Generating Few-cycle Energetic Mid-IR Pulses with Soliton Compression by Cascaded Quadratic Nonlinearities

We study nonlinear mid-IR crystals and assess their potential for ultrafast cascaded nonlinearities in the type 0 phase-matching interaction. Few-cycle, broadband energetic mid-IR pulses can be generated from compressing multi-cycle mid-IR pulses with self-defocusing solitons. Ultrashort mid-IR pulses is currently a hot topic since they can be used for probing and even manipulating the ultra-fast vibrational dynamics of hydrogen and carbon bonds, and to reach new frontiers in ultrafast and extreme nonlinear optics. For these applications energetic, few-cycle, broadband mid-infrared pulses are needed. Here we investigate whether ultra-fast cascaded optical nonlinearities can facilitate these needs. This method uses solitons generated with cascaded second-harmonic generation (SHG) to compresses energetic, multi-cycle laser pulses towards few-cycle duration. In cascaded SHG the frequency conversion from the fundamental wave (FW, ω1) to its second harmonic (SH, ω2 = 2ω1) is not phase matched ∆k = k2−2k1 6= 0: after a coherence length π/|∆k| only weak up-conversion occurs, after which back-conversion occurs after another coherence length. As this process is cyclically repeated (cascading) the FW effectively experiences a Kerr-like nonlinear refractive index change ∆n = ncascI proportional to its intensity I , and ncasc ∝ −deff/∆k, where deff is the effective quadratic nonlinearity. The total cubic nonlinear refractive index is then ncubic = ncasc + nKerr, where nKerr is the self-focusing (positive) material Kerr nonlinearity. When ∆k > 0 and |ncasc| > nKerr, the total cubic nonlinearity becomes negative (self-defocusing), and self-focusing problems are avoided making the input pulse energy practically unlimited [1]. Moreover, both spectral broadening and temporal compression can occur in a single nonlinear material through solitons [2]. Solitons are stable nonlinear waves that exist as a balance between nonlinearity and dispersion, which for a negative nonlinearity is achieved with normal dispersion. Thus, with cascading solitons can form in the near-IR where the majority of lasers operate and where most materials have normal dispersion. Historically, critical (type I) cascaded SHG has been used for energetic pulse compression [1, 2]. Despite not using the largest deff -values, in critical SHG the birefringence is exploited to achievencubic < 0 by angle-tuning the crystal close to phase-matching. However, when ∆k < ∆ksr = d12/2k (2) 2 , where d12 is the GVM parameter and k (2) 2 the SH GVD coefficient [3], this approach may result in a resonant (spectrally narrow) cascaded nonlinearity, impeding ultrafast applications. Recently we showed that large cascaded nonlinearities can be obtained from a noncritical (type 0) cascading without using quasi-phase matching (QPM) [4]. The cascading nonlinearity is (a) large due to the huge deff of noncritical interaction, (b) always self-defocusing because ∆k > 0, (c) ultrafast because the cascading is non-resonant (∆k > ∆ksr turns out to always be fulfilled). We used this to show fewcycle soliton compression in the near-IR (1300 nm pump wavelength) in a just 1 mm long bulk LiNbO3 crystal [4]. Here we show the potential aspects of this result by extending it to the important mid-IR regime. The idea is that noncritical cascaded SHG may occur in bulk semiconductor or dielectric materials that are transparent in the mid-IR. Often these have huge quadratic nonlinearities, but tend to be overlooked for nonlinear purposes because of the lack of phase matching. The premise of our approach is the availability of an energetic, but multi-cycle, midIR pulse obtained e.g. by parametric amplification of a near-IR laser pulse, and then use cascaded SHG to invoke soliton compression towards few-cycle duration, and to create strong coherent spectral broadening. We stress that 1 2 3 4 5 6 7 8 9 0.01 0.1 1 10