Binbin Zhou

Ultrafast and Octave-Spanning Optical Nonlinearities from Strongly Phase-Mismatched Quadratic Interactions

Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase mismatch ensures an ultrafast nonlinear response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals.

Ultrafast and broadband optical nonlinearities from strongly phase-mismatched second harmonic generation

The third order optical nonlinearities are often used to broaden the spectral bandwidth of ultrafast pulses for supercontinuum generation or pulse compression [1]. The self-focusing nature of cubic Kerr nonlinearity usually limits the applicable pulse energy. An alternative way is using the second order optical nonlinearity, for instance the nonlinearity generated with cascaded second harmonic generation process. In this case, the nonlinearity is controllable in both magnitude and sign through Δk. It could become a desirable self-defocusing nonlinearity if a positive Δk is chosen. However, there are only a handful of reports about the harness of cascaded nonlinearity. The Kerr-like cascading nonlinearity scales as n2, casc ∝ -d2eff/Δk. For a successful implementation, focus has been on having the birefringent phase matching first and then tune to small Δk to overcome the material Kerr nonlinearity and have overall negative nonlinearity. The dillema is in most such cases, the deff is small and quite low Δk values are needed. Such low Δk gives cascading response that is resonant due to the group-velocity mismatch (GVM), and therefore cannot support ultrafast interaction. Practically by this solution only very limited wavelength regimes support this kind of interaction, as done in e.g. [2].

Cross-correlation frequency-resolved optical gating by molecular vibration for ultrashort pulse

The frequency-resolved optical gating (FROG) technique is one of the most popular and robust methods for ultrashort laser pulse characterization, which involves an experimental apparatus to create a spectrogram of a target pulse resulting from its convolution with a gate function and a retrieval algorithm. This paper propose cross-correlation frequency-resolved optical gating (XFROG) technology based on molecular vibration, which is not limited by the wavelengths, and also has high sensitivity for the measurement of the weak pulse. It was demonstrated that molecular-vibration-gated XFROG is a powerful technique for the measurement of ultrashort pulses and ultrafast molecular vibration. Since the molecular vibrational coherence time is from fs to ps, we can expect to measure different ultrashort pulse durations by choosing different Raman modes.

Soliton delay driven by cascading and Raman responses

Summary form only given. Quadratic cascading response is evoked during the ultrafast and phase mismatched (cascading limit) second harmonic generation (SHG) process, which becomes more and more recognized alongside with typical nonlinear phenomena such as nonlinear phase change, pulse intrinsic self-steepening (SS) and material Raman effects. The mean value (local component) of this cascading response has been widely investigated and known as cascading quadratic nonlinearity (has a soliton number Ncasc) which gives rise to a Kerr-like phase change and is tailored by the phase mismatch (Δk) between the fundamental wave (FW) and the second harmonic (SH) [1]. Moreover, the first order of the cascading response is revealed as an effective SS term [2,3], which adds to the intrinsic SS and induces shock front on pulses. Then, such SS effects will cause pulse delay when operating with material dispersions. Meanwhile, first order Raman response will also cause pulse delay by continuously red-shifting the pulse spectrum. Hence, there comes a pulse delay competition between the cascading and Raman responses.In this work, we analytically and numerically study the soliton pulse delay driven by first order cascading and Raman responses and demonstrate a potential delay balance by tuning the cascading delay time through Δk.Analytically, in the cascading limit, the coupled wave equations governing the FW and SH can be degenerated to the famous nonlinear Schrödinger like (NLS-like) equation governing an undepleted FW , in which the cascading and Raman responses are both included [4]. Then by leaving the first order responses and eliminating the higher order terms, the FW amplitude and phase (written as: UFW = A(ξ,τ)eiφ(ξ,τ)) equations are derived as [4]: (in dimensionless form and in dispersionless condition) ∂ 2 2 = N ffA2 - 2τRNέ biCA α + 2N Ncubic + 2τN / I AZ ∂τ c c- c c NA2 aAaφ (4N as 3N ubi + 2τ ατ aξ aίj where N ff = N2casc - N2cubic scales the total self-defocusing nonlinearity necessary to hold the soliton propagation with normal dispersion, τc and τR are cascading and Raman delay time and τc ∝ GVM/Δk. It is noted that the pulse amplitude is strongly dependent on cascading terms (Ncasc and τc) while the phase is dominated by Raman effects (τc term), especially after the soliton formation (where ∂φ ∂τ = 0). Numerical results are shown by solving the above mentioned NLS-like equation. Fig. 1(a) shows that the cascading response gives rise to shock front in the dispersionless condition and causes slow pulses (Fig. 1(b)) with normal dispersion, tuned by Δk. Then, in Fig. 1(c), with strong material Raman effects over the cascading, fast pulses are driven as more red-shifted pulses would travel faster with normal dispersion. At last, introducing a stronger cascading delay time (with smaller Δk), fast pulses are tuned back to the zero delay position (Fig. 1(d)).

Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities

Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index change Δn = n_cascI, where n_case ∝ -d²_eff/Δk, and d_eff is the effective quadratic nonlinearity. Due to competing material nonlinearities n_Kerr the total nonlinear refractive is n_cubic = n_casc + n_Kerr. Interestingly n_cubic can become negative (self-defocusing), elegantly avoiding self-focusing problems, and making it possible to excite solitons with normal dispersion [1].

Completely background free broadband coherent anti-Stokes Raman scattering spectroscopy

For the first time it was proposed a numerical approach to obtain non-NRB time-frequency coherent anti-Stokes Raman scattering (CARS) spectrograms. In order to evaluate the validity of the CARS spectrogram for background free broadband CARS spectroscopy, the authors numerically constructed a CARS spectrogram for an assumed Gaussian probe pulse of 500 fs (FWHM).

Near- and Mid-IR few-cycle self-defocusing soliton compression in PPLN waveguide

Cascading quadratic nonlinearity is well known as an effective nonlinear phase change (n2,casc, Kerr-like) during the ultrafast and phase-mismatched second harmonic generation (SHG) process. The sign and intensity of such an equivalent Kerr nonlinearity (electronic cubic nonlinearity) is closely related to the phase mismatch (Ak) between the fundamental wave (FW) and the second harmonic (SH). Therefore, self-defocusing n2,casc is achievable by using a positive phase mismatch and can be large enough to counterbalance the native material Kerr nonlinearity (n2,Kerr, usually self-focusing). Then, having an overall self-defocusing nonlinearity, soliton compression may occur with normal dispersion.

The Kerr nonlinearity of the beta-barium borate crystal

A popular crystal for ultrafast cascading experiments is beta-barium-borate (β-BaB₂O₄, BBO). It has a decent quadratic nonlinear coefficient, and because the crystal is anisotropic it can be birefringence phase-matched for type I (oo → e) second-harmonic generation (SHG). For femtosecond experiments BBO is popular because of low dispersion and a high damage threshold. The main attractive property of ultrafast cascading is that the induced cascading nonlinearity n_2,casc^I can be negative, i.e. generate a self-defocusing Kerr-like nonlinearity. However, the material Kerr nonlinearity n_2,Kerr^I is self-focusing and competes with the cascading nonlinearity. Therefore, precise knowledge of its strength is crucial. We perform an experiment measuring the main c₁₁ tensor component, and together with literature experimental data [1], we propose a c₁₁ value composed of 14 different data points.