Effective phase matching strategies in high index contrast double-clad optical fibers for second and third harmonic generation of ultrashort pulses

While matching phase velocities in optical fibers is often sufficient for continuous-wave or long pulse length frequency conversion, it is critical to consider higher-order dispersion terms for ultrashort pulse conversion. In our previous works, we already demonstrated that fibers can be specially designed to achieve simultaneous modal phase and group velocity matching for both second and third harmonic generation. However, such designs often come with the penalty of being highly sensitive to geometrical parameters. As a solution to that problem, we propose implementing an effective phase matching strategy. The approach considers the cumulative effect of dispersion terms up to second order and does not enforce strict phase and group velocity matching, instead requiring that they jointly lead to effective phase matching. Here, we present a series of fiber designs and pump pulse specifications that enable effective phase matching for both second and third harmonic generation.