile
E_0 = aff.E_field(
dipole_orientation_angle=E_d_angle,
xi=beam_x_positions - p0_position[...,0],
y=0,
k=k
).T*drive_amp
E_1 = aff.E_field(
dipole_orientation_angle=E_d_angle,
xi=beam_x_positions - p1_position[...,0],
y=0,
k=k
).T*drive_amp
## Normalize fields to correct beam intensity
spot_size = 2*np.pi/k
spot_space = np.linspace(-spot_size, spot_size, 500)
spot_mesh = np.meshgrid(spot_space, spot_space)
focal_spot_field = aff.E_field(
dipole_orientation_angle=E_d_angle,
xi=spot_mesh[0],
y=spot_mesh[1],
k=k
).T
intensity_ofx = c/(8*np.pi) * np.sum(
focal_spot_field*np.conj(focal_spot_field), axis=-1)
area_image = (spot_space.max() - spot_space.min())**2.
num_pixels = len(spot_space)**2.
area_per_pixel = area_image / num_pixels
beam_power = np.sum(intensity_ofx)*area_per_pixel
## integral of (c/8pi)|E|^2 dA = beam_power
E_0 /= (beam_power)**0.5
E_1 /= (beam_power)**0.5
# print(f'np.sum(intensity_ofx) = {np.sum(intensity_ofx)}')
# print(f'(2*spot_size)**2. = {(2*spot_size)**2.}')
# print(f'beam_power = {beam_power}')
## Rotate polarizabilities into connecting vector frame
alpha_0_p0 = alpha0_diag
alpha_0 = rotation_by(-phi_0) @ alpha_0_p0 @ rotation_by(phi_0)
alpha_1_p1 = alpha1_diag
alpha_1 = rotation_by(-phi_1) @ alpha_1_p1 @ rotation_by(phi_1)
G_d = G(drive_hbar_w, d_col, n_b)
geometric_coupling_01 = np.linalg.inv(
np.identity(3) - alpha_0 @ G_d @ alpha_1 @ G_d
)
# p0 = (
# np.einsum(
# '...ij,...j->...i',
# geometric_coupling_01 @ alpha_0,
# E_0
# )
# +
# np.einsum(
# '...ij,...j->...i',
# geometric_coupling_01 @ alpha_0 @ G_d @ alpha_1,
# E_1
# )
# )
# p1 = (
# np.einsum(
# '...ij,...j->...i',
# geometric_coupling_01 @ alpha_1,
# E_1
# )
# +
# np.einsum(
# '...ij,...j->...i',
# geometric_coupling_01 @ alpha_1 @ G_d @ alpha_0,
# E_0
# )
# )
p0 = np.einsum(
'...ij,...j->...i',
geometric_coupling_01 @ alpha_0 @ (
np.identity(3) + G_d @ alpha_1
),
E_0
)
p1 = np.einsum(
'...ij,...j->...i',
geometric_coupling_01 @ alpha_1 @ (
np.identity(3) + G_d @ alpha_0
),
E_0
)
if not return_polarizabilities:
return [p0, p1]
## If using to compute absorption spectrum,
elif return_polarizabilities:
return [p0, p1, alpha_0, alpha_1]
def single_dip_mag_focused_beam(
angle,
p0_position,
beam_x_positions,
E_d_angle=None,
drive_hbar_w=None,
alpha0_diag=None,
n_b=None,
drive_amp=None,
return_polarizabilities=False,
):
""" Calculate dipole magnitude with generalized dyadic
polarizabilities driven by a focused dipole PSF beam.
Returns dipole moment vector as rows in array of shape
(# of seperations, # of beam positions, 3 cart. coords).
'p0_positions' is expected in shape
(3)
beam_x_positions is currelty just assuming a 1d slice, so it
should be shape
(number of points) on the x axis.
"""
# Initialize unit vector for molecule dipole in lab frame
phi_0 = angle ## angle of bf_p0 in lab frame
k = (drive_hbar_w*n_b/hbar) / c
## Define positions with shape (num_seperations, 3)
if p0_position.ndim is 1:
p0_position = p0_position[None, :]
## Buld focused beam profile
E_0 = aff.E_field(
dipole_orientation_angle=E_d_angle,
xi=beam_x_positions - p0_position[...,0],
y=0,
k=k
).T*drive_amp
## Normalize fields to correct beam intensity
spot_size = 2*np.pi/k
spot_space = np.linspace(-spot_size, spot_size, 500)
spot_mesh = np.meshgrid(spot_space, spot_space)
focal_spot_field = aff.E_field(
dipole_orientation_angle=E_d_angle,
xi=spot_mesh[0],
y=spot_mesh[1],
k=k
).T
intensity_ofx = c/(8*np.pi) * np.sum(
focal_spot_field*np.conj(focal_spot_field), axis=-1)
area_image = (spot_space.max() - spot_space.min())**2.
num_pixels = len(spot_space)**2.
area_per_pixel = area_image / num_pixels
beam_power = np.sum(intensity_ofx)*area_per_pixel
## integral of (c/8pi)|E|^2 dA = beam_power
E_0 /= (beam_power)**0.5
## Rotate polarizabilities into connecting vector frame
alpha_0_p0 = alpha0_diag
alpha_0 = rotation_by(-phi_0) @ alpha_0_p0 @ rotation_by(phi_0)
## Dipole mmoment
p0 = np.einsum(
'...ij,...j->...i',
alpha_0,
E_0
)
if not return_polarizabilities:
return [p0]
## If using to compute absorption spectrum,
elif return_polarizabilities:
return [p0, alpha_0]
def foc_field(self, dip_angle, x, y, k):
""" Dipole field of an x oriented dipole"""
E = aff.E_field(dipole_orientation_angle=dip_angle, xi=x, y=y, k=k)
return E