Efficient simulation of multimodal nonlinear propagation in step-index fibers

Abstract

A numerical approach to nonlinear propagation in waveguides based on real-space Gaussian quadrature integration of the nonlinear polarization during propagation is investigated and compared with the more conventional approach based on expressing the nonlinear polarization by a sum of mode overlap integrals. Using the step-index fiber geometry as an example, it is shown that the Gaussian quadrature approach scales linearly or at most quadratically with the number of guided modes and that it can account for mode profile dispersion without additional computational overhead. These properties make it superior for multimode nonlinear simulations extending over wide frequency ranges.

Numerical modelings of ultrashort pulse propagation and conical emission in multimode optical fibers

“…In that respect, recall that mode coupling tensors S ml pn (Eq. ( 19)) are calculated only at the central pump wavelength λ 0 [10,15]. It means that the MM-GNLSE model does not take into account the frequency dependence of nonlinear effects unlike the MM-UPPE.…”

“…However, most of the time, the derived numerical models only support qualitatively experimental results, in particular, when the number of modes involved becomes significant (i.e., higher than 10) and ultrabroadband frequency conversion processes (i.e., more than one octave) also occur [8,9]. Basically, two different approaches can be mentioned, namely the multimode generalized nonlinear Schrödinger equation (MM-GNLSE) [10,11] and the Gross-Pitaevskii equation (GPE) [12][13][14], even if some related alternatives were also investigated [15,16]. The first one considers a modal decomposition of the electrical field and then intermodal nonlinear couplings, whereas as the second one is based on a direct representation of the electric field in the space-time domain and the refractive index distribution acts as a potential term.…”

Approximation of mode profile dispersion in the generalized nonlinear Schrödinger equation superior to the constant overlap approach for weakly guiding fibers

“…The Generalized Nonlinear Schrödinger Equation (GNLSE) is discussed and used extensively in the literature to describe high power pulse propagation in optical fibres, as for example in [14], [17] and [18]. The purpose of this section is to briefly introduce the relevant equations, arriving to the overlap integral formulation of the GNLSE.…”

“…Both Super Continuum generation and DWG encompass large wavelength ranges, and modelling them using constant overlaps can be source of significant errors. In [14] it was shown that an efficient alternative to the overlap integral method is to evaluate the total field and nonlinear polarization on a reduced transverse grid, allowing to include their frequency dependence with an acceptable complexity penalty. This approach, here denoted Gaussian Quadrature (GQ), works well with smooth mode profiles, and is faster than the overlap method when the number of modes is large.…”

Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook

“…Before continuing to explain the MPA, it is worth pointing out that the MPA provides a means of parallelizing many similar equations/numerical schemes, including the (3+1)-D GNLSE, and the methods recently developed by Laegsgaard [82], [83] and Conforti et al [84]. These latter schemes are not discussed in more detail here due to their recency.…”