def phi_magnetic_i_te(radial, theta, phi, wave_number_k):
""" Computes the phi component of inciding magnetic field in TE mode.
"""
result = 0
n = 1
# Due to possible singularity near origin, we approximate null radial
# component to a small value.
radial = radial or 1E-16
riccati_bessel_list = _riccati_bessel_j(get_max_it(radial),
wave_number_k * radial)
d_riccati_bessel = riccati_bessel_list[1]
max_it = get_max_it(radial)
while n <= max_it:
for m in DEGREES:
increment = m \
* plane_wave_coefficient(n, wave_number_k) \
* beam_shape_g(n, m, mode='TE') \
* d_riccati_bessel[n] \
* legendre_pi(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
n += 1
return 1j * result / radial
def beam_shape_g_exa(degree, axicon=AXICON, bessel=True):
""" Computes exact BSC from equations referenced by the article
"""
if bessel:
return special.j0(float((degree + 1 / 2) * np.sin(axicon)))
return (1 + np.cos(axicon)) / (2 * degree * (degree + 1)) \
* (legendre_tau(degree, 1, np.cos(axicon)) \
+ legendre_pi(degree, 1, np.cos(axicon)))