def test_snellnormal(self):
'''Snell's law at normal incidence'''
n1 = 1.0
n2 = 1.5
theta_i = 0
snell_out = tf.snell_theta_t(n1, n2, theta_i)
self.assertEqual(snell_out, 0)
def test_snellangle(self):
'''Snell's law, incident at 45 degrees tested
against exact sine values for total internal reflection'''
n1 = 2
n2 = np.sqrt(2)
theta_i = 45*tf.degrees
snell_out = tf.snell_theta_t(n1, n2, theta_i)
self.assertAlmostEqual(snell_out, np.pi/2)
def test_fresnel_s_energyconservation(self):
'''Energy conservation for reflected and transmitted
amplitudes of s poarised light at an air-glass interface'''
theta_i = 15
n_1 = 1.0
n_2 = 1.5
theta_t = tf.snell_theta_t(n_1, n_2, theta_i)
r = tf.fresnel_r_s(n_1, n_2, theta_i, theta_t)
t = tf.fresnel_t_s(n_1, n_2, theta_i, theta_t)
R = r**2
T = t**2 * n_2*np.cos(theta_t)/n_1/np.cos(theta_i)
test_energy = R + T
self.assertAlmostEqual(test_energy, 1)
# Input
n_cov = 1.0
n_film = 1.45
n_subs = 3.8
t_film = 800
AOI = 30
lambda_0 = np.arange(500, 1000) # nm
# Angles
theta_i = AOI * tf.degrees # incident
theta_f = tf.snell_theta_t(n_cov, n_film, theta_i) # film
theta_t = tf.snell_theta_t(n_film, n_subs, theta_f) # transmitted
# Fresnel coefficients for both polarisations
fresnel_s = {
'r12': tf.fresnel_r_s(n_cov, n_film, theta_i, theta_f),
'r23': tf.fresnel_r_s(n_film, n_subs, theta_f, theta_t),
't12': tf.fresnel_t_s(n_cov, n_film, theta_i, theta_f),
't21': tf.fresnel_t_s(n_film, n_cov, theta_f, theta_i),
}
fresnel_p = {
'r12': tf.fresnel_r_p(n_cov, n_film, theta_i, theta_f),
'r23': tf.fresnel_r_p(n_film, n_subs, theta_f, theta_t),
't12': tf.fresnel_t_p(n_cov, n_film, theta_i, theta_f),
import numpy as np
import matplotlib.pyplot as plt
import thinfilm as tf
# Input
n_cov = 1.0
n_sub = 1.45
AOI = np.arange(0, 90)
# Calculation
theta_i = AOI * tf.degrees
theta_t = tf.snell_theta_t(n_cov, n_sub, theta_i)
r_s = tf.fresnel_r_s(n_cov, n_sub, theta_i, theta_t)
r_p = tf.fresnel_r_p(n_cov, n_sub, theta_i, theta_t)
# Graphical output
fig, ax = plt.subplots()
ax.plot(AOI, np.abs(r_s)**2, 'C0--', label="S polarisation")
ax.plot(AOI, np.abs(r_p)**2, 'C3--', label="P polarisation")
ax.set_xlabel('Angle of incidence (degrees)')
ax.set_ylabel('Reflectance')
ax.legend()
fig.savefig('./example_figures/brewsters.png')