import numpy as np
def _make_gaussian(x_pts, y_pts, mfd, x_offset=0, y_offset=0):
x0 = (x_pts[-1]+x_pts[0])/2 + x_offset
y0 = (y_pts[-1]+y_pts[0])/2 + y_offset
xx, yy = np.meshgrid(x_pts, y_pts)
sigma = mfd * 0.707 / 2.355
sigma_x = sigma
sigma_y = sigma
gaus_2d = np.exp(-((xx-x0)**2/(2*sigma_x**2)+
(yy-y0)**2/(2*sigma_y**2)))
gaus_2d /= np.sum(gaus_2d)
return gaus_2d
def _overlap(mode, gaussian):
mode_1 = mode
mode_2 = np.sqrt(gaussian) # square-root for E-field (not power)
eta = np.abs(np.sum(np.conj(mode_1)*mode_2))**2 / \
(np.sum(np.abs(mode_1)**2) * np.sum(np.abs(mode_2)**2))
return eta
[docs]def reflection(n1, n2):
'''
Calculate the power reflection at the interface
of two refractive index materials.
Args:
n1 (float): Refractive index of material 1.
n2 (float): Refractive index of material 2.
Returns:
float: The percentage of reflected power.
'''
r = abs((n1-n2) / (n1+n2))**2
return r
[docs]def transmission(n1, n2):
'''
Calculate the power transmission at the interface
of two refractive index materials.
Args:
n1 (float): Refractive index of material 1.
n2 (float): Refractive index of material 2.
Returns:
float: The percentage of transmitted power.
'''
return 1-reflection(n1, n2)
[docs]def coupling_efficiency(mode_solver, fibre_mfd,
fibre_offset_x=0, fibre_offset_y=0,
n_eff_fibre=1.441):
'''
Finds the coupling efficiency between a solved
fundamental mode and a fibre of given MFD.
Args:
mode_solver (_ModeSolver): Mode solver that
has found a fundamental mode.
fibre_mfd (float): The mode-field diameter
(MFD) of the fibre.
fibre_offset_x (float): Offset the fibre
from the centre position of the window
in x. Default is 0 (no offset).
fibre_offset_y (float): Offset the fibre
from the centre position of the window
in y. Default is 0 (no offset).
n_eff_fibre (float): The effective index
of the fibre mode. Default is 1.441.
Returns:
float: The power coupling efficiency.
'''
etas = []
gaus = _make_gaussian(mode_solver._structure.xc, mode_solver._structure.yc,
fibre_mfd, fibre_offset_x, fibre_offset_y)
for mode, n_eff in zip(mode_solver.modes, mode_solver.n_effs):
o = abs(_overlap(mode, gaus))
t = abs(transmission(n_eff, n_eff_fibre))
eta = o * t
etas.append(eta)
return etas