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Register a new userLimits to compression with cascaded quadratic soliton compressors
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We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths $lambda=1.0-1.3 mu{rm m}$ in a $beta$-barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. However, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account.
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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.
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.
We study soliton pulse compression in materials with cascaded quadratic nonlinearities, and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible.
By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schrodinger equation, we unveil the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space of near-zero group velocity mismatch. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches depending on the system parameters. We find the nonlinear interaction between the resonant pump and signal results in phenomena that resemble the dispersive two-photon absorption and the dispersive Kerr effect. Origin of the quadratic soliton perturbation is identified and strategy to mitigate its detrimental effect is developed. Terahertz comb bandwidth and femtosecond pulse duration are attainable in an example periodically poled lithium niobate waveguide resonator in the short-wave infrared and an example orientation-patterned gallium arsenide free-space cavity in the long-wave infrared. The quadratic soliton mode-locking principle can be extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.
We demonstrate soliton-effect pulse compression in mm-long photonic crystal waveguides resulting from strong anomalous dispersion and self-phase modulation. Compression from 3ps to 580fs, at low pulse energies(~10pJ), is measured via autocorrelation.
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