3.3. fmas.raman_response¶
This module implements several Raman response functions. Numerical models of the Raman response are important for the accurate theoretical description of the propagation of optical pulses with short duration and high peak power [MM1986] [G1986].
The following Raman response models are currently supported:
Blow-Wood type Raman response function [BW1989]. |
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Lin-Agrawal type Raman response function [LA2006]. |
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Hollenbeck-Cantrell type Raman response function [HC2002]. |
- MM1986
F. M. Mitschke, L. F. Mollenauer, Discovery of the soliton self-frequency shift, Opt. Lett. 11 (1986) 659, https://doi.org/10.1364/OL.11.000659.
- G1986
J. P. Gordon, Theory of the soliton self-frequency shift, Opt. Lett. 11 (1986) 662, https://doi.org/10.1364/OL.11.000662.
- BW1989(1,2,3)
K. J. Blow, D. Wood, Theoretical description of transient stimulated Raman scattering in optical fibers. IEEE J. Quantum Electron., 25 (1989) 1159, https://doi.org/10.1109/3.40655.
- LA2006(1,2,3)
Q. Lin, G. P. Agrawal, Raman response function for silica fibers, Optics Letters, 31 (2006) 3086, https://doi.org/10.1364/JOSAB.6.001159.
- HC2002
D. Hollenbeck and C. D. Cantrell, Multiple-vibrational-mode mopdel for fiber-optic Raman gain spectrum and response function, J. Opt. Soc. Am. B, 19 (2002) 2886, https://doi.org/10.1364/JOSAB.19.002886.
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fmas.raman_response.h_BW(t, tau1=12.2, tau2=32.0)¶ Blow-Wood type Raman response function [BW1989].
Implements simple Raman response function for silica fibers based on a single damped harmonic oscillator with Lorentzian linewidth [BW1989], given by
\[h_{\mathrm{BW}}(t) = \frac{\tau_1^2 + \tau_2^2}{\tau_1\tau_2^2}\, e^{-t/\tau_2}\, \sin(t/\tau_1)\,\theta(t),\]where causality is assured by the unit step fuction \(\theta(t)\). This Raman response model can be adapted to fit various types of nonlinear fibers. For example, using the parameters \(\tau_1=12.2\,\mathrm{fs}\), and \(\tau_2=32\,\mathrm{fs}\), toghether with a fractional Raman contribution \(f_R=0.18\) is adequate for modeling the Raman response of of silica fibers.
- Parameters
t (
numpy.ndarray) – temporal grid.tau1 (
float) – Raman response parameter (default: 12.2 fs).tau2 (
float) – Raman response parameter (default: 32.0 fs).
- Returns
Angular-frequency representation of the Raman response.
- Return type
numpy.ndarray
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fmas.raman_response.h_HC(t)¶ Hollenbeck-Cantrell type Raman response function [HC2002].
Implements intermediate broadening model for Raman response function of silica fibers based on multiple vibrational frequency modes of the Si-O-Si compound [HC2002]. The time-domain representation of this Raman response model is given by
\[h_{\mathrm{HC}}(t) = \sum_{n=1}^{13} A_n\, e^{-\gamma_n t - \Gamma_n^2 t^2/4}\,\sin(\omega_n t)\,\theta(t),\]with parameter sequences \(\{\omega_n\}_{n=1}^{13}\), \(\{A_n\}_{n=1}^{13}\), \(\{\gamma_n\}_{n=1}^{13}\), and \(\{\Gamma_n\}_{n=1}^{13}\), summarized in the table below.
n
omega_n (rad/fs)
A_n (-)
gamma_n (1/ps)
Gamma_n (1/ps)
1
0.01060
1.00
1.64
4.91
2
0.01884
11.40
3.66
10.40
3
0.04356
36.67
5.49
16.48
4
0.06828
67.67
5.10
15.30
5
0.08721
74.00
4.25
12.75
6
0.09362
4.50
0.77
2.31
7
0.11518
6.80
1.30
3.91
8
0.13029
4.60
4.87
14.60
9
0.14950
4.20
1.87
5.60
10
0.15728
4.50
2.02
6.06
11
0.17518
2.70
4.71
14.13
12
0.20343
3.10
2.86
8.57
13
0.22886
3.00
5.02
15.07
- Parameters
t (
numpy.ndarray) – temporal grid.- Returns
Angular-frequency representation of the Raman response.
- Return type
numpy.ndarray
-
fmas.raman_response.h_LA(t)¶ Lin-Agrawal type Raman response function [LA2006].
Implements an improved Raman response model, taking into account the anisotropic nature of Raman scattering [LA2006], given by
\[h_{\mathrm{LA}}(t) = (1-f_b)\,h_{\mathrm{BW}}(t) +f_b\,\frac{2\tau_b-t}{\tau_b^2} e^{-t/\tau_b}\,\theta(t),\]with \(h_{\mathrm{BW}}(t)\) given by
h_BW, and parameters \(\tau_b=96\,\mathrm{fs}\), and \(f_b = 0.21\).- Parameters
t (
numpy.ndarray) – temporal grid.- Returns
Angular-frequency representation of the Raman response.
- Return type
numpy.ndarray