Spectral broadening and nonlinear mode coupling in a gas-filled hollow core capillary

In this investigation, we explore the phenomenon of spectral broadening in a gas-filled hollow-core capillary induced by ultra-short pulses, with a focus on nonlinear mode coupling at a power lower than the critical power. As the pulse propagates through the capillary, the spectrum primarily broadens due to self-phase modulation, and concurrently, high-order modes are generated through interactions between different modes. Both experimental and numerical results consistently demonstrate that the spectral region near the center of the spectrum remains within the fundamental mode, while the spectral edges propagate in higher-order modes, predominantly in the LP \(_{12}\) ${}_{12}$ mode generated through nonlinear mode coupling within the gas-filled hollow-core capillary. This observation is relatively weak but is of paramount importance for the design of post-compression systems in gas-filled hollow-core capillaries with a high-quality beam profile when the power starts to reach the critical level. Understanding and then accommodating the dynamics of nonlinear mode coupling are crucial for achieving the desired characteristics and beam quality while optimising the performance of such systems.