raman#
- pynlo.utility.chi3.raman(n, dt, r_weights, b_weights=None, analytic=True)[source]#
Calculate the frequency-domain Raman and instantaneous nonlinear response function.
The equations used are the approximated formulations as summarized in section 2.3.3 of Agrawal’s Nonlinear Fiber Optics [1]. More accurate simulations may be obtainable using digitized experimental measurements, such as those shown in figure 2.2 of [1]. The coefficients listed in Agrawal for silica-based fibers are as follows:
r_weights = [0.245*(1-0.21), 12.2e-15, 32e-15] # resonant contribution b_weights = [0.245*0.21, 96e-15] # boson contribution
- Parameters:
- nint
The number of points in the time domain.
- dtfloat
The time grid step size.
- r_weightsarray_like of float
The contributions due to resonant vibrations. Must be given as
[fraction, tau_1, tau_2], where fraction is the fractional contribution of the resonance to the total nonlinear response function, tau_1 is the period of the vibrational frequency, and tau_2 is the resonance’s characteristic decay time. More than one resonance may be entered using an (n, 3) shaped array.- b_weightsarray_like of float, optional
The contributions due to boson peaks found in amorphous materials. Must be given as
[fraction, tau_b], where fraction is the fractional contribution of the boson peak to the total nonlinear response function, and tau_b is the boson peak’s characteristic decay time. More than one peak may be entered using an (n, 2) shaped array.- analyticbool, optional
A flag that sets the proper normalization for use with the analytic or real-valued representation. The default normalizes for the analytic representation, which is the proper format for use with the NLSE model. Set this parameter to False if using the UPE model.
- Returns:
- rv_gridndarray of float
The origin-continuous frequency grid associated with the nonlinear response function.
- nonlinear_vndarray of complex
The frequency-domain nonlinear response function. This is defined over the frequency grid given by
dv=1/(n*dt).
Notes
For the carrier-resolved or real-valued representation, an additional factor of 3/2 is necessary to properly normalize the Raman response. The formulas used in this method have been fit to the analytic representation, which is normalized assuming that all three self-phase modulation pathways fold through baseband. In the real-valued domain however, only two pass through baseband. The third pathway is through the second harmonic. Thus, in the real-valued representation the Raman response must be renormalized to produce the same nonlinear response against 2/3 the spectral amplitude.
References
[1] (1,2)Agrawal GP. Nonlinear Fiber Optics. Sixth ed. London; San Diego, CA;: Academic Press; 2019. https://doi.org/10.1016/B978-0-12-817042-7.00009-9