Topological beam stirring in a multicore fiber

Multicore fibers (MCF) are perspective media for telecommunications, sensing, imaging and laser technologies. Here, the effect of beam stirring between weakly coupled cores is observed for sub-nanosecond transform-limited pulses of several kW peak power propagating in ~10 m long 7-core fiber, for the first time to our knowledge. In contrast to low-power domain where the output power distribution in the cores is random with large fluctuations sensitive to fiber disturbances, at high power of the input pulse injected in the central core the output power becomes equalized between the cores with fluctuations reduced to <5% being insensitive to disturbances. Similar behavior is observed in cut-back experiments showing that equi-partition is approached at a distance of ~5 m. The performed modeling describes well the experimental results and clarifies mechanisms of the new effect reasoned by a large nonlinear phase shift changing along the pulse and thereby resulting in statistical averaging over the pulse length of multidirectional power transfer processes between cores, thus leading to the robust equilibrium (equi-partitition for hexagonal MCF topology). At the same time, the combined output beam measured in a far field takes a stable bell-shaped profile instead of speckled beam at low powers, similar to the beam self-cleaning effect in multimode fibers.

💡 Research Summary

This paper reports the discovery and thorough investigation of a nonlinear “beam‑stirring” effect in a weakly coupled seven‑core (hexagonal) multicore fiber (MCF). Sub‑nanosecond, transform‑limited pulses (435 ps, 1064 nm) with peak powers ranging from a few hundred watts up to several kilowatts were launched into the central core of an ~10 m long passive MCF. At low powers (≈0.13 kW) the output power distribution among the seven cores is highly random: the power in any individual core fluctuates by more than 30 % from shot to shot, reflecting the linear random coupling caused by micro‑bends and index inhomogeneities. When the input peak power is increased to the kilowatt level (≈6 kW), the situation changes dramatically. The power in each core converges to roughly 1/7 of the total output, and the spread between the maximum and minimum core powers drops below 5 %. This equalization appears after a propagation distance of about 5 m and is essentially independent of external perturbations such as bending or twisting of the fiber.

A cut‑back experiment confirmed that the equalization length shortens as the input power grows, indicating a power‑dependent stabilization length. Near‑field images show that at high power all seven cores emit comparable intensities, while far‑field images reveal a smooth, bell‑shaped beam profile, in stark contrast to the speckled pattern observed at low power. This far‑field self‑cleaning resembles the Kerr‑induced beam self‑cleaning previously reported in multimode fibers, suggesting that a similar statistical averaging mechanism is at work.

To elucidate the underlying physics, the authors developed a coupled‑mode model. The electric field is expressed as a sum of core‑localized modal amplitudes A_j(z,t) multiplied by the fundamental mode profile Ψ(r−r_j). Linear coupling is characterized by an overlap integral J, while random longitudinal variations of the core refractive indices are modeled by δn_j(z) with a characteristic correlation length of 1 mm and a maximum amplitude δn_max. Kerr nonlinearity is introduced via a self‑phase modulation coefficient γ = 5 × 10⁻³ (W·m)⁻¹. The resulting set of coupled nonlinear Schrödinger‑type equations is solved with a split‑step Fourier method (Δt = 5 ps, Δz = 250 µm). By sweeping δn_max (10⁻⁶–10⁻⁴) and J (10⁻⁷–10⁻⁵) and performing ~150 simulations for each experimental power, the authors identified a regime (δn_max ≈ 3 × 10⁻⁶, J ≈ 9 × 10⁻⁷) that reproduces the measured power equalization curves.

The simulations reveal that the equalization only occurs when the coupling is weak (J < δn_max). In this regime, the large nonlinear phase shift accumulated along the pulse (Φ_NL ≈ γ P_in z/7) varies across the temporal envelope, causing the instantaneous power transfer between cores to oscillate rapidly. Averaging over the pulse duration then suppresses the random fluctuations and drives the system toward a statistical equilibrium where each core carries the same average power. The number of phase cycles N ≈ 1 + (γ P_in z/7)² determines how effectively the averaging works; higher input powers increase N and thus accelerate the approach to equilibrium. When the coupling strength is increased by an order of magnitude, the simulations show persistent chaotic power oscillations and no equilibration, confirming the delicate balance between linear coupling and random index perturbations required for the effect.

The authors also compare the nonlinear energy‑transfer length with the nonlinear length L_NL = 1/(γ P_in/7). For the experimental powers, the effective transfer length exceeds L_NL, ensuring that the nonlinear phase dominates over linear coupling and enabling the statistical averaging mechanism. The model predicts that if the index fluctuations are reduced (δn_max → 0) the system reverts to linear random coupling and the equalization disappears, while excessively large fluctuations destroy the coherent phase evolution and again prevent equilibration.

From an application perspective, the beam‑stirring effect offers a passive means to achieve power balancing across multiple cores without active phase control, which is valuable for multicore fiber lasers, high‑power amplifiers, and space‑division multiplexed communication links. The associated far‑field beam self‑cleaning improves beam quality and could simplify beam‑combining architectures. Moreover, the robustness against mechanical disturbances makes the phenomenon attractive for sensing platforms where the fiber may be subject to bending or twisting.

In summary, this work demonstrates that, in weakly coupled multicore fibers, high‑peak‑power sub‑nanosecond pulses experience a nonlinear statistical averaging that drives the system to an equipartition of power among all cores and produces a clean, bell‑shaped output beam. The combined experimental and theoretical analysis clarifies the interplay of Kerr nonlinearity, random linear coupling, and longitudinal index fluctuations, opening new avenues for designing robust, high‑power multicore photonic devices.