Numerical simulation of incoherent optical wave propagation in nonlinear fibers

Abstract

The present work concerns the study of pulsed laser systems containing a fibre amplifier for boosting optical output power. In this paper, this fibre amplification device is included into a MOPFA laser, a master oscillator coupled with fibre amplifier, usually a cladding-pumped high-power amplifier often based on an ytterbium-doped fibre. An experimental study has established that the observed nonlinear effects (such as Kerr effect, four waves mixing, Raman effect) could behave very differently depending on the characteristics of the optical source emitted by the master laser. However, it has not been yet possible to determine from the experimental data if the statistics of the photons is alone responsible for the various nonlinear scenarios observed. Therefore, we have developed a numerical simulation software for solving the generalised nonlinear Schrödinger equation with a stochastic source term in order to validate the hypothesis that the coherence properties of the master laser are mainly liable for the behaviour of the observed nonlinear effects.

Embedded Runge–Kutta scheme for step-size control in the interaction picture method

“…In [1][2][3] it is solved by a Fourier spectral method. For the GNLSE, problem (16) where Ω = R can be solved by a direct use of Fourier transforms [4,14]. Moreover the cost of the evaluation of the 4 non-linear terms N(ϕ) is strongly dependent to the physical application.…”

“…In the framework of a project on the numerical simulation of incoherent optical wave propagation in non-linear fibers [14] we have implemented the ERK4(3)-IP method for solving the GNLS problem (2). We present in this section numerical results from the ERK4(3) method on 2 selected applications in optics: the propagation of optical solitons and the propagation of a picosecond pulse into a single-mode fiber where fiber losses, nonlinear Raman and Kerr effects and high order chromatic dispersion are taken into account.…”

“…The experimental investigation undertaken in [4] indicates that the RK4-IP method exhibits interesting convergence properties and provides more accurate numerical results than comparable SS methods. This work on the RK4-IP for solving the GNLSE has come to our attention while working on the numerical simulation of incoherent optical wave propagation in non-linear fibers [14]. In [15] we have investigated the numerical properties of the RK4-IP method and we have made a precise comparison between the RK4-IP method and the Symmetric Split-Step Fourier method with fourth-order Runge-Kutta scheme (S3F-RK4 method).…”

The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics

“…One practical consequence when dealing with problems in nonlinear optics is that the number of discretisation points m has usually to be chosen very large in order to have a frequency window wide enough to embrace all the physical relevant information (e.g. the study of pulsed laser systems with fiber amplifier described in [15] imposes values of m in the range 2 20 -2 23 ). Therefore, although there exists an additional error in the RK4-IP method related to the computation of FT, this error is generally several orders of magnitude lower than the approximation error in the RK4-IP method.…”

“…Equation (1.1) does not take into account other physical phenomena such as amplified spontaneous emission and Raman spontaneous emission. Our interest for the GNLSE originates from a study of pulsed laser systems of MOPFA type (a master oscillator coupled with fiber amplifier usually a claddingpumped high-power amplifier based on an ytterbium-doped fiber), see [15] for details. The PDE (1.1) is to be solved for all z in a given interval [0, L] where L denotes the length of the fiber and for all "local time" t ∈ R. It is considered together with the following boundary condition A(0, t) = a 0 (t) ∀t ∈ R, where a 0 is a given complex valued function.…”