def set(self, waves: Array[cst.NPFT], h: float, z: float) -> None:
self._step = int(round(z / h))
self._call_counter += 1
# Set parameters -----------------------------------------------
if (self._sigma_e_mccumber):
omega = FFT.ifftshift(
self._omega) # could also change in abstract equation
for i in range(len(self._center_omega_s)):
self._sigma_e_s[i] = McCumber.calc_cross_section_emission(
self._sigma_a_s[i], omega, 0.0, self.N_0[self._step - 1],
self.N_1[self._step - 1], self._T)
for i in range(len(self._center_omega_p)):
self._sigma_e_p[i] = McCumber.calc_cross_section_emission(
self._sigma_a_p[i], omega, 0.0, self.N_0[self._step - 1],
self.N_1[self._step - 1], self._T)
# Add pump and signal power space step -------------------------
if (not self._iter): # first iteration
to_add_s = np.zeros((1, ) + self._shape_step_s)
to_add_p = np.zeros((1, ) + self._shape_step_p)
self._power_s_f = np.vstack((self._power_s_f, to_add_s))
self._power_s_b = np.vstack((to_add_s, self._power_s_b))
self._power_p_f = np.vstack((self._power_p_f, to_add_p))
self._power_p_b = np.vstack((to_add_p, self._power_p_b))
self._power_ase_f = np.vstack((self._power_ase_f, to_add_s))
self._power_ase_b = np.vstack((to_add_s, self._power_ase_b))
if (self._coprop): # First iteration forward
self._N_1 = np.hstack((self._N_1, [0.0]))
else: # First iteration backward -> self._forward is False
self._N_1 = np.hstack(([0.0], self._N_1))
self._step = 0 # construct backward array in bottom-up
# Set signal power ---------------------------------------------
# Truth table:
# if coprop : iter |forward| to do
# 0 | T | set pump
# 1 | F | set pump
# 2 | T | set pump & set signal
# if counterprop: iter|forward| to do
# 0 | T | set pump
# 1 | F | set pump & set signal
if (self._step_update):
if (self._forward):
if (self._signal_on):
self._power_s_f[self._step - 1] = self._get_power_s(waves)
self._power_p_f[self._step - 1] = self._get_power_p(waves)
else:
if (self._signal_on):
self._power_s_b[self._step + 1] = self._get_power_s(waves)
self._power_p_b[self._step + 1] = self._get_power_p(waves)
def op_approx_cross(
self,
waves: Array[cst.NPFT],
id: int,
corr_wave: Optional[Array[cst.NPFT]] = None) -> Array[cst.NPFT]:
"""The approximation operator of the cross terms of the Raman
effect."""
res = np.zeros(waves[id].shape, dtype=cst.NPFT)
if (self._approx_type == cst.approx_type_1
or self._approx_type == cst.approx_type_2
or self._approx_type == cst.approx_type_3):
for i in range(len(waves)):
if (i != id):
res += waves[i] * np.conj(waves[i])
res = FFT.dt_to_fft(res, self._omega, 1)
return -1j * self._T_R * self._eta * res
def calc_raman_gain(omega_bw: float, h_R: Array[float],
center_omega: float, n_0: float, f_R: float,
n_2: float) -> Array[float]:
r"""Calculate the Raman gain.
Parameters
----------
omega_bw :
The angular frequency bandwidth. :math:`[ps^{-1}]`
h_R :
The raman response function. :math:`[ps^{-1}]`
center_omega :
The center angular frequency. :math:`[ps^{-1}]`
n_0 :
The refractive index.
f_R :
The fractional contribution of the delayed Raman response.
:math:`[]`
n_2 :
The non-linear index. :math:`[m^2\cdot W^{-1}]`
Returns
-------
:
The Raman gain.
Notes
-----
.. math:: g_R(\Delta \omega) = \frac{\omega_0}{c n_0} f_R
\chi^{(3)} \Im{\hat{h}_R(\Delta \omega)}
where:
.. math:: \chi^{(3)} = \frac{4\epsilon_0 c n^2}{3} n_2
:math:`\chi^{(3)}` is in :math:`[m^2 \cdot V^{-2}]`.
"""
n_2 *= 1e36 # m^2 W^{-1} = s^3 kg^-1 -> ps^3 kg^-1
chi_3 = 4 * cst.EPS_0 * cst.LIGHT_SPEED * n_0**2 * n_2 / 3
return (center_omega / cst.LIGHT_SPEED / n_0 * f_R * chi_3 *
np.imag(FFT.fft(h_R)))
def open(self, domain: Domain, *fields: List[Field]) -> None:
"""This function is called once before a Stepper began the
computation. Pass the time, wavelength and center wavelength
to all the effects in the equation.
"""
self._init_eq_ids(list(fields))
self._center_omega = np.array([])
for field_list in fields:
for field in field_list:
self._center_omega = np.hstack(
(self._center_omega, field.center_omega))
self._omega = FFT.fftshift(domain.omega)
effects = ["lin", "non_lin", "all"]
for effect in effects:
effect_list = getattr(self, "_effects_{}".format(effect))
for i in range(len(effect_list)):
effect_list[i].omega = self._omega
effect_list[i].time = domain.time
effect_list[i].center_omega = self._center_omega
def op_non_lin(self, waves: Array[cst.NPFT], id: int,
corr_wave: Optional[Array[cst.NPFT]] = None
) -> Array[cst.NPFT]:
r"""Represent the non linear effects of the approximated NLSE.
Parameters
----------
waves :
The wave packet propagating in the fiber.
id :
The ID of the considered wave in the wave packet.
corr_wave :
Correction wave, use for consistency.
Returns
-------
:
The non linear term for the considered wave.
Notes
-----
.. math:: \hat{N} = \mathcal{F}^{-1}\bigg\{i \gamma
\Big(1+\frac{\omega}{\omega_0}\Big)
\mathcal{F}\Big\{ (1-f_R) |A|^2
+ f_R \mathcal{F}^{-1}\big\{\mathcal{F}\{h_R\}
\mathcal{F}\{|A|^2\}\big\}\Big\}\bigg\}
"""
res = FFT.ifft(self.op_non_lin_rk4ip(waves, id) * waves[id])
if (corr_wave is None):
corr_wave = waves[id]
res = np.zeros_like(res)
res = np.divide(res, corr_wave, out=res, where=corr_wave!=0)
return res
def rk4ip_gnlse(f: AbstractFieldEquation, waves: np.ndarray, z: float,
h: float) -> np.ndarray:
r"""Optimized Runge-Kutta interaction picture method.
Parameters
----------
f :
The function to compute.
waves :
The value of the unknown (waves) at the considered
space step.
z :
The current value of the space variable.
h :
The step size.
Returns
-------
:
The one step euler computation results.
Notes
-----
Implementation:
.. math::
\begin{align}
&A^L_j = \exp\Big(\frac{h}{2}\hat{\mathcal{D}}\Big)
\mathcal{F}\{A_j(z)\} &\forall j=1,\ldots,K\\
&k_0 = h \exp\Big(\frac{h}{2}\hat{\mathcal{D}}\Big)
\hat{\mathcal{N}}_0\big(A_1(z), \ldots, A_j(z),
\ldots, A_K(z)\big)&\forall j=1,\ldots,K\\
&k_1 = h \hat{\mathcal{N}}_0\Big(\mathcal{F}^{-1}
\Big\{A^L_{1} +\frac{k_{0,1}}{2},\ldots,
A^L_{j}+\frac{k_{0,j}}{2},\ldots, A^L_{K}
+ \frac{k_{0,K}}{2}\Big\} \Big)
&\forall j=1,\ldots,K\\
&k_2 = h \hat{\mathcal{N}}_0\Big(\mathcal{F}^{-1}
\Big\{A^L_{1} +\frac{k_{1,1}}{2},\ldots, A^L_{j}
+\frac{k_{1,j}}{2},\ldots, A^L_{K}
+ \frac{k_{1,K}}{2}\Big\} \Big)
&\forall j=1,\ldots,K\\
&k_3 = h \hat{\mathcal{N}}_0\Big(\mathcal{F}^{-1}
\Big\{\exp\Big(\frac{h}{2}\hat{\mathcal{D}}\Big)
(A^L_1 + k_{2, 1}) \Big\},\ldots, \nonumber \\
& \qquad \qquad \quad \mathcal{F}^{-1}\Big\{\exp
\Big(\frac{h}{2}\hat{\mathcal{D}}\Big)(A^L_j
+ k_{2,j}) \Big\}, \ldots,\nonumber\\
& \qquad \qquad \quad \mathcal{F}^{-1}\Big\{\exp\Big(
\frac{h}{2}\hat{\mathcal{D}}\Big)(A^L_K + k_{2,K})
\Big\}\Big)&\forall j=1,\ldots,K\\
&A(z+h) = \mathcal{F}^{-1}\Big\{\frac{k_{3,j}}{6}
+\exp\Big(\frac{h}{2}\hat{\mathcal{D}}\Big)
\big(A^L_{j}+\frac{k_{0,j}}{6}+\frac{k_{1,j}}{3}
+\frac{k_{2,j}}{3}\big)\Big\} &\forall j=1,\ldots,K
\end{align}
where :math:`K` is the number of channels.
"""
if (isinstance(f, GNLSE) or isinstance(f, AmpGNLSE)):
h_h = 0.5 * h
exp_op_lin = np.zeros_like(waves)
A_L = np.zeros_like(waves)
k_0 = np.zeros_like(waves)
k_1 = np.zeros_like(waves)
k_2 = np.zeros_like(waves)
k_3 = np.zeros_like(waves)
for i in range(len(waves)):
exp_op_lin[i] = f.exp_op_lin(waves, i, h_h)
for i in range(len(waves)):
A_L[i] = exp_op_lin[i] * FFT.fft(waves[i])
for i in range(len(waves)):
k_0[i] = h * exp_op_lin[i] * f.term_rk4ip_non_lin(waves, i, z)
for i in range(len(waves)):
waves[i] = FFT.ifft(A_L[i] + 0.5*k_0[i])
for i in range(len(waves)):
k_1[i] = h * f.term_rk4ip_non_lin(waves, i, z)
for i in range(len(waves)):
waves[i] = FFT.ifft(A_L[i] + 0.5*k_1[i])
for i in range(len(waves)):
k_2[i] = h * f.term_rk4ip_non_lin(waves, i, z)
for i in range(len(waves)):
waves[i] = FFT.ifft(exp_op_lin[i] * (A_L[i] + k_2[i]))
for i in range(len(waves)):
k_3[i] = h * f.term_rk4ip_non_lin(waves, i, z)
for i in range(len(waves)):
waves[i] = ((k_3[i]/6.0)
+ (exp_op_lin[i] * (A_L[i] + k_0[i]/6.0
+ (k_1[i]+k_2[i])/3.0)))
waves[i] = FFT.ifft(waves[i])
else:
raise RK4IPGNLSEError("Only the the gnlse can be computed with "
"the rk4ip_gnlse method.")
return waves
