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Abstract
Intrapulse difference-frequency generation (IPDFG) is a relatively simple technique to produce few-cycle mid-infrared (MIR) radiations. The conversion efficiency of IPDFG could be potentially improved by using the long driving wavelength to reduce the quantum defect. In this paper, we report a high-energy MIR IPDFG source with a record-high conversion efficiency of up to 5.3%, driven by 3 µm, 35 fs, 10 kHz pulses. The IPDFG output has a 5 µJ pulse energy and 50 mW average power. It spans over a spectral range from 6 to 13.2 µm. A 68 fs of IPDFG pulse width is measured, corresponding to 2.1 cycles, centered at 9.7 µm. The high-energy, two-cycle IPDFG pulses are used to produce a 3-octave supercontinuum in a KRS-5 crystal, spanning from 2 to 16 µm, with a 2.4 µJ pulse energy and a 24 mW average power.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-energy, few-cycle, mid-infrared (MIR) sources at 3-20 µm are attracting the remarkable attention from researchers for the various applications, particularly for the study of high-harmonic generation (HHG) in solids or gases [1,2], laser-induced electron diffraction for ultrafast molecular dynamics imaging [3], wave-controlled ultrafast electronics in dielectrics and semiconductors [4,5], and the study of ultra-broadband supercontinuum generation (SCG) [6,7]. The techniques based on nonlinear frequency down-conversion, such as optical parametric oscillators (OPOs) [8], optical parametric amplifiers (OPAs) [9–12] and difference-frequency generation (DFG) [13–15], are commonly used to access the wavelength region of 3-20 µm in the few-cycle region. Recently, the intrapulse-DFG (IPDFG) is emerging as a simple and stable technique [16–26], mainly benefitting from its several advantages: 1) no requirement of the signal pulse generation; 2) no need the accurate control of the time delay as for OPOs, OPAs and DFGs; 3) no time jitter between pump and signal; and 4) the passively stable carrier-envelope phase as the pump and signal are from the same pulse.
So far, the IPDFGs have been demonstrated for the broadband, few-cycle MIR pulse generation in non-oxide nonlinear crystals by using driving pulses at different wavelengths [16–26]. T. Morimoto et al. demonstrated an 800 nJ, few-cycle IPDFG source covering 8 to 13 µm, driven by spectrally broadened 0.8 µm, 1 kHz, Ti:sapphire laser pulses [16]. I. Pupeza et al. used nonlinearly compressed, 1 µm, 100 MHz Yb:YAG laser pulses to produce few-cycle IPDFG pulses with the spectrum from 6.8 to 16.4 µm (at –30 dB) and 103 mW average power, in a $\textrm{LiGa}{\textrm{S}_2}$ crystal [17]. However, the IPDFG efficiency driven by 0.8 µm or 1 µm pulses is relatively low (in the order of 0.1%). More efficient down conversion into the wavelengths of >5 µm has been achieved by using the longer-wavelength driving pulses for the lower quantum defect and the reduced nonlinear absorption in the non-oxide crystals. Using the 2 µm self-compressed, MHz laser pulses from the Tm-doped fiber lasers, C. Gaida et al. and T. P. Butler et al. demonstrated the 450 mW (at 1.25 MHz) and 500 mW (at 50 MHz) MIR output via IPDFG with the spectral coverage of 6 to18 µm in GaSe crystals, at the conversion efficiencies of 1.8% and 2%, respectively [21,22]. S. Vasilyev et al. reported the IPDFG source spanning from 5.8 to 12.5 µm with a conversion efficiency of 3.3%, using few-cycle, 78 MHz, 2.5 µm driving pulses from a Cr: ZnS laser and a $\textrm{ZnGe}{\textrm{P}_2}$ nonlinear crystal [25]. These reports represent the state-of-the-art IPDFG sources for the high conversion efficiency.
In this paper, we further boost the IPDFG conversion efficiency to 5.3% which leads to a new record, by using the driving pulses at 3 µm. The driver of IPDFG we use is 3 µm, 10 kHz, 95 µJ, 35 fs pulses from an optical parametric chirped-pulse amplifier (OPCPA). 5 µJ, 50 mW, 68 fs corresponding to 2.1 cycles centered at 9.7 µm IPDFG pulses with a spectrum spanning from 6 to 13.2 µm are produced from a GaSe crystal. The resulted field strength of the IPDFG pulses can exceed 0.27 V/Å. As a demonstration of the application in the nonlinear optics in solid materials, pumped by the IPDFG output, a 2.4 µJ, 24 mW SC with 3-octave bandwidth covering 2 to 16 µm is generated in a KRS-5 crystal.
2. Experimental setup
The schematic of the experimental setup is depicted in Fig. 1, which consists of the 3 µm few-cycle driver and the IPDFG stage.
Fig. 1. The schematic of experimental setups. IPDFG: intrapulse difference-frequency generation. OPCPA: optical parametric chirped-pulse amplifier. LPF: long-pass filter.
The 3 µm few-cycle driving source starts with a home-made multi-stage OPCPA based on periodically poled lithium niobate (PPLN) and periodically poled stoichiometric lithium tantalate (PPSLT) crystals driven by a 10 kHz Yb: YAG Innoslab laser. It can deliver ∼300 µJ, few-cycle, 3 µm pulses [26,27]. The 120 µJ, 3 µm pulses are used and focused into a 2-mm-thick uncoated YAG crystal by an anti-reflection coated $\textrm{Ca}{\textrm{F}_2}$ lens with a 75-mm focal length, for the nonlinear compression. Here, the YAG is chosen for its large nonlinear refractive index and good mechanical properties. It is placed at a position slightly after the focal spot to avoid the damage and the strong ionization. Inside the YAG, 3 µm pulses are spectrally broadened by the self-phase modulation (SPM), and simultaneously compressed in the temporal domain with the anomalous dispersion in YAG at 3 µm. The measured pulse energy after the YAG is ∼105 µJ, with the loss mainly from the Fresnel reflection and the weak ionization.
In the IPDFG stage, a GaSe with a thickness of 2 mm is chosen as the nonlinear crystal, for its broad transmission window (0.65-18 µm) [28], large second-order nonlinearity (∼50 pm/V from SNLO [29]), good phase-matching (PM) bandwidth [29], and high damage threshold (${\sim} 1.7\;\textrm{TW}/\textrm{c}{\textrm{m}^2}$) [21]. An uncoated $\textrm{Ca}{\textrm{F}_2}$ lens with the focal length of 100 mm is used to focus the self-compressed 3 µm beam from the YAG plate to a beam diameter of ∼600 µm at its beam waist. The pulse energy measured behind the uncoated $\textrm{Ca}{\textrm{F}_2}$ lens is 95 µJ. In our experiment, the GaSe crystal is placed at a type-II PM angle of ${\sim} {13.2^\circ }$ (azimuthal angle (φ)=${0^\circ }$) [26], and the IPDFG output is optimized for the output energy so as the conversion efficiency after the LPF with a cut-off wavelength of 7.3 µm. The parameters of optimization include: the pump intensity on GaSe by adjusting the position of GaSe from the beam waist and the energy distribution of the 3 µm driving pulses on the o-axis and e-axis by rotating the crystal along the propagation direction of the driving pulses. The long-wavelength and the short-wavelength components on the o-axis and e-axis serve as the signal and pump, respectively, in the DFG process, and the IPDFG output is generated as the idler. The IPDFG pulses are collimated by a gold-coated parabolic mirror (Thorlabs [MPD229-M01]) and separated from the driving pulses by the different long-pass filters (LPFs). The characterizations of IPDFG pulses are accomplished by a series of setups, such as the thermal power meter, the monochromator with a liquid-nitrogen-cooled HgCdTe detector, the MIR beam profiler and a home-built interferometric autocorrelator (IAC).
3. Experimental results and discussion
The spectrum of the 3 µm OPCPA (the red dashed curve) is shown in Fig. 2(a) [26], which has a spectral coverage from 2.8 to 3.4 µm. The temporal profile of the 3 µm OPCPA pulses measured by second-harmonic generation frequency-resolved optical gating (SHG-FROG) is revealed in Figs. 2(b)–2(d) [26]. A 65 fs pulse width is measured as shown in Fig. 2(d). In [26], we used these pulses to produce the MIR IPDFG output with a 1%–1.6% conversion efficiency. However, such pulses are not optimized for the efficient IPDFG conversion due to that the necessary ‘signal’ components above 3.6 µm must be generated via SPM in GaSe. In this work, the ‘signal’ components above 3.6 µm are readily generated using YAG before driving the IPDFG stage. The spectrum of self-compressed pulses from YAG (the black solid curve) is shown in Fig. 2(a), with a spectral span from 2.3 to 4.5 µm. Here, the long-wavelength tail is carefully measured with all the energy behind the 3.6 µm LPF coupled into the monochromator. It is worth mentioning that the new generated spectral components in the range of 3.4-4.5 µm which serves as the signal in the process of IPDFG are crucial for the efficient conversion of MIR pulses via IPDFG. The good Gaussian beam profiles before and after nonlinear compression are compared in the inset of Fig. 2(a), manifesting no degradation of the beam profile in the nonlinear compression process. The temporal profile of the self-compressed pulse is also characterized by using SHG-FROG, as shown in Figs. 2(e)–2(g). A 35 fs pulse width is measured with a FROG error of ∼0.9%, which corresponds to a 1.08 times transform limited (TL) pulse width.
Fig. 2. Characterization of the 3 µm driving pulses. (a) The spectra before [26] and after the nonlinear compression. Inset: the beam profiles before and after the nonlinear compression. (b)-(d) show the measured frequency-resolved optical gating (FROG) trace, the retrieved FROG trace and the pulse shape, respectively, for the 3 µm pulses before nonlinear compression [26]. (e)-(g) show the measured FROG trace, the retrieved FROG trace and the pulse shape, respectively, for the 3 µm pulses after nonlinear compression.
The dependence of the IPDFG output and conversion efficiency on the pump intensity is shown in Fig. 3. It is found that the roll-over of the IPDFG output occurs when the pump intensity is increased to ${\sim} 295\;\textrm{GW}/\textrm{c}{\textrm{m}^2}$, and the measured maximum IPDFG output pulse energy behind the 7.3 µm LPF is 5 µJ (50 mW in average power). This corresponds to a 5.3% conversion efficiency from the 3 µm driving pulses to IPDFG output, which, to the best of our knowledge, represents the highest IPDFG efficiency to date. Taking into account the losses from the LPF (10%), the parabolic mirror (6%) and the surface reflections of the uncoated GaSe crystal, the internal conversion efficiency is up to 8.3%. This proves the advantage of the 3-µm-driven IPDFG in enhancing the conversion efficiency due to the lower quantum defect compared to IPDFG sources driven at 0.8, 1, 2 or 2.5 µm [16,17,21,22,25]. In addition, it is worth mentioning that the 5 µJ output pulse energy is much higher than that of the reported advanced IPDFG sources at high repetition rates [21,22,25], which makes our source suitable for some particular applications, such as HHG or SCG in solids. The inset of Fig. 3 shows that the IPDFG output has a Gaussian beam profile at 5 µJ output energy, which allows good focus for the strong-field applications.
Fig. 3. The IPDFG output energy and conversion efficiency measured behind a 7.3 µm LPF at different pump intensities. The inset shows the measured beam profile for 5 µJ IPDFG output.
The IPDFG spectrum at the highest output energy is shown in Fig. 4(a), which spans from 6 to 13.2 µm. Some large dips are found in the IPDFG spectrum, which are mainly caused by the spectral shapes of the short-wavelength pump and the long-wavelength signal in the driving pulses. For example, the $\textrm{C}{\textrm{O}_2}$ absorption line at 4.3 µm in the signal spectrum is transferred to the IPDFG spectrum in the IPDFG process (3.07 µm serving as pump), leading to a spectral dip at 10.7 µm as presented in Fig. 4(a). We also measured the amplified signal of >3.6 µm using the 3.6 µm LPF, which is shown in Fig. 4(b). It is found that the amplified signal covers up to 6 µm in spectrum, however, the long-wavelength tail from the 3 µm driving pulses can only reach 4.5 µm, as shown in Fig. 2(a). Thus, some new spectral components at 4.5-6 µm are generated, serving as signal in the IPDFG process. The origin is attributed to the SPM caused spectral broadening [18,20,26] and the cascaded processes [24]. Figure 4(c) shows the measured signal spectrum after the GaSe crystal by rotating the azimuthal angle (φ) of GaSe to ${90^\circ }$, in order to suppress the amplification. One finds the signal without amplification is spectrally broadened due to the high nonlinear refractive index of GaSe ($450 \times {10^{ - 16}}\textrm{c}{\textrm{m}^2}/\textrm{W}$ [30]. The spectral components of 4.5-6 µm are emerged, which provides an explanation for what is found in the amplified signal. In addition, the intrinsic cascaded processes can also be responsible for the origin of the 4.5-6 µm spectral components. One example of the cascaded process is that with the same PM angle, the 7.5 µm idler is firstly generated via IPDFG between the 2.5 µm and 3.75 µm components in the driving pulses. Subsequently, the generated 7.5 µm idler serves as a new ‘signal’, and is amplified by the 3 µm pump to obtain the 5 µm spectral component in the amplified signal. Similarly, other 4.5-6 µm signal spectral components could be produced by similar cascaded processes. Therefore, it is suggested that the IPDFG process is assisted by both the SPM and the cascaded effect.
Fig. 4. (a) The measured IPDFG spectrum with p-polarization at 5 µJ output energy. (b) The amplified signal spectrum measured behind the 3.6 µm LPF. (c) The broadened signal spectrum via self-phase modulation (SPM), measured behind the 3.6 µm LPF by rotating the azimuthal angle (φ) of GaSe to ${90^\circ }$, to turn off the amplification. In this case, the energy behind the 3.6 µm LPF is 4 times higher than that without GaSe, giving another evidence that SPM makes contribution.
The energy stability of the MIR sources is an important parameter for the molecular spectroscopy and strong-field applications. The measured energy fluctuation of the IPDFG output is 1.1% rms for 1-hour measurement duration, as shown in Fig. 5(a). The good energy stability of the IPDFG mainly benefits from the stable driving pulses with less than 0.7% rms fluctuation. Moreover, the IPDFG pulse width is characterized using the home-built IAC in which a 0.5 mm-thick GaSe is used as the SHG crystal for its good SHG PM bandwidth at ∼10 µm. The measured IAC trace of the IPDFG output after the 7.3 µm LPF is shown in Fig. 5(b). It is worth noting that the 7.3 µm LPF cuts some spectral components from 6 to 7.3 µm, and the temporal profile measurement with the full IPDFG spectrum could be achieved by using a LPF with the cut-off wavelength of 6 µm. Figure 5(b) reveals a 68 fs pulse width corresponding to 2.1 cycles centered at 9.7 µm, and 1.2 times the TL pulse width. It agrees well with the calculated IAC trace, which is obtained by adding the −1300 $\textrm{f}{\textrm{s}^2}$ second-order dispersion into the TL pulse based on the measured spectrum behind the 7.3 µm LPF. The residual dispersion is mainly from the 2-mm-thick GaSe and the 7.3 µm LPF with a 1-mm-thick Ge substrate. The field strength of 5 µJ, 68 fs IPDFG pulses could reach 0.27 V/Å at a beam diameter of 70 µm, disclosing new opportunities to investigate nonlinear phenomena like SCG or strong-filed physics in solids.
Fig. 5. (a) The measured energy stability of IPDFG output behind the 7.3 µm LPF. (b) The measured and calculated interferometric autocorrelator (IAC) traces behind the 7.3 µm LPF. The calculated IAC is obtained by adding the −1300 $\textrm{f}{\textrm{s}^2}$ dispersion which is mainly from the 2-mm-thick GaSe and the 7.3 µm LPF with a 1-mm-thick Ge substrate into the TL pulse based on the measured spectrum.
The 5 µJ, 68 fs IPDFG pulses centered at 9.7 µm are focused into an 8-mm-thick KRS-5 crystal using a parabolic mirror with an effective focal length of 38 mm, as shown by the schematic in the inset of Fig. 6. The KRS-5 crystal has a very broad transmission window (0.58-42 µm) and a high nonlinear refractive index ($105 \times {10^{ - 16}}\textrm{c}{\textrm{m}^2}/\textrm{W}$ [31]). The zero-dispersion wavelength of KRS-5 calculated from the dispersion equation provided in [32] and the critical peak power of self-focusing at 9.7 µm are 6.6 µm and 5.6 MW, respectively. Therefore, the IPDFG output is located at the anomalous dispersion region in KRS-5, and is sustainable for the self-channeled filamentation in KRS-5. In order to avoid the multi-filamentation generation, the KRS-5 crystal is placed after the focus point of the parabolic mirror, and the pump intensity on the crystal is carefully adjusted. Taking into account the loss from the parabolic mirror and the surface reflection of KRS-5, the peak power inside KRS-5 is 57 MW which is ∼10 times higher than the critical peak power. The spectrum and the beam profile of the generated SC assisted by a single filament are shown in Fig. 6. It is found that the SC spectrum spans 3 octaves from 2 to 16 µm, with a 2.4 µJ pulse energy and 24 mW average power. The sharp dips at 4.3 µm and 15 µm are due to the $\textrm{C}{\textrm{O}_2}$ absorption in air. It is worthy to mention that the generated MIR spectrum covering 2 to 16 µm is of particular interest for molecular fingerprint spectroscopic studies.
Fig. 6. The SC spectrum assisted by a single filament from the KRS-5 crystal driven by the IPDFG pulses. The insets show the corresponding SC beam profile and the setup of SCG, respectively. SCG: supercontinuum generation.
4. Conclusions
We have demonstrated a GaSe-based MIR IPDFG source with a conversion efficiency of 5.3%, using 3 µm, 10 kHz, 35 fs pulses as the IPDFG driver. This, to the best of our knowledge, represents the highest IPDFG efficiency to date. The 5 µJ, 50 mW, 68 fs pulses with a spectrum spanning from 6 to 13.2 µm are delivered, which could lead to a field strength of 0.27 V/Å at a beam diameter of 70 µm. More applications such as SCG and HHG in solids could be pursued by the demonstrated high-energy IPDFG, compared to current state-of-the-art IPDFG sources at high repetition rates. Pumped by the IPDFG pulses, a 3-octave SC covering 2 to 16 µm, with a pulse energy of 2.4 µJ and an average power of 24 mW is demonstrated in a KRS-5 crystal, which is suitable for the molecular fingerprint spectroscopy.
Funding
Agency for Science, Technology and Research (1426500050, 1426500051, A1890b0049); Ministry of Education - Singapore (MOE 2016-T2-1-128).
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