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Added Vincetti model of revolver fibers

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Benoît Sierro
2023-03-01 17:16:25 +01:00
parent 89ea3cafc7
commit c06275565e
1 changed files with 224 additions and 0 deletions
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src/scgenerator/physics/fiber.py
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@@ -914,3 +914,227 @@ def extinction_distance(loss: T, ratio=1 / e) -> T:
def L_eff(loss: T, length: float) -> T: def L_eff(loss: T, length: float) -> T:
return -np.expm1(-loss * length) / loss return -np.expm1(-loss * length) / loss
def core_radius_from_capillaries(tube_radius: float, gap: float, n_tubes: int) -> float:
k = 1 + 0.5 * gap / tube_radius
return tube_radius * (k / np.sin(np.pi / n_tubes) - 1)
def gap_from_capillaries(core_radius: float, tube_radius: float, n_tubes: int) -> float:
s = np.sin(np.pi / n_tubes)
return 2 * (s * (tube_radius + core_radius) - tube_radius)
def normalized_frequency_vincetti(
wl: np.ndarray, thickness: float, n_clad_2: np.ndarray, n_gas_2: np.ndarray
) -> np.ndarray:
"""
eq. 3 of [1] in n_eff_vincetti
Parameters
----------
wl : ndarray
wavelength array
thickness : float
thickness of the capillary tube
n_clad_2 : ndarray
real refractive index of the cladding squared corresponding to wavelengths in wl
n_gas_2 : ndarray
real refractive index of the filling gas squared
"""
return 2 * thickness / wl * np.sqrt(n_clad_2 - 1)
def effective_core_radius_vincetti(
wl: np.ndarray, f: np.ndarray, r: float, g: float, n: int
) -> np.ndarray:
"""
Parameters
----------
wl : ndarray
wavelength array
f : ndarray
corresponding normalized frequency
r : float
capillary external radius
g : float
gap size bewteen capillaries
n : int
number of tubes
"""
r_co = core_radius_from_capillaries(r, g, n)
factor = 1.027 + 0.001 * (f + 2 / f**4)
# | Missing in paper
# V
inner = r_co**2 + n / np.pi * 0.046875 * r**2 * (1 + (3 + 20 * wl / r_co) * g / r)
return factor * np.sqrt(inner)
def li_vincetti(f_2: T, f0_2: float) -> T:
k = f0_2 - f_2
return k / (k**2 + 9e-6 * f_2)
def cutoff_frequency_he_vincetti(mu: int, nu: int, t_ratio: float, n_clad_0: float) -> np.ndarray:
"""
eq. (4) in [2] of n_eff_vincetti
Parameters
----------
mu : int
azimuthal mode number
nu : int
radial mode number
t_ratio : float
t/r_ext
n_clad_0 : float
refractive index of the cladding material, generally at the pump wavelength
"""
if nu == 1:
base = np.abs(0.21 + 0.175 * mu - 0.1 * (mu - 0.35) ** -2)
corr = 0.04 * np.sqrt(mu) * t_ratio
return base * t_ratio ** (0.55 + 5e-3 * np.sqrt(n_clad_0**4 - 1)) + corr
elif nu >= 2:
return 0.3 / n_clad_0**0.3 * (0.5 * nu) ** -1.2 * np.abs(mu - 0.8) * t_ratio + nu - 1
else:
raise ValueError(f"nu must be a strictly positive integer, got {nu}")
def cutoff_frequency_eh_vincetti(mu: int, nu: int, t_ratio: float, n_clad_0: float) -> np.ndarray:
"""
eq. (5) in [2] of n_eff_vincetti
Parameters
----------
mu : int
azimuthal mode number
nu : int
radial mode number
t_ratio : float
t/r_ext
n_clad_0 : float
refractive index of the cladding material, generally at the pump wavelength
"""
if nu == 1:
base = 0.73 + 0.1425 * (mu**0.8 + 1.5) - 0.04 / (mu - 0.35)
expo = 0.5 - 0.1 * (n_clad_0 - 1) * (mu + 0.5) ** -0.1
corr = 0
elif nu >= 2:
base = (
(11.5 * nu**-1.2 / (7.75 - nu))
* (0.34 + 0.25 * mu * (n_clad_0 / 1.2) ** 1.15)
* (mu + 0.2 / n_clad_0) ** -0.15
)
expo = 0.75 + 0.06 * n_clad_0**-1.15 + 0.1 * np.sqrt(1.44 / n_clad_0) * (nu - 2)
corr = nu - 1
else:
raise ValueError(f"nu must be a positive integer, got {nu}")
return base * t_ratio**expo + corr
def v_sum_vincetti(f: np.ndarray, t_ratio: float, n_clad_0: np.ndarray, n_terms: int) -> np.ndarray:
f_2 = f**2
out = np.zeros_like(f)
for nu in range(1, n_terms + 1):
out[:] += li_vincetti(f_2, cutoff_frequency_he_vincetti(1, nu, t_ratio, n_clad_0) ** 2)
out[:] += li_vincetti(f_2, cutoff_frequency_eh_vincetti(1, nu, t_ratio, n_clad_0) ** 2)
out *= 2e3
return out
def n_eff_correction_vincetti(
wl: np.ndarray, f: np.ndarray, t_ratio: float, r_co: float, n_clad_0: float, n_terms: int
) -> np.ndarray:
"""
eq. 6 from [1] in n_eff_vincetti
Parameters
----------
wl : np.ndarray
wavelength array
f : np.ndarray
corresponding normalized frequency
t_ratio : float
t (tube thickness) / r (external tube radius)
r_co : float
core radius
n_clad_0 : float
refractive index of the cladding (usu. at pump wavelength)
n_terms : int
how many resonances to calulcate
"""
factor = 4.5e-7 / (1 - t_ratio) ** 4 * (wl / r_co) ** 2
return factor * v_sum_vincetti(f, t_ratio, n_clad_0, n_terms)
def n_eff_vincetti(
wl_for_disp: np.ndarray,
wavelength: float,
n_gas_2: np.ndarray,
thickness: float,
tube_radius: float,
gap: float,
n_tubes: int,
n_terms: int = 8,
n_clad_2: np.ndarray | None = None,
):
"""
Parameters
----------
wl_for_disp : ndarray
wavelength (m) array over which to compute the refractive index
wavelength : float
center wavelength / pump wavelength
n_gas_2 : ndarray
n^2 of the filling gas
thickness : float
thickness of the structural capillary tubes
tube_radius : float
external radius of the strucural capillaries
gap : float
gap between the structural capillary tubes
n_tubes : int
number of capillary tubes
n_terms : int
number of resonances to calculate, by default 8
n_clad_2: ndarray | None
n^2 of the cladding, by default Silica
Returns
-------
effective refractive index according to the Vincetti model
Internal symbols help
---------------------
f: normalized frequency
r_co_eff: effective core radius
References
----------
[1] ROSA, Lorenzo, MELLI, Federico, et VINCETTI, Luca. Analytical Formulas for Dispersion and
Effective Area in Hollow-Core Tube Lattice Fibers. Fibers, 2021, vol. 9, no 10, p. 58.
[2] VINCETTI, Luca et ROSA, Lorenzo. A simple analytical model for confinement loss estimation
kin hollow-core Tube Lattice Fibers. Optics Express, 2019, vol. 27, no 4, p. 5230-5237.
"""
if n_clad_2 is None:
n_clad_2 = mat.Sellmeier.load("silica").n_gas_2(wl_for_disp)
# n_clad_0 = np.sqrt(n_clad_2[argclosest(wl_for_disp, wavelength)])
n_clad_0 = np.sqrt(n_clad_2)
f = normalized_frequency_vincetti(wl_for_disp, thickness, n_clad_2, n_gas_2)
r_co_eff = effective_core_radius_vincetti(wl_for_disp, f, tube_radius, gap, n_tubes)
r_co = core_radius_from_capillaries(tube_radius, gap, n_tubes)
d_n_eff = n_eff_correction_vincetti(
wl_for_disp, f, thickness / tube_radius, r_co, n_clad_0, n_terms
)
n_gas = np.sqrt(n_gas_2)
# eq. (21) in [1]
return n_gas - 0.125 / n_gas * (u_nm(1, 1) * wl_for_disp / (np.pi * r_co_eff)) ** 2 + d_n_eff