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

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

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

STME Hydrogen Mixer Study

The hydrogen mixer for the Space Transportation Main Engine is used to mix cold hydrogen bypass flow with warm hydrogen coolant chamber gas, which is then fed to the injectors. It is very important to have a uniform fuel temperature at the injectors in order to minimize mixture ratio problems due to the fuel density variations. In addition, the fuel at the injector has certain total pressure requirements. In order to achieve these objectives, the hydrogen mixer must provide a thoroughly mixed fluid with a minimum pressure loss. The AEROVISC computational fluid dynamics (CFD) code was used to analyze the STME hydrogen mixer, and proved to be an effective tool in optimizing the mixer design. AEROVISC, which solves the Reynolds Stress-Averaged Navier-Stokes equations in primitive variable form, was used to assess the effectiveness of different mixer designs. Through a parametric study of mixer design variables, an optimal design was selected which minimized mixed fuel temperature variation and fuel mixer pressure loss. The use of CFD in the design process of the STME hydrogen mixer was effective in achieving an optimal mixer design while reducing the amount of hardware testing

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

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

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