Multiple-octave spanning mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystal like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal pumped in the mid-IR gives multiple-octave spanning supercontinua. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed (covering 1.6-$7.0~\mu$m). The results were recorded in a commercially available crystal LiInS$_2$ pumped in the 3-$4~\mu$m range, but other mid-IR crystals can readily be used as well.Comment: submitted to APL Photonic

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schr\"odinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with the previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from literature and provide updated values for the real and imaginary part of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.Comment: J. Opt., in pres

Experimental observation of long-wavelength dispersive wave generation induced by self-defocusing nonlinearity in BBO crystal

We experimentally observe long-wavelength dispersive waves generation in a BBO crystal. A soliton was formed in normal GVD regime of the crystal by a self-defocusing and negative nonlinearity through phase-mismatched quatradic interaction. Strong temporal pulse compression confirmed the formation of soliton during the pulse propagation inside the crystal. Significant dispersive wave radiation was measured in the anomalous GVD regime of the BBO crystal. With the pump wavelengths from 1.24 to 1.4 $\mu$m, tunable dispersive waves are generated around 1.9 to 2.2 $\mu$m. The observed dispersive wave generation is well understood by simulations.Comment: in preparatio

On type I cascaded quadratic soliton compression in lithium niobate: Compressing femtosecond pulses from high-power fiber lasers

The output pulses of a commercial high-power femtosecond fiber laser or amplifier are typically around 300-500 fs with a wavelength around 1030 nm and 10s of $\mu$J pulse energy. Here we present a numerical study of cascaded quadratic soliton compression of such pulses in LiNbO$_3$ using a type I phase matching configuration. We find that because of competing cubic material nonlinearities compression can only occur in the nonstationary regime, where group-velocity mismatch induced Raman-like nonlocal effects prevent compression to below 100 fs. However, the strong group velocity dispersion implies that the pulses can achieve moderate compression to sub-130 fs duration in available crystal lengths. Most of the pulse energy is conserved because the compression is moderate. The effects of diffraction and spatial walk-off is addressed, and in particular the latter could become an issue when compressing in such long crystals (around 10 cm long). We finally show that the second harmonic contains a short pulse locked to the pump and a long multi-ps red-shifted detrimental component. The latter is caused by the nonlocal effects in the nonstationary regime, but because it is strongly red-shifted to a position that can be predicted, we show that it can be removed using a bandpass filter, leaving a sub-100 fs visible component at $\lambda=515$ nm with excellent pulse quality.Comment: 14 pages, 10 figures, 1 table, submitted to PR

The anisotropic Kerr nonlinear refractive index of the beta-barium borate (\beta-BaB2O4) nonlinear crystal

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (\beta-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant $\chi^{(3)}$ cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We find that the Kerr nonlinear tensor component responsible for self-phase modulation in cascading is considerably larger than what has been used to date. We evaluate the impact of using such a cubic anisotropic response in ultrafast cascading experiments.Comment: Updated version, comments on experiments from the literature welcom

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

Poor-man's model of hollow-core anti-resonant fibers

We investigate various methods for extending the simple analytical capillary model to describe the dispersion and loss of anti-resonant hollow-core fibers without the need of detailed finite-element simulations across the desired wavelength range. This poor-man's model can with a single fitting parameter quite accurately mimic dispersion and loss resonances and anti-resonances from full finite-element simulations. Due to the analytical basis of the model it is easy to explore variations in core size and cladding wall thickness, and should therefore provide a valuable tool for numerical simulations of the ultrafast nonlinear dynamics of gas-filled hollow-core fibers.Comment: In preparatio

Directional supercontinuum generation: the role of the soliton

In this paper we numerically study supercontinuum generation by pumping a silicon nitride waveguide, with two zero-dispersion wavelengths, with femtosecond pulses. The waveguide dispersion is designed so that the pump pulse is in the normal-dispersion regime. We show that because of self-phase modulation, the initial pulse broadens into the anomalous-dispersion regime, which is sandwiched between the two normal-dispersion regimes, and here a soliton is formed. The interaction of the soliton and the broadened pulse in the normal-dispersion regime causes additional spectral broadening through formation of dispersive waves by non-degenerate four-wave mixing and cross-phase modulation. This broadening occurs mainly towards the second normal-dispersion regime. We show that pumping in either normal-dispersion regime allows broadening towards the other normal-dispersion regime. This ability to steer the continuum extension towards the direction of the other normal-dispersion regime beyond the sandwiched anomalous-dispersion regime underlies the directional supercontinuum notation. We numerically confirm the approach in a standard silica microstructured fiber geometry with two zero-dispersion wavelengths