Modeling Light Propagation and Amplification Efficiency in Highly Multimode, Yb-doped Fiber Amplifiers

Abstract

Multimode fibers have been proposed for mitigating nonlinear effects in high-power fiber amplifiers, allowing for significant power scaling. Most previous studies on light propagation in continuous-wave fiber amplifiers focus on single mode or few mode fibers. Here we develop a tractable numerical model to simulate light propagation in narrowband, highly multimode fiber amplifiers, which takes into account gain saturation, pump depletion and mode-dependent gain. We consider a frequency domain, field based model, with modal gain being dependent on both intramodal gain and gain-induced mode coupling. We derive coupled equations for the evolution of signal modal amplitudes, pump power and population inversion, and numerically solve these equations using a finite-difference method. For highly multimode excitations, the optical intensity in the fiber is speckled and various modes grow at different rates, due to differential overlap with the gain medium and spatial hole burning. Our analysis is applied to Yb-doped fibers, with a quasi-quantitative analysis of the specific case of Yb, identifying different regimes in which either spontaneous emission (SE) or amplified spontaneous emission (ASE) limit amplifier efficiency, especially for larger core and multimode fibers. Finally, we incorporate ASE and spectrally resolved optical channels into our model and demonstrate the experimentally verifiable phenomenon of ASE suppression with sufficient input signal power. Our model can be combined with existing models for various nonlinear effects, providing a useful tool for quantitatively studying nonlinearity mitigation and power scaling in multimode fiber amplifiers.

Figures (5)

• Figure 1: Results of the multimode fiber amplifier model. 500 W of pump power and 10 W of signal power, distributed evenly amongst the 24 supported modes (accounting for the two polarizations corresponding to each propagation constant), are launched into the fiber described in \ref{['ParametersA']}. (a) Signal and pump power as a function of z. The maximum possible signal, as set by the Stokes efficiency, is displayed with the dashed line. (b) Power carried by each individual mode as a function of z. (c) Transverse multimode speckle pattern (2D plot on left) and resulting population inversion (3D mesh plot on right) at (i) z = 0 m, (ii) 0.56 m and (iii) 4.48 m (indicated on (a)).
• Figure 2: (a) Modal gain as a function of z for four selected modes from the fiber described in \ref{['ParametersA']}. (b) Modal gain for all 24 supported modes of the fiber, zoomed-in to the inset section of (a). (c) Slice of the population inversion along the x-z plane. (d) The $g_{mn}$ matrix, as defined in \ref{['gmn']}, at z=5.6 m.
• Figure 3: (a) Amplifier efficiency with respect to the Stokes efficiency as a function of core diameter (with the cladding diameter scaled by a constant factor of the core diameter - here $d_{cl}=5d_{co}$). Nominal power is defined as 1 kW input pump and 30 W input signal at 10 $\upmu$m core diameter, with constant intensity demanding this power is increased as per the square of the core size increase. Dopant density is scaled as 1/$d_{co}^2$ such that the dopant number remains constant as core size is changed. In this way, the pump absorption length remains similar for all cases. The first 20 modes of each fiber are chosen for fibers supporting more than 20 modes for comparison and for computational reasons. (b) Amplifier efficiency with respect to the Stokes efficiency for the cases of co- and counterpumping, with parameters otherwise the same as the red curve in (a).
• Figure 4: Progression of pump power, signal power and backwards and forwards propagating ASE for an 80 $\upmu$m core diameter Yb-doped fiber with 1 kW pump input, and varying signal inputs. The input signal is expressed as the normalized signal power $S_S$ (as used in \ref{['N?']}), where for the given fiber parameters, $P_{sat,S}=36$ mW. This input signal power is divided equally amongst the first 20 modes of the 173 guided modes in the fiber, to avoid highly multimode effects such as high mode-dependent loss of modes near the cutoff.
• Figure 5: (a) Input signal power and (b) normalized signal power ($S_S$) required to reach 95% output signal efficiency at a length of 95% pump absorption as a function of core diameter. The cladding diameter is set to 5$d_{co}$, hence for constant input pump power, the intensity and saturation decreases as $\sim d_{co}^{-2}$. The primary limits on amplifier efficiency for the regimes of small core, high pump saturation vs large core, low pump saturation are labelled as ASE limit and SE limit respectively.