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field_components.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Nov 9 14:28:55 2019
@author: luizv
"""
# -*- coding: utf-8 -*-
"""
Created on Tue May 14 10:02:23 2019
@author: luizv
"""
import numpy as np
from glmtscatt.specials import (_riccati_bessel_j, _riccati_bessel_y,
legendre_p, legendre_tau, legendre_pi,
riccati_bessel_j, riccati_bessel_y,
d_riccati_bessel_j, d_riccati_bessel_y,
d2_riccati_bessel_j, d2_riccati_bessel_y,
riccati_bessel_radial_i, riccati_bessel_radial_s)
from glmtscatt.utils import (get_max_it, one, exp_im, m_exp_im,
inverse, multiply_function)
def plane_wave_coefficient(degree, wave_number_k):
""" Computes plane wave coefficient :math:`c_{n}^{pw}` """
return (1 / (1j * wave_number_k)) \
* pow(-1j, degree) \
* (2 * degree + 1) / (degree * (degree + 1))
def radial_electric_i_tm(radial, theta, phi,
wave_number_k, degrees=[-1, 1],
bscs={}):
""" Computes the radial component of incident electric field in TM mode.
"""
result = 0
n = 1
riccati_bessel_list = _riccati_bessel_j(get_max_it(radial, wave_number_k),
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
max_it = get_max_it(radial, wave_number_k)
# while n <= get_max_it(radial, wave_number_k):
while n <= max_it:
for m in degrees:
if n >= m:
increment = plane_wave_coefficient(n, wave_number_k) \
* bscs[(n, m)] \
* (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 theta_electric_i_tm(radial, theta, phi, wave_number_k,
degrees=[-1, 1], bscs={}):
""" Computes the theta component of inciding electric field in TM 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),
wave_number_k * radial)
d_riccati_bessel = riccati_bessel_list[1]
max_it = get_max_it(radial, wave_number_k)
while n <= max_it:
for m in degrees:
if n >= m:
increment = plane_wave_coefficient(n, wave_number_k) \
* bscs[(n, m)] \
* d_riccati_bessel[n] \
* legendre_tau(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
n += 1
return result / radial
def theta_electric_i_te(radial, theta, phi, wave_number_k,
degrees=[-1, 1], bscs={}):
""" Computes the theta component of inciding electric 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),
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
max_it = get_max_it(radial, wave_number_k)
while n <= max_it:
for m in degrees:
if n >= m:
increment = m \
* plane_wave_coefficient(n, wave_number_k) \
* bscs[(n, m)] \
* riccati_bessel[n] \
* legendre_pi(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
n += 1
return result / radial
def phi_electric_i_tm(radial, theta, phi, wave_number_k,
degrees=[-1, 1], bscs={}):
""" Computes the phi component of inciding electric field in TM 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),
wave_number_k * radial)
d_riccati_bessel = riccati_bessel_list[1]
max_it = get_max_it(radial, wave_number_k)
while n <= max_it:
for m in degrees:
if n >= m:
increment = m \
* plane_wave_coefficient(n, wave_number_k) \
* bscs[(n, m)] \
* 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 phi_electric_i_te(radial, theta, phi, wave_number_k,
degrees=[-1, 1], bscs={}):
""" Computes the phi component of inciding electric field in TE mode.
"""
result = 0
n = 1
m = 0
# 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),
wave_number_k * radial)
riccati_bessel = riccati_bessel_list[0]
max_it = get_max_it(radial, wave_number_k)
while n <= max_it:
for m in degrees:
if n >= m:
increment = plane_wave_coefficient(n, wave_number_k) \
* bscs[(n, m)] \
* riccati_bessel[n] \
* legendre_tau(n, abs(m), np.cos(theta)) \
* np.exp(1j * m * phi)
result += increment
n += 1
return 1j * result / radial