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

We study nonlinear mid-IR crystals and assess their potenti al for ultrafast cascaded nonlinearities in the type 0 phase-matching interaction. Fewcycle, broadband energetic mid-IR pulses can be generated from compressing multi-cycle mid-IR pulse s 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 bon ds, and to reach new frontiers in ultrafast and extreme nonlinear optics. For these applications energetic, few-c ycle, broadband mid-infrared pulses are needed. Here we investigate whether ultra-fast cascaded optical nonlinea r ti s can facilitate these needs. This method uses soliton s generated with cascaded second-harmonic generation (SHG) to compresses energetic, multi-cycle laser pulses towards few-cycle duration. In cascaded SHG the frequency c onversion 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 oc curs after another coherence length. As this process is cyclically repeated (cascading) the FW effectively experi ences a Kerr-like nonlinear refractive index change ∆n = ncascI proportional to its intensityI, andncasc ∝ −deff/∆k, wheredeff is the effective quadratic nonlinearity. The total cubic nonlinear refractive index is then ncubic = ncasc + nKerr, wherenKerr 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 avoide d making the input pulse energy practically unlimited [1]. Moreover, both spectral broadening and temporal compressi on can occur in a single nonlinear material through solitons [2]. Solitons are stable nonlinear waves that exis t as a balance between nonlinearity and dispersion, which for a negative nonlinearity is achieved with normal dispers ion. Thus, with cascading solitons can form in the near-IR where the majority of lasers operate and where most m aterials have normal dispersion. Historically,critical (type I) cascaded SHG has been used for energetic pulse compr ession [1, 2]. Despite not using the largest deff -values, in critical SHG the birefringence is exploited to a chievencubic < 0 by angle-tuning the crystal close to phase-matching. However, when ∆k < ∆ksr = d12/2k (2) 2 , whered12 is the GVM parameter and k (2) 2 the SH GVD coefficient [3], this approach may result in a reson ant (spectrally narrow) cascaded nonlinearity, impeding ultrafast applications. Recently we showed that l arge 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 be cause∆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 wavel ength) in a just 1 mm long bulk LiNbO 3 crystal [4]. Here we show the potential aspects of this result by extendin g it to the important mid-IR regime. The idea is that noncritical cascaded SHG may occur in bulk semiconduct or or dielectric materials that are transparent in the mid-IR. Often these have huge quadratic nonlinearities, bu t tend to be overlooked for nonlinear purposes because of the lack of phase matching. The premise of our approach is t he availability of an energetic, but multi-cycle, midIR pulse obtained e.g. by parametric amplification of a nearIR laser pulse, and then use cascaded SHG to invoke soliton compression towards few-cycle duration, and to cre ate strong coherent spectral broadening. We stress that 1 2 3 4 5 6 7 8 9 0.01 0.1 1 10