Energetic few-cycle laser pulses in the short-wavelength infrared (SWIR, 1–3 μm) range are important for numerous fields of research, ranging from high harmonic generation [1], manipulation of ultrafast vibrational modes in manganite [2] to solar cell inspection and imaging applications. Another application of rising importance is the generation of single-cycle pulses in the terahertz (THz) spectral region (1–20 THz, so-called THz gap) via optical rectification in organic crystals [3–6]. For ultrabroadband THz pulse generation, such crystals require to be pumped with ultrashort pulses at 1.2–1.6 μm wavelength to achieve efficient energy conversion. Since the bandwidth of these THz pulses is intrinsically linked to that of the pump pulse, intense and broadband SWIR pulses are beneficial.

In past years various techniques have been studied in order to produce intense and ultrashort SWIR pulses. Based on spectral broadening by self-phase modulation of SWIR pulses in a gas-filled hollow-core fiber pulses of 400 μJ and 13.1 fs FWHM (2.9 cycles) could be produced [7]. In another work, intense and self-compressed pulses were achieved by filamentation in xenon, which resulted in 270 μJ, 17.8 fs FWHM (2.8 cycles) pulses [8]. In a different approach, four-wave mixing in a filament between the fundamental and the second harmonic (SH) of a Ti:sapphire laser, yields 1.5 μJ, 13 fs FWHM (1.3 cycles) pulses [9]. For filaments, however, the pulse energy is limited due to the critical power [10], which hinders upscaling to higher energies. Finally, we mention few-cycle pulse generation via cross-polarized wave (XPW) generation in nonlinear crystals (e.g., ${\mathrm{CaF}}_2$, ${\mathrm{BaF}}_2$) [11], achieving sub-20-fs FWHM pulses. Again, the spectrally broadened and temporally cleaned pulses are limited to a few microjoules pulse energy due to the intrinsic properties of the XPW effect [12].

In this Letter, we experimentally demonstrate another technique to generate intense few-cycle pulses in the SWIR. The approach is based on ultrafast (i.e., nonresonant), phase-mismatched, cascaded frequency conversion [13] in the highly nonlinear organic DAST (4-N, N-dimethylamino-4′-N′-methylstilbazolium tosylate) crystal [14]. Previous works have demonstrated spectral broadening of a pump pulse via cascaded frequency conversion in nonlinear crystals [13,15,16] but none of them using DAST. Here we show that DAST is the best candidate for this process due to its exceptionally large effective nonlinearity at 1600 nm ($d_{\text{eff}}\approx 250\mathrm{pm}/\mathrm{V}$ [14]), which is almost an order of magnitude higher than the one of the dielectric or semiconductor crystals previously studied in the literature [15]. In our experiment, intense two-cycle pulses are generated by using DAST. The nonlinear interaction leads to a cascading of ${\chi }^2(2\omega ;\omega ;\omega )$ and ${\chi }^2(\omega ;2\omega ;-\omega )$ processes, which results in octave-spanning spectral broadening (i.e., 1.2–2.5 μm) and pulse durations down to 12.5 fs (1.9 cycles) (8.9 fs transform-limit) with 115 μJ energy at 1850 nm. Thanks to the absence of phase matching, the process can profit plainly from the large effective nonlinearity of the DAST over the entire propagation length in the thin crystal. Moreover, the involved self-defocusing Kerr-like nonlinearity allows the technique to be up-scalable to millijoule energies by using large aperture crystals. Finally, the setup is very compact.

Octave-spanning, self-defocusing cascaded nonlinear frequency conversion can be obtained in strongly phase-mismatched condition between the fundamental wave (FW) and its SH, like it is the case in our experiment ($\mathrm{\Delta }k\approx 1750{\mathrm{mm}}^{-1}$). During this process, the ${\chi }^2(2\omega ;\omega ;\omega )$ nonlinearity allows the FW ($\omega$) to be converted into SH ($2\omega$). The absence of phase matching implies that after a coherence length only weak SH conversion occurs. It is then followed by a back conversion via ${\chi }^2(\omega ;2\omega ;-\omega )$ into the FW after another coherence length. During the propagation in the crystal, this process repeats itself and cascaded frequency conversion occurs. Moreover, the FW experiences nonlinear phase shift, similarly to a Kerr-like nonlinear refractive index change, which is proportional to its intensity $I\text{:}\mathrm{\Delta }n=n_{\text{casc}}I$. When the process is strongly phase-mismatched the refractive index can be approximated as: $n_{\text{casc}}\approx -2{\omega }_1{d}_{\text{eff}}^2/(c^2{\epsilon }_0{n}_1^2{n}_2\mathrm{\Delta }k)$ [16], where $\mathrm{\Delta }k=k_2-2k_1$ ($k_1$ and $k_2$ are the wave vectors of the fundamental and second-harmonic waves).

As shown in Fig. 1 (black solid line), $\mathrm{\Delta }k$ is approximately $1.75{\mathrm{\mu m}}^{-1}$ for the pump wavelength (1600 nm). Therefore, in order to have an effective negative Kerr-like nonlinearity, $|n_{\text{casc}}|$ must be larger than $n_{\text{Kerr}}$ ($n_{\text{Kerr}}$ is the nonlinear refractive index stemming from the Kerr effect). Moreover, to achieve octave-spanning frequency conversion, the cascaded nonlinearity must not be resonant. From [13], this condition is achieved when $\mathrm{\Delta }k>\mathrm{\Delta }{k}_R$, where $\mathrm{\Delta }{k}_R={\mathrm{GVM}}_{12}^2/2{\mathrm{GDD}}_2$ is a threshold for resonance. Here, ${\mathrm{GVM}}_{12}$ is the group velocity mismatch between the FW and the SH, and ${\mathrm{GDD}}_2=\partial k_2/\partial {\omega }^2$ is the SH group velocity dispersion. For DAST dispersion varies only from $1.04{\mathrm{fs}}^2/\mathrm{mm}$ at 1100 nm to $0.46{\mathrm{fs}}^2/\mathrm{mm}$ at 2600 nm (computed from [14]).

 

Fig. 1. (a) Calculated wavelength dependence of $\mathrm{\Delta }k$ originating from material dispersion (black solid line), $\mathrm{\Delta }{k}_r$ threshold for resonant cascaded nonlinearity (black dashed line), and $d_{\text{eff}}$ (circles) in DAST. The Sellmeier formulas and values of $d_{\text{eff}}$ are taken from [13]. (b) Calculated $|n_{\text{casc}}|$ ($n_{\text{casc}}<0$) for DAST at 1600 nm and for $d_{\text{eff}}\approx 250\mathrm{pm}/\mathrm{V}$. The red square indicates the measured $n_{\text{Kerr}}$ at 1064 nm from [18] with its uncertainty.

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At 1600 nm, which is the pump wavelength used in our experiment, and taking into account the uncertainty on $n_{\text{Kerr}}$ [Fig. 1(b), red dashed line delimited area], the condition $|n_{\text{casc}}|>n_{\text{Kerr}}$ can be fulfilled, as shown in Fig. 1(b). The values for $n_{\text{casc}}$ are computed using the Miller’s scaling law [17]. $n_{\text{Kerr}}$ was measured for DAST only for $\lambda =1064\mathrm{nm}$ to be $1\times {10}^{-17}{\mathrm{m}}^2\cdot {\mathrm{W}}^{-1}$ with a large uncertainty of $\pm 25\%$ [18]. To verify whether the off-resonance condition is fulfilled, the dependence of $\mathrm{\Delta }{k}_r$ with wavelength was computed and the corresponding curve is shown in Fig. 1(a) (black dashed curve). One can see that over the spectral range of the pump (1200–2080 nm), $\mathrm{\Delta }k$ is effectively larger than $\mathrm{\Delta }{k}_r$, insuring that off-resonance, octave-spanning frequency conversion is feasible.

The experimental setup is shown in Fig. 2. A Ti:sapphire amplifier system [19] is used to drive a commercial optical parametric amplifier (OPA). In order to generate the broadest supercontinuum, it is of primary interest to seed the DAST crystal with a pump pulse exhibiting a broad spectral bandwidth. We thus decided to postcompress the pulses from the commercial OPA with the filamentation technique. The produced few-cycle pulses are used to pump the DAST in a noncritical interaction geometry; a detailed description of the source can be found in [20].

 

Fig. 2. Experimental setup. Sub-20-fs FWHM pulses generated via filamentation in a Xenon filled gas cell are used to generate octave spanning spectrum by phase-mismatched cascaded nonlinear interaction in DAST crystal. All pulses are characterized spectrally and temporally with a WIZZLER apparatus.

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The spectral bandwidth of the pump pulse (after filamentation) covers 1450–1650 nm FWHM [Fig. 4(c), black line]. The pump pulse duration is 18.1 fs FWHM, as shown in Fig. 3 (red line), almost Fourier limited. This corresponds to 3.1 optical cycles at 1600 nm. The 240 μJ pulses are then used to pump the DAST crystal ($6\mathrm{mm}\times 6\mathrm{mm}\times 0.18\mathrm{mm}$) with an intensity of $6.8\times {10}^{10}\mathrm{W}\cdot {\mathrm{cm}}^{-2}$.

 

Fig. 3. Single-shot reconstructed temporal profile of the pump pulse (18.1 fs FWHM, red line) at 1600 nm. The Fourier limit is 15.6 fs FWHM (black dots).

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Fig. 4. (a) Single-shot reconstructed temporal profile of the 12.5 fs FWHM pulse (red line) after the phase-mismatched cascaded nonlinear interaction in DAST. The Fourier limit is 8.9 fs FWHM (black dots). (b) Output spectrum covering 1200–2540 nm (black) when the crystal orientation is set such that the pump laser polarization coincides with the crystal axis having the largest $d_{\text{eff}}$. The corresponding measured spectral phase is also shown in red. Output spectra when the crystal is rotated by 45 deg (green) and 90 deg (blue) with respect to the previous position are also shown. (c) Measured linear transmission of the crystal for the fundamental beam (blue) and input spectrum (black).

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As shown in Fig. 4(b), maximum spectral broadening covering 1200–2540 nm (full width) occurs when the crystal orientation is set such that the pump laser polarization coincides with the crystal axis having the largest $d_{\text{eff}}$ (black solid line). The spectrum gets narrower covering only 1300–2300 nm when the crystal is rotated by 45 deg with respect to the previous position (green solid line). Finally, when the crystal is rotated by 90 deg, spectral broadening is not present anymore (blue solid line): the spectrum covers 1260–1760 nm, identical to the input spectrum shown in Fig. 4(c) (black solid line). An interesting feature is that the spectral broadening mainly occurs toward the longer wavelengths. The observed spectral broadening is much more pronounced than in previously reported results using lithium niobate crystal [13].

The redshift and asymmetry in the FW spectrum can be explained by the strong absorption of DAST between 600 and 900 nm [Fig. 4(c)]. The SH of the pump pulse is in this spectral range. The SH short wavelengths are strongly absorbed in the DAST so that only long SH wavelengths can be back-converted into the FW. Since the process repeats itself along all the crystal length, this gives rise to a strong extension of the FW spectrum toward the long wavelengths and spectral asymmetry enhanced by DAST absorption above 2200 nm [Fig. 4(c)]. Due to the small thickness of the crystal, it was not possible to find with the available diagnostics an experimental evidence of defocusing effect due to negative Kerr effect.

The pulse spectral bandwidth expands over 1200–2540 nm full width [Fig. 4(b), black line] and supports 8.9 fs FWHM Fourier limited pulses, as shown in Fig. 4(a) (black dots). This corresponds to 1.3 optical cycles at 1850 nm. The temporal pulse shape of the spectrally broadened pulse has been reconstructed using the self-referenced spectral interferometry technique [20] after the DAST. The octave-spanning pulse exhibits a positive chirp, which has been compensated by introducing a 2-mm thick fused silica plate into the beam path. After compression the pulse duration reached 12.5 fs FWHM [Fig. 4(a), red line], corresponding to 1.9 cycles at 1850 nm. The observed prepulses shown in Fig. 4 are a signature of the residual third-order dispersion [Fig. 4(b), red dashed line], which could not be compensated for by the simple bulk compression scheme applied in our experiment. However, further efforts in compression need to be undertaken to reach the transform-limited pulse duration being 8.9 fs. The total pulse energy measured after compression is 115 μJ, which results in an overall efficiency of 48%. This includes all losses induced by the DAST crystal and the uncoated fused silica plate. This is less than the 80% reported in [13]; however, the authors did not mention exactly what criteria were taken into account to obtain this number, making the direct comparison difficult.

In conclusion, we demonstrated that phase-mismatched cascaded frequency conversion profiting from the record-large second-order nonlinearity of the DAST crystal is well suited to generate intense, ultrabroadband few-cycle pulses in the SWIR spectral range. The simple and very compact scheme provides 1.9 cycle pulses at 1850 nm (12.5 fs FWHM), with 115 μJ energy and the extensive spectral broadening over more than one octave (1200–2540 nm) supports 1.3 cycle TL pulses (8.9 fs FWHM).