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 radial_electric_tm_increment(max_it,
radial,
theta=np.pi / 2,
phi=0,
wave_number_k=WAVE_NUMBER):
result = 0
riccati_bessel_list = _riccati_bessel_j(get_max_it(radial),
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
for n in range(1, max_it):
for m in DEGREES:
increment = plane_wave_coefficient(n, wave_number_k) \
* beam_shape_g(n, m, mode='TM') \
* (d2_riccati_bessel_j(n, wave_number_k * radial) \
+ riccati_bessel[n]) \
* legendre_p(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
return abs(wave_number_k * result)
def radial_magnetic_i_te(radial, theta, phi, wave_number_k):
""" Computes the radial component of inciding magnetic field in TE mode.
"""
result = 0
n = 1
riccati_bessel_list = _riccati_bessel_j(get_max_it(radial),
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
while n <= get_max_it(radial):
for m in DEGREES:
increment = plane_wave_coefficient(n, wave_number_k) \
* beam_shape_g(n, m, mode='TE') \
* (d2_riccati_bessel_j(n, wave_number_k * radial) \
+ riccati_bessel[n]) \
* legendre_p(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
n += 1
return wave_number_k * result
def test_increment_decay():
from glmt.specials import _riccati_bessel_j, d2_riccati_bessel_j, legendre_p
from glmt.glmt import plane_wave_coefficient, beam_shape_g
max_it = 1000
r = np.linspace(0, 100E-6, 5)
wave_number_k = WAVE_NUMBER
theta = np.pi/2
phi = 0
for radial in r:
riccati_bessel_list = _riccati_bessel_j(max_it,
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
s = []
result = 0
n = 1
print(radial)
while n < max_it:
for m in [-1, 1]:
increment = plane_wave_coefficient(n, wave_number_k) \
* beam_shape_g(n, m, mode='TM') \
* (d2_riccati_bessel_j(n, wave_number_k * radial) \
+ riccati_bessel[n]) \
* legendre_p(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
s.append(abs(wave_number_k * result))
n += 1
plt.plot(range(1, max_it), s)
plt.title("%s micrômetros" % (radial / 1E-6))
plt.xlabel('N')
plt.ylabel('|E| [V/m]')
N = get_max_it(radial)
plt.plot(N, s[N], 'rx', label='N(r) = %s' % N)
plt.legend()
print(result)
plt.show()