def _op_approx_self(self,
waves: np.ndarray,
id: int,
corr_wave: Optional[np.ndarray] = None) -> np.ndarray:
"""The approximation of the operator of the
self-steepening effect for the considered wave."""
A = waves[id]
res = np.zeros(A.shape, dtype=cst.NPFT)
if (self.approx_type == cst.approx_type_1):
res = FFT.dt_to_fft(A * np.conj(A) * A, self._omega, 1)
if (corr_wave is None):
corr_wave = waves[id]
res[corr_wave == 0] = 0
res = np.divide(res, corr_wave, out=res, where=corr_wave != 0)
if (self.approx_type == cst.approx_type_2):
res = (np.conj(A) * FFT.dt_to_fft(A, self._omega, 1) +
FFT.dt_to_fft(A * np.conj(A), self._omega, 1))
if (self.approx_type == cst.approx_type_3):
res = (2 * np.conj(A) * FFT.dt_to_fft(A, self._omega, 1) +
A * FFT.dt_to_fft(np.conj(A), self._omega, 1))
return -1 * self._S[id] * res
def _op_approx_cross(self,
waves: np.ndarray,
id: int,
corr_wave: Optional[np.ndarray] = None) -> np.ndarray:
"""The approximation of the operator of the cross terms of the
self-steepening effect."""
A = waves[id]
res = np.zeros(A.shape, dtype=cst.NPFT)
if (corr_wave is None):
corr_wave = waves[id]
if (self.approx_type == cst.approx_type_1):
for i in range(len(waves)):
if (i != id):
res += waves[i] * np.conj(waves[i]) * A
res = FFT.dt_to_fft(res, self._omega, 1)
res[corr_wave == 0] = 0.
res = np.divide(res, corr_wave, out=res, where=corr_wave != 0)
if (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_ = np.zeros(A.shape, dtype=cst.NPFT)
res_ = np.divide(res, corr_wave, out=res_, where=corr_wave != 0)
res = (res_ * FFT.dt_to_fft(A, self._omega, 1) +
FFT.dt_to_fft(res, self._omega, 1))
return -1 * self._S[id] * res
def op_approx_self(
self,
waves: Array[cst.NPFT],
id: int,
corr_wave: Optional[Array[cst.NPFT]] = None) -> Array[cst.NPFT]:
"""The approximation of the operator of the Raman effect for the
considered wave."""
A = waves[id]
res = np.zeros(A.shape, dtype=cst.NPFT)
if (self._approx_type == cst.approx_type_1
or self._approx_type == cst.approx_type_2):
res = FFT.dt_to_fft(A * np.conj(A), self._omega, 1)
if (self._approx_type == cst.approx_type_3):
res = (np.conj(A) * FFT.dt_to_fft(A, self._omega, 1) +
A * FFT.dt_to_fft(np.conj(A), self._omega, 1))
return -1j * self._T_R * res
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