The mid-infrared (MIR) spectral region contains numerous strong, characteristic molecular absorption features, making it attractive for a variety of scientific, industrial, and defense applications. Pulsed picosecond MIR sources at approximately 3 µm have huge potential for precise ablation in applications including surgical interventions [1,2] and fundamental biology aided by mass spectrometry imaging (MSI) [3]. However, there are currently a lack of commercial sources designed to target these parameters and applications. As a result, MIR sources for these purposes instead use bulk solid-state laser systems which can be difficult to maintain and use, preventing their widespread use by non-experts in clinical and field settings.

Commonly, parametric downconversion of near-infrared solid-state pulsed lasers is used to generate pulses in the MIR spectral region using second-order ($\chi ^{(2)}$) nonlinear three-wave mixing in nonlinear crystals [4]. The downconversion techniques which can be used in a single-pass architecture—optical parametric amplification (OPA) and difference frequency generation (DFG)—offer significant flexibility in output pulse duration and repetition rates that is not possible in the corresponding cavity-based architecture, an optical parametric oscillator (OPO). In contrast to OPOs, which require cavities that can be bulky and vulnerable to external disturbances, the simpler single-pass approaches therefore lend themselves to robust, reliable, and compact devices.

MIR sources based on OPA and DFG require two inputs at the correct wavelengths, a pump and a signal, which also have to be synchronized temporally to maximize their interaction in the crystal. This signal seeding requirement can be satisfied with a broad range of laser sources. Using two independent laser sources is possible [5,6]. Alternatively, a common approach is to use a fraction of the initial pump source to generate the seed signal via nonlinear effects in nonlinear crystals [4], including Raman active materials [7], or a fiber. Fiber-based signal generation schemes can be particularly attractive due to their robustness and ability to maintain high beam quality. The $\chi ^{(3)}$ processes, such as soliton self-frequency shifting [8] or supercontinuum generation [9–11], have been employed to generate MIR light using cascaded $\chi ^{(3)}$ and $\chi ^{(2)}$ nonlinear wavelength conversion stages.

In this manuscript, we demonstrate a new method of generating MIR pulses by difference frequency mixing the output of unseeded four-wave mixing (FWM) in a photonic crystal fiber (PCF). FWM in fibers pumped in the low normal dispersion region can produce intense Stokes and anti-Stokes pulses widely spaced in frequency ($>100$ THz) from the pump [12,13]. Crucially, the specific pump–Stokes frequency spacing is determined by the PCF dispersion which can be readily tailored by changing the air hole geometry [14]. This enables targeted wavelengths to be generated across the MIR via DFG of the pump and Stokes pulses. In addition, the Stokes and anti-Stokes pulses generated by FWM in a fiber are overlapped spatially and temporally with the remaining pump pulse at the output of the fiber, provided the fiber is short compared to the dispersive walk-off length. Consequently, focusing the fiber output directly into an appropriately phase matched $\chi ^{(2)}$ nonlinear crystal enables Stokes amplification and MIR idler generation via DFG. A similar approach to pulsed visible generation via sum frequency generation has been demonstrated by Mosley et al. [15], although they used additional CW-seeding of the FWM which added to the complexity of the system. Exploiting this inherent overlap of the pump and Stokes pulses at the fiber output removes the requirement for beam recombination and delay optics, which have been required by other MIR sources which used Stokes pulses as seed pulses [10]. The directly cascaded architecture used here is therefore particularly attractive for its simplicity, which could be further enhanced by fiber integration of the pump laser and PCF [16–18].

We have demonstrated the feasibility of this cascaded FWM-DFG architecture by generating MIR pulses at approximately 3 µm in periodically poled lithium niobate (PPLN). A schematic of the experimental setup is shown in Fig. 1(a). The phase matching profiles for the FWM and DFG stages are shown in Figs. 1(c) and 1(d), respectively, highlighting the common Stokes/signal wavelength (red dashed line). We used a PCF which generates a Stokes pulse at approximately 1.65 µm when pumped at 1.064 µm, and a crystal poling period which was phase matched for a 1.65-µm signal wavelength when pumped at 1.064 µm. Thus, the Stokes pulses generated in the FWM stage could be used as the seed signal for generation of pulses at approximately 3 µm by DFG. The downconversion in the crystal was on the boundary of DFG and OPA, as classified in terms of the relative pump and signal intensities [19]. We refer to the three-wave mixing stage here as DFG, not OPA, because the signal gain achieved at full pump power was low (3.5 dB).

 

Fig. 1. (a) FWM seeded DFG source schematic. (b) Pump laser spectrum centered at 1.064 µm with a 10-dB bandwidth of 7.1 nm. (c) Pump peak power dependent phase matching curves for the PCF, inset shows SEM of the PCF, see text for dimensions. (d) Temperature dependent DFG phase matching curves for MgO:PPLN (poling period = 31.3 µm). Dashed red lines indicate the Stokes/signal wavelength common to both processes. Circ., fiber circulator; AOM, acousto optic modulator; YDFA, ytterbium-doped fiber amplifier; SP1000 and LP1100, dichroic mirrors; ISO, isolator; PBS, polarizing beam splitter; HWP, half-wave plate; PCF, photonic crystal fiber; TC, temperature controller.

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Our pump laser was an in-house developed ytterbium fiber master oscillator power amplifier system [Fig. 1(a)]. The source consisted of a 50-MHz mode-locked fiber oscillator that produced 5-ps pulses, stretched to 35 ps in a double pass of 145 m of a polarization-maintaining fiber (PM980-XP, Nufern), picked down to $\sim$8 MHz by an acousto-optic modulator, and amplified in two ytterbium-doped fiber amplifiers (second YDFA: Yb1200-10/125DC-PM, Liekki). After collimation out of the final amplifier, a shortpass filter with a cutoff wavelength of 1000 nm (SP1000) was used to filter out residual YDFA pump power ($\lambda$ = 976 nm). A free space isolator (ISO) was used to prevent backreflections into the YDFA, and a half-wave plate (HWP) and polarizing beam splitter (PBS) were used to control the pump power coupled into the PCF. A long-pass filter with a cut-on wavelength of 1100 nm (LP1100) was then used to filter out light at 1120 nm resulting from stimulated Raman scattering in the final amplifier stage. The pump spectrum, which had a 10-dB spectral width of 7.1 nm, is shown in Fig. 1(b) at maximum power.

The polarization-maintaining photonic crystal fiber employed had a hole diameter and spacing of 1.65 µm and 3.9 µm, respectively, except for two larger holes surrounding the core (see scanning electron image in Fig. 1 inset). The zero dispersion wavelengths were calculated as 1.101 µm and 1.103 µm on the fast and slow axes, respectively [13]. Pumping a 0.35-m length of PCF with the maximum available pump power on the slow axis generated 1.65-µm Stokes and 0.785-µm anti-Stokes sidebands [Fig. 2(a)]. The pump coupling efficiency into the PCF was reliably $>70$%. Rotating the launched pump polarization demonstrates the birefringence of the PCF [Fig. 2(b)], as the two independent axes have different dispersion profiles which phase match different FWM Stokes and anti-Stokes sidebands. As the pump power was increased, nonlinear spectral broadening of the Stokes spectra was observed [Fig. 2(c)].

 

Fig. 2. (a) Spectrum generated by FWM in the PCF showing remaining 1.064-µm pump and Stokes and anti-Stokes sidebands. (b) Variation of Stokes spectra with launched pump polarization. Dashed lines show spectra at intermediate polarizations on neither the slow nor fast axis. (c) Variation of Stokes spectra with launched pump power.

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The output of the PCF was then focused directly into a PPLN crystal doped with 5 mol.% MgO (HC Photonics) to amplify the Stokes signal pulses and generate idler pulses by DFG. The crystal had a length of 10 mm, an aperture of $3\times 3$ mm$^2$ and a poling period of 31.3 µm. The PPLN was held in a crystal oven to enable temperature tuning. Following an empirical focusing optimization, an achromatic lens ($f=35$ mm) was used to focus the collimated PCF output into the crystal with a focal spot diameter of 35 µm. This corresponded to a confocal parameter of 1.7 mm in the crystal. The maximum pump peak intensity in the crystal was estimated to be $\leq$1.7 GW/cm$^2$. This upper limit arises by assuming a Gaussian temporal pulse shape (i.e., ignoring temporal distortion of the pump pulses in the FWM stage), and is well below the crystal damage threshold [9]. An offset of 0.8 mm was measured between the pump and signal beam waists due to chromatic aberrations which are difficult to remove even with achromatic lenses [20].

The Stokes seed generated in the FWM stage was spectrally broader than the DFG spectral acceptance bandwidth. As a result, tuning the crystal temperature in the range of 40–100$^{\circ }$C resulted in tuning of the idler spectra, as shown in Fig. 3(a) for a power of 3.1 W coupled out of the PCF. The Stokes and anti-Stokes average powers generated at this power level were 150 mW and 260 mW, respectively. As the temperature of the crystal was increased, the longer wavelengths of the signal seed experienced higher gain due to the change in phase matching. A corresponding shift in the idler spectra toward shorter wavelengths was seen for higher temperatures. The idler spectra had significant structure which was assumed to be a result of the large bandwidth of both the pump and signal seed pulses. Absorption lines due to propagation through a few meters of air could also be seen. The variation in the generated idler and output signal powers as the crystal temperature was tuned are shown in Fig. 3(b), corrected for losses resulting from passing through post-crystal optics. Moving away from the temperature at which the seed signal was phase matched resulted in no idler generation. This confirmed that the pulses being generated in the FWM stage were seeding the DFG, and the MIR power generated was not a result of spontaneous optical parametric generation.

 

Fig. 3. (a) Normalized signal and idler spectral tuning with crystal temperature on a linear scale. The signal seed spectrum (dashed) is scaled to show relative signal amplification at each temperature. (b) Generated signal and idler powers as a function of temperature. The seed Stokes (signal) power is shown as a dashed line.

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Figure 4(a) shows the Stokes, signal, and idler powers as a function of power out of the PCF. The powers were measured at a fixed crystal temperature of 60$^{\circ }$C, chosen to maximize the generated MIR idler power, and are corrected for measurement losses. The corresponding signal gain in the DFG stage is shown in Fig. 4(b). As the power coupled into the PCF increased, the power in the Stokes sideband and hence the signal seed power increased to a maximum of 255 mW. Likewise, the signal and idler output powers increased for increasing PCF output power. A maximum 161 mW of generated DFG idler alongside 581 mW of amplified DFG signal was generated at a PCF output power of 3.28 W. The signal gain decreased as the PCF output power increased and a corresponding roll-off in the generated MIR idler power was also seen. The agreement between the independently measured powers (signal, idler, and Stokes) was checked by verifying the consistency between the measured and expected powers, i.e., $P_{idler}^{expected} = (P_{signal}-P_{Stokes})\lambda _{signal}/\lambda _{idler}$. The agreement between the expected and measured signal and idler powers ($P_{idler}^{expected}/P_{idler}$) was within $10\%$ for PCF output powers between 2 and 3.28 W.

 

Fig. 4. Power curve at constant crystal temperature (60$^{\circ }$C): (a) signal and idler powers after the crystal, and Stokes power before the crystal, as a function of PCF output power; (b) corresponding signal gain in the DFG stage; (c) evolution of the estimated percentage conversion in the FWM and DFG stages during the power scan.

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The evolution of the conversion efficiency of the cascaded MIR source is shown in Fig. 4(c). For each PCF output power, an approximation of the pump conversion in each of the FWM and DFG stages was made by estimating $1-P_{pump}^{out}/P_{pump}^{in}$. To make the estimation for the FWM stage, it was assumed that the measured Stokes power could be used to infer the generated anti-Stokes power, i.e., Stokes and anti-Stokes photons were generated in pairs during FWM, and wavelength-dependent loss in the PCF and PCF output coupling was neglected. Therefore, the absolute conversion percentages are approximations. Nevertheless, the graphical representation of the conversion efficiency evolution as the pump power was varied is a useful tool for discussion of the limits of this MIR generation architecture. The trade-off between FWM conversion and DFG conversion is illustrated by plotting the data on top of the ultimate conversion efficiency, $\eta$, from original pump power to generated MIR idler power ($\eta = P_{idler}/P_{pump}$). If conversion is high in the FWM stage, $\eta$ is limited by the reduction in the number of pump photons which can be converted to idler photons in the DFG stage. In the case of our source, the maximum conversion efficiency into MIR idler power, 5.1$\%$, occurred at a PCF output power of 3.1 W. While the total pump depletion continued to increase up to the maximum PCF output power, this pump depletion was a result of FWM conversion, not DFG conversion, hence $\eta$ decreased. The conversion efficiency $\eta$ was likely to have been limited by two factors: spectral broadening of the Stokes (signal seed) spectrum [Fig. 2(c)] beyond the bandwidth that could be simultaneously phase matched in the crystal; and DFG pump pulse distortion due to pump pulse depletion in the PCF stage, which had the effect of decreasing the peak pump intensity in the crystal.

A shorter PCF length may increase total conversion into the MIR by limiting the spectral bandwidth of pump and Stokes seed pulses. However, finding this optimum overall conversion efficiency is complicated by the cascaded nonlinear dynamics involved in this architecture. For maximum conversion into the MIR idler, a balance between Stokes generation and pump depletion in the PCF must be found.

In our system, pump pulse stretching was necessary to increase the FWM conversion. Un-stretched pulses (5 ps) experienced greater self-phase modulation induced spectral broadening in the PCF as well as reduced conversion into the FWM Stokes and anti-Stokes pulses. Additionally, a lower pump pulse duration limit is also set by temporal walk-off between the pump and generated FWM pulses, which can limit both the generated Stokes power and the temporal overlap between the pump and generated Stokes pulses at the output of the PCF. The MIR pulse parameters which may be achieved with this architecture are therefore constrained by the FWM stage. Further investigations into the interplay between pump depletion and seed pulse generation, as well as spectral broadening and pulse temporal overlap at the PCF output are ongoing and offer a route to increase the total conversion efficiency into the MIR.

Scaling the average power of this architecture is possible by using a higher repetition rate pump source [21]. However, scaling the peak power is more difficult because the mode areas of PCFs suitable for efficient FWM at frequency shifts relevant to subsequent DFG are constrained by the required dispersion properties [14]. While gas filled hollow-core fibers could be used [22], they are not practical for use in the simple scheme demonstrated here. Similarly, while better control of the phase and amplitude properties of the generated MIR pulses is possible with additional seeding of the FWM [15], this would increase the architecture complexity.

In summary, we have demonstrated that fiber FWM can be used to directly pump and seed $\chi ^{(2)}$ three-wave mixing to generate pulses in the MIR. In a first demonstration of this architecture, we use FWM in PCF in combination with DFG in PPLN to generate pulses at approximately 3 µm. This architecture is attractive due to its simplicity and flexibility: the FWM fiber ensures the necessary temporal and spatial overlap of the pump and signal pulses, and any arbitrary wavelength can be generated provided the appropriate combination of pump laser source, PCF, and nonlinear crystal. In addition, an all-fiber integrated system can be readily made with this architecture, enabling maintenance-free, field-deployable ultrafast MIR laser sources to be realized.