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Synchronously pumped optical parametric oscillator (OPO) at degeneracy is ideal for generating ultrafast laser pulses. Normally, however, group velocity mismatch (GVM) is ubiquitous among the interacting pulses at widely separated wavelengths. A versatile quasi-phase-matching (QPM) technique is proposed for temporal synchronizing of the signal and idler pulses relied on a less common Type-II QPM (oe-o interaction). The proposed group-velocity regulation technology is advantageous to constructing a degeneracy-analogous femtosecond OPO for dual-wavelength operation. Qualitative prediction for the proposed design is conducted based on a commercial femtosecond pump source at 1064 nm while the signal/idler wavelengths are 3.2 μm and 1.59 μm respectively. Compared with the conventional Type-0 QPM based counterpart (ee-e interaction), the uncompensated temporal distortion caused by temporal walk-off is strongly suppressed while the idler spectrum gets significantly broader. The versatility of the proposed scheme is also clearly demonstrated by its fairly stable performance within a broad tuning range of 2.9-3.5 μm and 1.68-1.53 μm. The demonstrated configuration might be promising for synchronously obtaining dual-wavelength ultrafast pulses with higher spectral and temporal qualities.
© 2017 Optical Society of America
1. Introduction
Synchronous laser pulses operating at widely separated wavelengths are highly desirable for various applications, such as pump-probe measurements, generation of mid-infrared (mid-IR) and terahertz (THz) sources through difference frequency generation (DFG), differential absorption laser radar, coherent anti-Stokes Raman scattering (CARS) microscopic imaging, etc [1–4]. In the past several decades, mode-locked solid-state and fiber lasers have undergone remarkable advances, and been used as the primary source of ultrafast pulses from tens of picoseconds down to few tens of femtoseconds. Dual and even more wavelength mode-locking have been successfully demonstrated with Ti:sapphire lasers at 800 nm [5, 6], and various rare earth doped solid-state lasers at 1.0-2.0 μm [7–11]. With a single rare earth doped medium, however, it is still impossible to get stable mode-locking on two widely wavelength-separated channels, because of the limited gain bandwidth. By contrast with the real level gain media based on population inversion, synchronously pumped optical parametric oscillator (SPOPO) is another well-established laser device capable of broad bandwidth and wide tuning range. Ascribed to the three-wave parametric interaction, OPO intrinsically supports dual-wavelength outputs and offers an opportunity for synchronized pulses generation in different spectral regions.
Nowadays, studies on dynamic processes of physical, chemical or biological interest enter an unprecedented microcosmic time-scale. Both of the pump-probe measurements and CARS have to employ ultrafast laser pulses for higher temporal resolution capabilities [12, 13]. The laser pulse with a shorter temporal duration will be greatly required thanks to the development in various research areas. However, femtosecond OPOs are much more difficult than their nanosecond and picosecond counterparts. Normally, group velocity mismatch (GVM) is ubiquitous among the interacting pulses in the oscillating cavity [Fig. 1(a)]. In general, the GVM between pump and signal pulses limits the interaction length over which parametric amplification takes place, while the GVM between signal and idler pulses restricts the spectral acceptance of the phase matching (PM) condition [14, 15]. For dual-wavelength OPOs, the temporal walk-off between signal and idler plays a more critical role on achieving the ultrafast dual-wavelength outputs. Besides the limited PM bandwidth, in time domain, significant pulse distortion would be another consequence of the unequal signal/idler velocities. To eliminate this detrimental effect, there is always an embarrassing dilemma that the crystal should be thick enough to provide high gain but thin enough to limit the GVM influence. To construct an OPO more suitable for delivering dual-wavelength ultrafast lasers, various deliberately refined configurations have been proposed. For a broader output spectrum and the subsequent shorter pulse duration, a common method is to design the femtosecond OPO operating close to the net-zero dispersion regions or using a non-collinear geometry for group velocity matching [16–18]. To improve the temporal qualify and lower the pump threshold, doubly resonant OPO was suggested [19, 20]. For the doubly resonant configurations, the ultrafast-pulse-pumped OPO can operate at dual wavelengths only when the resonated pulses at different wavelengths have a same cavity group velocity [21]. The GVM brought by the nonlinear crystal thus should be compensated in femtosecond scale before the return pass. A widely used design is to use two independent optical cavities [22, 23]. All of these improvements in structure aim to deal with the undesired GVM within the parametric interactions in essence.
Fig. 1 Group velocity mismatch plays a critical role on the parametric interactions. (a) Normally, GVM is ubiquitous among the interacting pulses and subsequent temporal walk-off limits the interaction length and PM bandwidth. (b) The degeneracy-analogous situation when signal and idler pluses are perfectly group-velocity matched.
As we all know, degenerate OPO is ideal for generating ultrafast laser pulses because of the unique group velocity of signal and idler pulses [24–27]. In this article, we proposed an attractive quasi-phase-matching (QPM) configuration capable of group velocity matching between the signal and idler pulses and then significantly improved their temporal quality with ultrabroad spectrum. Usually, there exist intrinsic differences in the temperature derivations of group-velocity (i.e., ∂υgroup/∂T) for orthogonally polarized near- and mid-IR pulses. We can thus manipulate the group-velocity relationship and construct a degeneracy-analogous OPO by synchronizing the signal and idler pulses [Fig. 1(b)]. Taking advantage of flexible QPM conditions, phase matching conduction can be satisfied simultaneously. Supposing a 8% doped periodically poled LiNbO3 (PPLN) is employed as the nonlinear medium and only maturely-developed femtosecond pump sources at 790 and 1064 nm are considered, the group-velocity matched signal-idler wavelengths can entirely cover an ultrabroad spectral region form 1.0 μm to 3.5 μm. To verify its potential behavior on ultrafast dual-wavelength applications, focusing on a typical mid-IR wavelength of 3.2 μm and the corresponding idler wavelength of 1.59 μm, we numerically simulated the behavior of proposed degeneracy-analogous OPO relied on a commercial femtosecond pump source at 1064 nm. As presented in the simulation results, compared with its conventional counterpart based on Type-0 QPM (ee-e interaction), the spectral bandwidth of idler was enhanced by at least two times plus a remarkably improved temporal quality. Such a scheme might be promising for synchronously obtaining dual-wavelength ultrafast pulses with higher spectral and temporal qualities.
2. Group-velocity management
With significant progress in recent decades, QPM has been proven to be satisfactory for phase matching in OPOs. In the QPM structure, the sign of nonlinear coefficient is reversed just at the depth where the generated pulses would start to oscillate out of phase. It ensures that sustaining parametric amplification builds up coherently all along the crystal. However, there is no analogous method in the temporal domain that can eliminate the influence of GVM with reversible temporal walk-off. Previously, we have suggested and numerically validated a novel QPM design capable of eliminating the GVM between near- and mid-IR pulses [28]. Normally, there exist intrinsic differences in the temperature derivations of group-velocity (i.e., ∂υgroup/∂T) for orthogonally polarized near- and mid-IR pulses. Their group-velocities in periodically poled LiNbO3 thus may be identical at certain specified temperature. Under that time-synchronization framework, pump and signal travel with identical group velocity. Significantly improved conversion efficiency thus can be obtained ascribed to the theoretically unlimited interaction length. However, since the group velocities of signal and idler remain far from degeneracy, the gain bandwidth is still limited for long crystals. Although simultaneously group velocity matching for all three interacting pulses is still impossible, we can manipulate the group-velocity relationship on purpose. The crucial phase-velocity matching can be satisfied simultaneously by virtue of the flexible QPM conditions. In some senses, this versatile QPM scheme equivalently offers an extra degree of freedom to design the temporal-synchronized interacting pulses. For ultrafast dual-wavelength OPOs, both of the spectral and temporal qualities can be significantly optimized by synchronizing the signal and idler pulses, resulting in a degeneracy-analogous parametric interaction. In the proposed QPM structure, we can only abandon the largest effective nonlinear coefficient of d33 and choose a less common Type-II QPM instead, which is capable of satisfying the QPM condition (oe-o interaction) with orthogonally polarized signal and idler pulses.
In the beginning, we explored the attainable spectral range for the proposed degeneracy-analogous design based on available periodically poled crystals. Periodically poled lithium niobate (PPLN) has emerged as an important nonlinear material for use in OPOs. Compared with other common periodically poled crystals of PPKTP and PPKTA, it is much more temperature-sensitive, which is helpful in group-velocity management. Unfortunately, there is not any appropriate mature pump source which can unify the group velocities of near- and mid-IR pulses based on the commercial 5% doped MgO:PPLN [29]. Nevertheless, apart from the temperature tuning, MgO doping concentration is also closely related to the refractive index of PPLN and the subsequent group velocity. Figure 2 shows the theoretical identical group velocities and the corresponding crystal temperature for a series of correlated signal-idler wavelength-pairs in 8% doped MgO:PPLN, when the pump wavelengths are 790 nm and 1064 nm, respectively. All the data were calculated based on the published temperature-dependent Sellmeier equations of 8% doped MgO:PPLN [30]. Taking the 1064 nm pump source as an example, ultrafast laser pulses at 2.9-3.5 μm and 1.7-1.5 μm can be simultaneously delivered at uniform group-velocities, within a rational temperature range of 20-250 °C. These signal and idler wavelengths just fall into the near- and mid-IR regions respectively, which helps to meet various application purposes. The wavelength-pairs can be group-velocity matched definitely strongly depend on the pump sources. An extremely broad spectrum of 1.0-3.5 μm from near- to mid-IR can be completely covered when only maturely-developed femtosecond pump sources at 790 and 1064 nm are considered. The spectrum can be further extended to ~5.0 μm, the upper transparency limit of PPLN with other pump sources. It should be noted that though MgO doping management can also realize group-velocity management, it is inconvenient to alter the doping concentration in practical operations for wavelength tuning. Therefore, in our opinion, these group-velocity management methods mentioned can be classified that doping concentration limits the spectral range of application, while the temperature tuning determines the specific group-velocity matched wavelength-pair. Restricted to the orthogonal polarization of signal and idler pulses, Type-II QPM (oe-o interaction) has to be chosen to satisfy the phase matching condition while the pump pulse is o-polarized.
Fig. 2 (a) Temperature-depended signal-idler wavelength-pairs for various pump sources in the degeneracy-analogous situation. o and e indicate the o- and e-polarization respectively. (b) and (c) The theoretical tuning curves for correlated signal (blue) and idler pulses (red) with identical group velocities, when the pump wavelengths are (b) 1064 nm and (c) 790 nm, respectively. All the data were calculated based on the published temperature-dependent Sellmeier equations of 8% doped MgO:PPLN [30].
3. Dual-wavelength OPO in degeneracy-analogous situation
To qualitatively predict the potential behavior about the proposed degeneracy-analogous OPOs, based on a basic singly resonant configuration, temporal and spectral characterizations of the output signal and idler pulses were carried out by numerically solving the coupled three-beam time-dependent nonlinear propagation equations in the plane wave approximation. In the calculations, we only considered the second order nonlinear interactions and included material dispersion to all orders. The conventional Type-0 QPM based configuration using d33 was also investigated and compared with the Type-II scheme. As shown in Fig. 3, the SPOPO is designed with a ring cavity and singly resonant for the 3.2 μm mid-IR wavelength. A commercial mode-locking femtosecond oscillator at 1064 nm serves as the pump source, and the wavelengths of pump, signal, and idler are 1.06 μm, 3.2 μm and 1.59 μm, respectively. The prerequisite to generate ultrafast signal pulse is a net zero group delay dispersion at the resonant wavelength for one cavity round-trip and the cavity thus needs to be dispersion controlled. A pair of Brewster-cut GaF2 prisms is used for intra-cavity dispersion compensation for the negative dispersion of MgO:PPLN [31]. The transmission of output coupler (M2) for signal pulses is set at 20% when the round-trip loss has been taken into account. As presented in the temperature tuning curves in Fig. 2(b), to unify the group-velocities of signal and idler pulses at 3.2 μm and 1.59 μm, 8% doped MgO:PPLN should be maintained at ~145 °C with a grating period of Λ = 40 μm. The realistic parameters calculated based on the temperature-dependent Sellmeier equations of 8% doped MgO:PPLN are all listed in Table 1. By comparison, parameters for the common Type-0 QPM at the same temperature is also included.
Fig. 3 Schematic of the singly resonant SPOPO with a basic ring-cavity. M1 is a dielectric mirror for in-coupling; M2 and M3 represent the out-coupler and high-reflective mirror respectively. The cavity length is matched to the repetition rate of pump laser.
Table 1. Nonlinear Optical Crystal Parameters for 8% doped MgO:PPLN. (λp = 1064 nm, λs = 3.2 μm, λi = 1.59 μm)
Effective interaction length is crucial for the parametric interactions, which indicates the propagation length through which the interacting pulses will completely separate from each other. In the degeneracy-analogous situation, the GVM between pump and signal/idler is ~57 fs/mm. For the conventional Type-0 QPM configuration which is far from degeneracy, the GVM between pump and signal is reduced to be ~11 fs/mm while that one between signal and idler becomes ~77 fs/mm. Supposing moderate pump duration of 100 fs, the crystal lengths for configurations based on Type-0 and Type-II QPM are thus designated to be 1.5 mm and 2 mm respectively, which is equivalent to the slipping length for interacting pulses. Figure 4 presents the simulated dependence of quantum efficiency and spectral bandwidth versus pump intensities. For ultrafast operation, of particular interest are the pulse duration, i.e., the spectral bandwidth equivalently. As we can see, a remarkable bandwidth gap exists between these two distinct configurations, especially for the idler pulses, the spectral bandwidth of the degeneracy-analogous design is roughly two times as large as that of the Type-0 QPM based scheme. Under a similarly moderate conversion efficiency of 30%, the temporal envelopes and spectra are given in Fig. 5, for both of signal and idler pulses. To obtain the shortest pulse durations, extra-cavity dispersion compensation, which is necessary to remove the second-order chirp acquired within the parametric interaction, was included for both signal outputs, separately. For the conventional Type-0 QPM cases, due to the small temporal walk-off between pump and signal, and proper intra-cavity dispersion management, both of the spectrum and pulse envelope are preserved in an acceptable level for the resonant signal pulses. However, the idler wave is not so lucky. Ascribed to the temporal walk-off between signal and idler, in addition to a considerable restricted phase-matching bandwidth, in time domain, the idler pulses was generated over a wide temporal range, resulting in a severely distorted pulse envelope with a non-negligible trailing edge. On the contrary, in the degeneracy-analogous situation, besides the ultra-broader output spectrum, more importantly, benefited from the temporal synchronization of signal and idler pulses, the signal amplification and the concomitant idler generation can only exist within the temporal frame of each other, leading to an extremely higher temporal quality and similar spectral bandwidth for these synchronous pulses. The time-bandwidth product is about dυ·dτ = 0.44 and 0.47 for 3.2 μm (signal) and 1.59 μm (idler) respectively, confirming the near-transform-limited pulses. Note that, it shows obvious pulse shortening compared with the initial pump duration, which can be ascribed to the relatively short crystal length and the subsequent significant pulse shortening effects [32, 33].
Fig. 4 The simulated dependence of quantum efficiency and spectral bandwidth versus pump intensities, for both of the degeneracy-analogous (a) and the common Tpye-0 QPM based (b) configurations, while the initial pump duration is 100 fs.
Fig. 5 The simulated temporal envelopes outputs of the dual-wavelength SPOPO under a similarly moderate conversion efficiency of 30%, for both of the degeneracy-analogous (a) and the common Tpye-0 QPM based (b) configurations. Inset: The corresponding spectra and spectral phases. As shown, in means of the center wavelength, the spectral bandwidth in full width at half-maximum (FWHM) for signal/idler waves are 380 nm/90 nm (a) and 285 nm/50 nm (b), respectively.
4. Versatility and wavelength tuning
For ultrafast nonlinear interactions, the behavior of OPO is definitely more vulnerable as the pump duration gets even shorter, due to the subsequent shorter effective interaction length. To present the pulse duration influence, we explore the duration-depended spectral bandwidth for both of the degeneracy-analogous configuration and its traditional counterpart. Figures 6(a)-6(b) presents the spectral bandwidth versus various pump durations. In the simulations, we followed the same model and parameters given above except a various pump duration. As clearly shown in this figure, the shorter pump duration is, the larger bandwidth gap gets, which shows a more crucial influence of GVM. In comparison, for the proposed configuration, the bandwidth for both of the signal and idler pulses are considerably broadened and characterizes an approximately linear relationship with the pump bandwidth. The detailed temporal envelopes and spectra while pump duration is 60 and 150 fs are exhibited in Figs. 6(c)-6(f) as well, which visually demonstrates the significant influence of GVM on ultrafast dual-wavelength OPOs. In the degeneracy-analogous situation, ultrafast laser pulses with high temporal and spectral qualities can still be generated even when the OPO operates under extremely short pump duration. Such QPM scheme might be promising for synchronously obtaining dual-wavelength ultrafast pulses based on a really simple configuration.
Fig. 6 The variation of spectral bandwidth with pump durations for both signal and idler pluses, for the degeneracy-analogous (a) and the common Tpye-0 QPM based (b) configurations. Spectral bandwidth of the initial pump pulses is also indicated with dashed lines. The spectrum data were all extracted at a similar conversion efficiency of 30%. (c) - (f) Temporal envelopes outputs of the dual-wavelength SPOPO for various pump durations τp, where both of the degeneracy-analogous (c) τp = 60 fs and (e) τp = 150 fs and the Tpye-0 QPM based (d) τp = 60 fs and (f) τp = 150 fs configurations are included. Inset: The corresponding spectra and spectral phase.
As presented in the temperature tuning curves in Fig. 2. Within a rational temperature range of 20-250 °C, the degenerate-analogous OPO can deliver synchronized ultrafast laser pulses at various temperature-depended wavelength-pairs based on a fixed femtosecond pump source. To be sure, the simultaneous satisfaction of both group-velocity and phase-velocity matching essentially requires that the periodically poled crystal has to operate at certain particular temperature with a specified grating period of Λ. There is a strict association between Λ and the crystal temperature. To realize wavelength tuning based on the proposed QPM scheme, the periodically poled crystal can be designed with a continuous fan-out structure [Fig. 7]. The fan-out pattern provides a practicable means of independently controlling both of the grating period and temperature [34, 35]. We can easily translate the nonlinear crystal for grating period regulation and alter its temperature correlatively. Supposing a mode-locking femtosecond oscillator at 1064 nm serve as the pump source, Fig. 7 shows the spectral bandwidth versus wavelength-pairs of signal and idler while the pump duration is 100 fs. Though the spectra suffer slightly decreasing as the signal wavelength increases, fairly stable performance is theoretically predicted within the entire spectral region. To achieve the similar conversion efficiency, the OPO operating at a longer signal wavelength may reach deeper saturation, compared with the shorter ones. The bandwidth falling in longer signal wavelength may be caused by the discrepant gain saturation and the subsequent spectrum narrowing. Versatility of the proposed scheme is also clearly demonstrated by the stable spectral bandwidth.
Fig. 7 The spectral bandwidth as a function of group-velocity matched signal-idler wavelength-pairs based on a fixed femtosecond pump source at 1064 nm, while the initial pump duration is 100 fs. The spectrum data were all extracted at a similar conversion efficiency of 30%.
5. Conclusion
In conclusion, we propose a versatile QPM scheme which is advantageous to constructing degeneracy-analogous OPOs by synchronizing the signal and idler pulses. In the proposed QPM structure, we abandon the largest effective nonlinear coefficient of d33 and choose a less common Type-II QPM instead. Via appropriate temperature control of the periodically poled crystal, the GVM between orthogonally polarized signal and idler pulses can be fully eliminated while the phase-velocities matching is satisfied simultaneously by virtue of the Type-II QPM. Taking a typical mid-IR wavelength of 3.2 μm and the corresponding idler wavelength of 1.59 μm as an example, we numerically simulated the behavior of degeneracy-analogous OPO based on a commercial femtosecond pump source at 1064 nm. In the proposed degeneracy-analogous situation, both of the temporal and spectral outputs can be remarkably improved compared with its conventional counterpart. For the idler pulses especially, the uncompensated temporal distortion in normal Type-0 QPM design is strongly suppressed with nearly two-fold broader spectrum. The versatility of the proposed scheme is clearly demonstrated by its fairly stable performance within the entire spectral region. The demonstrated configuration at degeneracy-analogous might be promising for synchronously obtaining dual-wavelength ultrafast pulses with higher spectral and temporal qualities.
Funding
Natural Science Foundation of China (NSFC) (61505113); Guangdong Natural Science Foundation (2014A030310009); China Postdoctoral Science Foundation (2016M592527); Science and Technology Project of Shenzhen (JCYJ20160308091733202); Science and Technology Planning Project of Guangdong Province (2016B050501005).
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