Designing microstructured polymer optical fibers for cascaded quadratic soliton compression of femtosecond pulses

The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatch between the pump and the second-harmonic waves. Therefore the potential for cascaded quadratic second-harmonic generation is investigated in particular for soliton compression of fs pulses. We found that excitation of temporal solitons from cascaded quadratic nonlinearities requires an effective quadratic nonlinearity of 5 pm/V or more. This might be reduced if a polymer with a low Kerr nonlinear refractive index is used. We also found that the group-velocity mismatch could be minimized if the design parameters of the microstructured fiber are chosen so the relative hole size is large and the hole pitch is on the order of the pump wavelength. Almost all design-parameter combinations resulted in cascaded effects in the stationary regime, where efficient and clean soliton compression can be found. We therefore did not see any benefit from choosing a fiber design where the group-velocity mismatch was minimized. Instead numerical simulations showed excellent compression of $\lambda=800$ nm 120 fs pulses with nJ pulse energy to few-cycle duration using a standard endlessly single-mode design with a relative hole size of 0.4.Comment: 11 pages, 8 figures, submitted to JOSA

Phase-Sensitive Mode Conversion and Equalization in a Few Mode Fiber Through Parametric Interactions

The parametric interaction in few mode fibers is theoretically and numerically studied in the particular case in which the signal and the idler waves are frequency degenerate but mode nondegenerate. Under simplifying hypotheses, we derive analytical formulas for the phase-insensitive and phase-sensitive amplification gain and conversion efficiency. The analytical formulas are in very good agreement with the numerical solutions of a full vectorial model that takes into account losses, mode coupling, and all possible four-wave mixing interactions. In the phase-sensitive regime, we predict that for small input pump powers, a large and tunable phase-sensitive extinction ratio can be achieved on one mode, whereas the other mode power remains essentially unaffected. Finally, in the high-gain regime, the self-equalization of the output power on different modes can be also achieved

Intermodal Four-Wave-Mixing and Parametric Amplification in km-long Fibers

We theoretically and numerically investigate intermodal four-wave-mixing in km-long fibers, where random birefringence fluctuations are present along the fiber length. We identify several distinct regimes that depend on the relative magnitude between the length scale of the random fluctuations and the beat-lengths of the interacting quasi-degenerate modes. In addition, we analyze the impact of polarization mode-dispersion and we demonstrate that random variations of the core radius, which are typically encountered during the drawing stage of the fiber, can represent the major source of bandwidth impairment. These results set a boundary on the limits of validity of the classical Manakov model and may be useful for the design of multimode parametric amplifiers and wavelength converters, as well as for the analysis of nonlinear impairments in long-haul spatial division multiplexed transmission

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (\textit{i.e.}, the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -- related to the difference between the SHG and the Kerr soliton numbers -- and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, which control the behaviour of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a $\beta$-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.Comment: 11 pages, 8 figures, resubmitted version, to appear in October issue of J. Opt. Soc. Am. B. Substantially revised, updated mode