def confinement(self, lambda_i, x_germ):
n1 = sellmeier(SiO2, GeO2, x_germ, lambda_i)
n2 = sellmeier(SiO2, GeO2, 0, lambda_i)
NA = np.sqrt(n1**2 - n2**2)
k0 = 2 * np.pi / lambda_i
V = k0 * NA * self.ac
u = miyagi(V, True)
gamma = get_gamma(0, u, V)
print(gamma)
return gamma
np.lib.scimath.sqrt(kappa**2 - sigma**2) * L)) - sigma**2 / kappa**2
return np.real(num / denum)
# a)
best_wl = 0
best_delta = 100000
ref = []
wavelengths = np.linspace(1347e-9, 1350e-9, 10000)
for wl in wavelengths:
n1 = sellmeier(SiO2, GeO2, x_germ, wl)
n2 = sellmeier(SiO2, GeO2, 0, wl)
NA = np.sqrt(n1**2 - n2**2)
k0 = 2 * np.pi / wl
V = k0 * NA * a
u = miyagi(V, True)
n_eff = get_ref_index(u, k0, n1, a)
r = reflextivity(wl, n_eff)
ref.append(r)
new_wl = bragg_lambda(n_eff, Lambda, 1)
if abs(new_wl - wl) < best_delta:
best_delta = abs(new_wl - wl)
best_wl = wl
print(
f"La longueur d'onde de Bragg de premier ordre est de {best_wl * 1e6} µm")
# b)
plt.figure()
plt.plot(wavelengths * 1e6, ref)
plt.xlabel("Longueur d'onde [µm]")
# Parametètres
wl = 1.55e-06
k0 = 2 * np.pi / wl
n1_1 = 1.4519
n2 = 1.44402
a_1 = 2.4e-6
a_2 = 3.69e-6
d = 12e-6
# Calcul n_eff de la première fibre (qui doit être égal au n_eff de la deuxième fibre)
NA = np.sqrt(n1_1**2 - n2**2)
V_1 = k0 * NA * a_1
u_1 = miyagi(V_1, True)
n_eff = get_ref_index(u_1, k0, a_1, n1_1)
print(f"L'indice effectif de la première fibre est {round(n_eff, 6)}")
best_n = 0
best_n_eff = 0
best_V = 0
best_u = 0
best_delta = 10000
for n1 in np.linspace(n2, 1.5, 10000):
NA = np.sqrt(n1**2 - n2**2)
V = k0 * NA * a_2
mi_u = miyagi(V, True)
new_n = get_ref_index(mi_u, k0, a_2, n1)
if abs(new_n - n_eff) < best_delta:
import numpy as np
wl = 633e-9
k0 = 2 * np.pi / wl
NA_values = [0.04, 0.06, 0.08, 0.10, 0.12]
V = np.linspace(1.8, 2.6, 100)
def waist(a, u, w):
return np.sqrt(a**2 * 2 / 3 *
(jv(0, u) / (u * jv(1, u)) + 1 / 2 + 1 / w**2 - 1 / u**2))
if __name__ == '__main__':
for NA in NA_values:
a = V / (k0 * NA)
u = np.array([miyagi(V_val, True) for V_val in V])
w = np.sqrt(V**2 - u**2)
w_0 = waist(a, u, w)
plt.figure(0)
plt.plot(V, w_0 * 1e6, label=f'NA={NA}')
plt.ylabel('Diamètre w$_0$ [µm]')
plt.xlabel('Fréquence normalisée V [-]')
plt.xlim([1.8, 2.6])
plt.ylim([1, 5.8])
plt.legend(ncol=3)
plt.savefig('figs/Num2_w0.pdf', bbox_inches='tight')
plt.show()