Broadly, independent-tunable, dual-wavelength mid-infrared ultrafast optical parametric oscillator

We demonstrate a two-crystal mid-infrared dual-wavelength optical parametric oscillator, synchronously pumped by a high power femtosecond Yb:fiber laser. The singly-resonant ring cavity, containing two periodically poled lithium niobate crystals, is capable of generating two synchronized idler wavelengths, independently tunable over 30 THz in the 2.9 - 4.2 {\mu}m wavelength region, due to the cascaded quadratic nonlinear effect. The independent tunability of the two idlers makes the optical parametric oscillator a promising source for ultrafast pulse generation towards the THz wavelength region, based on different frequency generation. In addition, the observed frequency doubled idler within the crystal indicates the possibility to realize a broadband optical self-phase locking between pump, signal, idler and higher order generated parametric lights.


I. INTRODUCTION
Dual-wavelength operation within a single laser cavity is promising for a variety of applications such as coherent pulse synthesis, THz generation, pump-probe experiments and CARS [1][2][3][4] . For conventional solid-state ultrafast lasers, dual-wavelength operations were observed and demonstrated with Ti:sapphire lasers at 800 nm 5,6 and Tm:CaYAlO 4 lasers at 2 µm 7 . Besides, dual-wavelength operation was also realized with a Q-switched cascade fiber laser at 3 µm 8 . Optical parametric oscillators (OPOs) are well-established mid-infrared sources offering coherent light, high power, broad bandwidth and broad tuning range. Nowadays, OPOs are also widely used for a variety of applications such as mid-infrared frequency comb generation and spectroscopy [9][10][11] . Specifically, synchronously pumped OPOs offer an new opportunity for synchronized pulses generation at two different wavelength regions [12][13][14][15][16][17][18][19] , that can be directly used for THz generation based on different frequency generation (DFG) [20][21][22][23][24] . In the case of an OPO with a single cavity, the dual-wavelength operation is realized when the two resonant pulse trains have the same round trip time delay 12 . In literature, the simultaneous dual-wavelength operation is explained by the balance between phase matching and group-velocity mismatching between the two resonant pulses 14,16 . Experimental results also indicate a stable relative carrier-envelope phase-slip frequencies within a dual-wavelength femtosecond OPO, which is of great interest for various applications such as quantum control and coherent pulse synthesis 13 . However, most dual-wavelength OPOs reported provide limited dual-wavelength tunability and broadband arbitrary wavelength tuning of the two idelers is not possible.
In this paper, we present the experimental observation of dual-wavelength operation within a two-crystal OPO pumped by a femtosecond Yb:fiber laser. By tuning the cavity length, the simultaneous dual-wavelength operation is realized when the two crystals are at different poling periods. To our knowledge, this is the first demonstration of an independently-tunable, synchronously-pumped, dual-wavelength, ultrafast OPO generating arbitrarily tunable idlers across a 30 THz spectral region between 2.9 µm and 4.2 µm. To characterize the OPO, we have also observed the behavior of several cascaded parametric processes within the nonlinear crystals, such as the second harmonic generation(SHG) of the idler, indicating the possibility to achieve optical self-phase locking between pump, signal and idler when the spectrum of the frequency doubled idler overlaps the spectrum of the 2 signal. It is worth mentioning that previously, self-phase locking of continuous-wave (CW) OPOs has been achieved by using the intra-cavity frequency-doubled idler 25-28 .

PARAMETRIC OSCILLATOR
The experimental setup of the synchronously pumped singly-resonant OPO is similar to the one described previously 11,29 . As illustrated in Fig. 1, the difference is that the two crystals To measure the output spectra of the OPO, the poling period of one crystal is fixed at   period is directly pumped by the femtosecond laser. When the two crystals are pumped by the femtosecond laser, two idlers are generated simultaneously within the two crystals at different wavelengths. It can be noticed that the first idler is not spectraly affected when both crystals are pumped. By changing the poling period of the second crystal, dual-wavelength operation across a 30 THz spectral region between 2.9 -4.2 µm is realized ( Fig. 2 The two idler wavelengths are operating independently and as such can be tuned to arbitrary wavelength regions.
The behavior of the dual-wavelength operation is cavity length dependent. Measurements have been done when the poling periods of the two crystals are set to be 28.28 and 29.52 µm.
As illustrated in  scaling measurements are performed when the poling periods of the two crystals are set to be 29.08 µm. As illustrated in Fig. 4(a), the spectra of signals between 1.4 and 1.7 µm and the spectra of frequency doubled idlers between 1.8 and 1.9 µm are recorded. The corresponding idler spectra between 3.2 and 4.1 µm are also shown in Fig. 4(b). A spectral broadening effect is observed while increasing the pump power. At a 1.7 W average pump power, the signal covers a 300 nm spectral range corresponding to a 1000 cm −1 (30 THz) bandwidth, revealing a modulated multi-peak structure. Both the spectral broadening effect and the modulated multi-peak structure indicate the presence of a nonlinear phase modulation, which is plausibly due to the cascaded quadratic nonlinearity for the signal that is treated as the fundamental wave in this case 31 . These cascaded quadratic processes have been shown to resemble a χ (3) process 32-36 , and the most common cascaded quadratic effect involves a single-step process, such as non-phase-matched SHG in a dispersive quadratic media.
Meanwhile, cascaded quadratic processes due to third-harmonic generation(THG) have also been discussed previously [37][38][39] .  To further confirm the presence of the cascaded quadratic processes, a series of measurements are performed with a 1.7 W pump power. By tuning the poling periods of two crystals from 27.91 to 31.02 µm, spectra between 400 and 800 nm (375 to 749 THz) are recorded.
In these measurements, both the THG and SHG of the signal are observed as demonstrated in gray sections (1) and (2) within Fig. 5(a), respectively. In this case, both the phasemismatching for SHG and THG of the signal can be calculated by the following formulae ∆ k 1 = 2π(λ 2s /n 2s − 2λ s /n s − 1/Λ) and ∆ k 2 = 2π(λ 3s /n 3s − 3λ s /n s − 1/Λ), respectively, where λ s , λ 2s , λ 3s are the wavelengths of the signal, the SHG of the signal, and the THG of the signal; n s , n 2s , n 3s are corresponding refractive indices; Λ represents poling period of the crystal. Figure 5 7 residual pump light (p), leaked signal light (s) from the cavity, and the generated idler light (i), are recorded with an optical spectrum analyzer (OSA). As illustrated in Fig. 6(a), the dominating, nonlinearly generated intensities are: the sum frequencies of pump and signal (p+s), pump and idler, and doubling frequency of pump (2p), next to other frequencies (2s, 3s, p + 2s, 2p + i, 2p + s). By monitoring the light leaking from mirror CM3 by using a fast visible light detector, two beating frequencies are observed centered on half the repetition frequency (45 MHz) of the pump laser ( Fig. 6(b)). This beating frequency originates from the overlap between different generated parametric lights as shown in the gray sections in Fig. 6(a). Assume that the frequencies of the pump and the idler are f p and f i , the beating frequencies observed at the three gray sections are f 2p+i − f p+2s , f 3s − f 2p , and f 2s − f p+i , respectively. The value of these beating frequencies are all equal to f p −3f i , considering that f p = f s + f i . Moreover, the same beating frequency in the mid-infrared wavelength region is also observed by using a fast infrared detector (Vigo, PVI-4TE, 50 MHz bandwidth) at the output of the OPO after a Germanium collimating lens.
To explain the observed beating frequencies both in the mid-infrared and visible regions, the parametric processes within the OPO are illustrated in Fig. 7(a). Firstly, the pump wavelength (f p ) is divided into a signal wavelength (f s ) and an idler wavelength (f i ). The SHG of the idler is at 2f i while the different frequency generation (DFG) between the frequency doubled idler (2f i ) and the pump (f p ) is at f p − 2f i . By changing the poling periods in the crystal at 27.91 µm, 28.28 µm and 29.52 µm, the frequency doubled idler (2f i ) and the signal (f s ) start to merge as can be seen in Fig. 7(b), generating a beating frequency at f p − 3f i . Figure 7(c) illustrates the merging of the THG of the signal (3f s ) with the SHG of the pump (2f p ), also generating a beating frequency at f p − 3f i . In addition, the beating frequency detected in the mid-infrared is calculated to be which is the same value when compared to the beating frequencies both in the near infrared and the visible wavelength region. It is expected that from the overlap between the signal and the frequency doubled idler (Fig. 7(a)), self-phase locking can be achieved from this   40 . Once the self-phase locking is realized, f p is constantly equal to 3f i , and one can achieve phase coherent generation at frequencies of N · f i (N = 1 − 8) from a single OPO laser source, simultaneously, which are illustrated in Table 1.

IV. DISCUSSION AND CONCLUSION
For a femtosecond OPO with a single gain medium, pumped at a fixed repetition frequency, the central wavelength of the signal wave shifts by changing the cavity length, maintaining the round trip time delay corresponding to the fixed cavity length 14,29 . Asynchronous pumping can also be achieved at a fixed cavity length by using two femtosecond lasers with different repetition frequencies 29,41 . In this case, two pulse trains (signal) at different central wavelengths maintain the same round trip time delay due to the difference of group velocities within the crystal. Conventionally, dual-wavelength operation within a single cavity at one repetition frequency can be realized when the two resonant pulse trains have the same round trip time delay, implying that the tuning of the two wavelengths is strongly correlated and not arbitrary 12,14,16 . In this work, the two-crystal OPO offers arbitrary dualwavelength generation, due to the use of different poling periods in the crystals offering different gain bandwidths. Next to this, the OPO is singly-resonant on the signal without output coupler, reserving extremely high signal power within the cavity. This two crystal OPO cavity is capable of generating two synchronized idler beams that are independently tunable across a 30 THz spectral region between 2.9 -4.2 µm. The independent tunability of the two idlers can be explained by taking higher order nonlinear effects into account, such as the cascaded quadratic nonlinearity. These cascaded processes in quadratic media induce a nonlinear phase shift on the fundamental wave by back-conversion of the phase-mismatched second harmonic wave, which is equivalent to third-order nonlinearity 32,33,42,43 . In practice, active group velocity control within a PPLN crystal has already been achieved based on the cascaded quadratic nonlinearity 43,44 . We believe that the group velocity mismatch between the two wavelengths are compensated by the nonlinear phase shift, due to the cascaded quadratic nonlinearities that is analogous to the third-order nonlinearity in a conventional mode-locked laser in the case of Kerr modulation 33,45 .
In conclusion, for the first time, we have experimentally demonstrated dual-wavelength operation within a two-crystal OPO cavity, generating two broadband idler beams that are independently tunable across a 30 THz spectral range between 2.9 -4.2 µm. Such passively synchronized dual-wavelength pulses could be coupled to a nonlinear crystal, such as OP-GaAs 22 , to generate light from the far-infrared to THz wavelength region based on the different frequency generation. Besides, the spatially separated pulses are also ideal sources for mid-infrared pump-probe experiments. To characterize the OPO, we have observed second harmonic generation of the idler (2i) directly, without using a tandem crystal. The observed merging effect between the signal and the frequency doubled idler indicates a possibility to realize self-phase locking between them.

ACKNOWLEDGMENTS
This work is financially supported by the Technology Foundation STW, under project number 11830.