Effect of nonlinear lensing on the coupling of ultrafast laser pulses to hollow-core waveguides

Gas-filled hollow-core fibers are a flexible platform for the manipulation of ultrafast laser pulses through a variety of nonlinear optical effects. Efficient high-fidelity coupling of the initial pulses is very important for system performance. Here we study the effect of self-focusing in gas-cell windows on the coupling of ultrafast laser pulses into hollow-core fibers using (2+1)-dimensional numerical simulations. As expected, we find that the coupling efficiency is degraded and the duration of the coupled pulses changed when the entrance window is too close to the fiber entrance. The interplay of nonlinear spatio-temporal reshaping and the linear dispersion of the window create different results depending on the window material, pulse duration, and pulse wavelength, with longer-wavelength beams more tolerant of high intensity in the window. While shifting the nominal focus to compensate can restore some of the lost coupling efficiency, it improves the pulse duration only marginally. From our simulations we derive a simple expression for the minimum distance between the window and the HCF entrance facet. Our results have implications for the often space-constrained design of hollow-core-fiber systems, especially where the input energy is not constant.