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Recent progress in strong-field physics has stimulated the quest for intense mid-infrared ultrashort light sources. Optical parametric amplification (OPA) is one promising method to build up such sources, however, its development significantly relies on the availability of suitable nonlinear crystals. Here, we introduce a positive uniaxial crystal La3Ga5.5Nb0.5O14 (LGN), which exhibits a favorable set of optical properties for the application in a mid-IR OPA. We theoretically evaluate the performance of LGN as the nonlinear crystal of a mid-infrared OPA, with an emphasis on the bandwidth characteristic. We find that this crystal can support broadband amplifications across its entire mid-infrared transparent region up to 6 μm, outperforming other commonly-used mid-infrared crystals in terms of gain bandwidth. Few-cycle mid-infrared pulses at various wavelengths can be generated from the LGN-based optical parametric chirped-pulse amplifiers.
© 2016 Optical Society of America
1. Introduction
Recently, the frontiers of strong-field physics and attosecond science starve for intense ultrashort light sources in the mid-infrared (mid-IR) spectral band [1–3]. Such demand is fundamentally attributed to the wavelength-dependent ponderomotive potential Up∝Iλ2 (I and λ refer to the intensity and wavelength of the driving laser), which determines the physical effects of laser-plasma interactions [4]. High-Up sources at moderate intensity and a longer wavelength open the door to previously inaccessible regimes of light-matter interactions and in particular they allow experimental investigations of the λ-scaling laws of strong-filed physics (e.g., high-harmonic generation cutoff ∝λ2, minimum attosecond pulse duration ∝λ‒1/2) [5]. For example, a high-harmonic generation process driven by an intense 3.9 μm source has produced 1.6 keV bright coherent X-ray [2], substantially higher than that (80 eV) obtained by using a 0.72 μm laser at a comparable intensity [6].
The physical interests for intense mid-IR lasers have forced considerable efforts to develop such sources. Unfortunately, it is hard to produce intense mid-IR lasers directly from laser oscillators or laser amplifiers, due to the lack of gain medium and/or the limited power scaling. One exception to this is the CO2 laser at 10.6 μm, the peak power of which can now reach 15 TW [7]. However, the long pulse duration, large bulk and high cost hinder its wide applications. The current mainstream method is to convert the mature near-IR intense lasers to the mid-IR spectral range by optical parametric amplification (OPA) [8,9] or optical parametric chirped pulse amplification (OPCPA) [10‒16]. The peak powers of intense near-IR lasers have exceeded 1 PW both in Ti:sapphire (0.8 μm) and Nd:glass (1.054 μm) gain media [10,11]. Compared to OPA, the near-IR laser pumped OPCPA is more promising for generating high-energy mid-IR lasers without inducing notable nonlinear pulse distortion or causing medium damage. Femtosecond mid-IR pulses with millijoule- to tens of millijoule-level energy are now readily available from mid-IR OPCPAs [12,13].
Nonlinear crystals play significant roles in OPAs and OPCPAs, which provide the environment for phase matching between the interacting waves. In contrast to the plenty choices of near-IR crystals, mid-IR crystals are relatively scarce. A qualified crystal for applications in mid-IR OPCPAs should have following specifications: 1) a transparent range extended to the mid-IR waveband, 2) a wide phase-matching bandwidth, 3) a large effective nonlinear coefficient, 4) a high damage threshold, 5) scalability to a large size, and 6) good thermo-mechanical properties. For the 2 μm OPCPAs, the commonly used crystals include the beta-barium borate (β-BBO) [12,14], lithium niobate (LiNbO3) [15], and periodically poled LiNbO3 (PPLN) [12,15]. For the 3 μm OPCPAs, the LiNbO3 [16], PPLN [17,18] and Potassium Titanyl Arsenate (KTA) [13,19] are widely used. Limited by the available size, PPLN only applies to low-energy OPCPAs or is used in the front-end of high-energy OPCPAs. β-BBO also suffers the problem of a limited-size imposed by its growth method. While LiNbO3 can be grown to a large size, it has a low damage threshold, typically lower than that of β-BBO by one order of magnitude [20]. Therefore, it is essential to develop new nonlinear crystals with more balanced performances.
We introduce a La3Ga5.5Nb0.5O14 (LGN) crystal to the fields of mid-IR OPA and OPCPA, which was mainly used as the electro-optic or piezoelectric elements in the past. LGN is transparent between 0.28 μm and 7.4 μm, much wider than that of LiNbO3 and KTA. It has a nonlinear coefficient of d11 = 2.61 pm/V and a damage threshold of 1.4 GW/cm2 (for 10 ns pulses), both of which are comparable to those of β-BBO [21]. More importantly, LGN is grown by the Czochralski method, so it has a great potential to have a size up to 10 cm [22]. Its specific heat (~0.5 Jg−1K−1) and thermal conductivity coefficients (estimated similar to those of La3Ca5SiO14, ~1.7 Wm−1K−1 along Z axis and ~1.4 Wm−1K−1 along X axis) are comparable to those of β-BBO [20,23,24]. Whereas, the thermal expansion coefficients of LGN (~4.8 × 10−6 K−1 along Z axis and ~6.1 × 10−6 K−1 along X axis) exhibit weaker anisotropy than those of β-BBO and LiNbO3, so LGN will be quite solid against thermal crack [23]. However, as a key parameter to OPCPA, the bandwidth characteristics of LGN have not been studied, which is the subject of this work.
In this paper, we present a theoretical study on the phase-matching bandwidth of LGN and try to evaluate its potential as a nonlinear crystal to generate broadband mid-IR pulses from a near-IR laser pumped OPA and/or OPCPA. The paper is organized as follows. First, we calculate the phase-matching parameters for collinear and noncollinear configurations in LGN. Then, we compare the gain bandwidths supported by LGN and several other commonly-used mid-IR crystals. Finally, we numerically simulate the generation of few-cycle mid-IR pulses by LGN-based OPCPAs.
2. Phase matching in LGN
2.1 Collinear Phase matching
All the calculations in this paper are based on the Sellmeier equations of LGN given in [21],
where λ denotes the wavelength in μm. Equation (1) shows that LGN is a positive uniaxial crystal (ne>no). We firstly calculated all possible angular phase-matching wavelengths allowed in a collinear OPA [Fig. 1(a)], by solving the phase-matching condition ∆k = kp−ks−ki = 0, where kp, ks, and ki are the wave vectors of the pump, signal and idler, respectively. In following calculations, the seeding pulse is defined as the signal, while the newly generated pulse is defined as the idler. Given these definitions, the mid-IR pulses are referred to as the signal in most parts of this paper, because we mainly concern the amplification of mid-IR pulses. The current available pump sources for mid-IR OPAs are mainly at wavelengths of 0.8 μm (Ti:sapphire), 1.030 μm (Yb:YAG), 1.054 μm (Nd:glass), and 1.064 μm (Nd:YAG). The large bandgap energy of 4.43 eV (corresponding to a photon energy at 280 nm) allows LGN to be directly pumped by these pump sources without the onset of two-photon absorption effect [21]. In following calculations, only two pump wavelengths of 0.8 μm and 1.054 μm are used to show the phase-matching characteristic of LGN. Figure 2 shows that LGN allows phase matching across its entire IR transparent region by Type-I OPA (es + ei→op) for both pump wavelengths. In the OPA pumped at 0.8 (1.054) μm, Type-II phase matching (os + ei→op) can be realized for the signal wavelength above 2.2 (2.4) μm. The phase matching angle in the OPA pumped at 0.8 μm shows less pronounced wavelength dependence for Type-I with respect to Type-II phase matching, while the result in the OPA pumped at 1.054 μm is just the opposite.
Fig. 1 Schematic of collinear (a) and noncollinear (b) phase matching. θ is the phase matching angle, defined as the angle between kp and optical axis. θs (θi) is the angle between ks (ki) and optical axis. α (β) is the angle between kp (ki) and ks.
Fig. 2 Angle tuning curves for a collinear OPA pumped at 800 nm (a) and 1054 nm (b). The black curves represent type I (es + ei→op) phase matching. The red curves represent type II (os + ei→op) phase matching with the mid-IR pulse as the signal.
The critical parameter that defines the gain bandwidth of an OPA process is the phase mismatch Δk among the interacting waves. The gain of OPA reaches a maximum when Δk = 0, and decreases as Δk deviates from zero. Under the approximation of neglected pump depletion, the parametric gain for the seeding wave (at either the signal or idler wavelength) can be estimated by [25]:
where , . Ip, deff, L, ε0, and c are the pump intensity, effective nonlinear coefficient, crystal length, vacuum permittivity, and light speed in vacuum, respectively. The gain bandwidth can be determined by the criterion of. To the first dispersion order of Δk, the gain bandwidth can be expressed by [25],where is the group-velocity mismatch between the signal and idler waves. From Eq. (3), we can see that the gain bandwidth strongly depends on the GVMsi: a smaller GVMsi corresponds to a larger gain bandwidth. The broadband phase matching can be obtained when GVMsi = 0. The dependence of GVMsi on signal wavelengths is shown in Fig. 3. The broadband phase matching is naturally achieved in a degenerate Type-I OPA, i.e., λs = 1.6 μm for λp = 0.8 μm and λs = 2.108 μm for λp = 1.054 μm. Besides, there may also exists nontrivial signal wavelengths at which GVMsi = 0, including λs = 4.0 μm for λp = 0.8 μm under Type-I phase matching, λs = 5.25 μm for λp = 0.8 μm under Type-II phase matching, and λs = 4.44 μm for λp = 1.054 μm under Type-II phase matching.Fig. 3 Calculated GVMsi for a collinear OPA pumped at 0.8 μm (a) and 1.054 μm (b). Black (red) curves represent Type-I (Type-II) phase matching.
2.2 Noncollinear Phase matching
In the collinear OPA, the broadband phase matching can be achieved only at several specific wavelengths. To release such a limitation, a noncollinear configuration of phase matching can be employed, in which a small angle β is set between the ks and ki, as shown in Fig. 1(b). In this configuration, the group-velocity mismatch along the direction of ks can be written as [26]. The broadband phase matching can be obtained by selecting a proper β. This also implies that the noncollinear broadband phase matching only exists under the condition of . Under such a noncollinear geometry, the phase mismatching along the ks direction can be written as . The perfect noncollinear phase matching corresponds to Δk = 0 and GVMsi = 0, simultaneously.
For a Type-I (es + ei→op) OPA in LGN, it’s hard to directly solve the equations of Δk = 0 and GVMsi = 0, because both the signal dispersion and idler dispersion depend on the angle between their wave vectors and the optical axis. Numerical calculations can be used to search the possible solutions by tuning θs and θi in a large range. The rest angle parameters in Fig. 1(b) can be calculated according to the simple triangle relations. The calculation results for a Type-I OPA with λp = 1.054 μm and λs = 3.5 μm are summarized in Fig. 4. There exist two sets of solutions, one is θs = 50.14°, θi = 55.31°, and the other one is θs = 61.58°, θi = 54.69°. The rest angles for the two solutions are calculated to be β = 5.17°, α = 3.63°, θ = 53.77°; and β = 6.89°, α = 4.83°, θ = 56.74°, respectively. None solutions are found for the Type-II OPA with λp = 1.054 μm and λs = 3.5 μm.
Fig. 4 Phase mismatch Δk (a) and group-velocity mismatch GVMsi (b) as a function of θs and θi. The units of Δk and GVMsi are cm−1 and fs/mm, respectively. (c) Extracted the pairs of θs and θi that satisfy Δk = 0 (black lines), and the corresponding GVMsi under different angle pairs (blue lines). Points A and B mark the two pairs of (θs, θi) that simultaneously satisfy Δk = 0 and GVMsi = 0.
No matter in a collinear (β = 0) or a noncollinear (β≠0) OPA, when GVMsi = 0 is satisfied, the gain bandwidth is determined by the second-order dispersion, which can be calculated as [26],
where, and GVD is the group velocity dispersion of corresponding waves. For the Type-I OPA with λp = 1.054 μm and λs = 3.5 μm, when Ip = 1 GW/cm2 and L = 10 mm, the gain bandwidth reaches 11.5 THz (∆ν/νs = 0.134, νs = c/λs) for θs = 50.14°, θi = 55.31°, and 10.3 THz (∆ν/νs = 0.120) for θs = 61.58°, θi = 54.69°. By contrast, the gain width is only ~1.8 THz (∆ν/νs = 0.021) in a collinear OPA (θ = 50.4°) from Eq. (3).In the noncollinear Type-I OPA pumped at 0.8 μm, there exists one specific seeding wavelength of ~1.24 μm for which GVMsi = 0 and D2 = 0 are simultaneously satisfied when θs and θi are tuned to 55.32° and 60.15°, respectively. At this point, α = 1.69°, β = 4.83°, and θ = 57.02°. In this case, the gain bandwidth becomes defined by the third-order dispersion, and it has great potentials to exceed one octave [27]. This unique phase matching is also called magic phase matching [28]. Deviated from this magic point, the gain bandwidth will decrease and will be re-decided by Eq. (4). Such an OPA operating at the magic phase matching can be used to generate ultra-broadband mid-IR seed pulses for further amplification.
3. Bandwidth comparison between different crystals
In this section, we compare LGN with other nonlinear crystals commonly used for mid-IR OPCPA in terms of gain bandwidth. Two typical OPA processes pumped at 1.054 μm are calculated, one is the collinear degenerate OPA at 2.108 μm, and the other is the noncollinear OPA at 3.5 μm. These two wavelengths are widely adopted in the current mid-IR OPCPAs [12,14–19]. The Type-I phase matching is mainly considered in the following calculations, because it is more suitable to support a larger bandwidth compared to the Type-II interaction [25], which is also suggested in Figs. 2 and 3. However, in the case of KTA, Type-II (os + ei→op) instead of Type-I phase matching is adopted, because the Type-I phase matching is not supported. The bandwidth is numerically calculated according to Eq. (2). In the simulations, the pump intensity Ip is fixed at 10 GW/cm2. The comparisons between different crystals are made firstly under the same crystal length (L = 1 cm), and then under the same maximum gain (G = 1000). In the second case, the crystal length L is adjusted to realize the same gain between different crystals. Refer to [20] for the Sellmeier equations of different crystals.
The Type-I degenerate OPA at 2.108 μm is firstly calculated, with the results summarized in Fig. 5 and Table 1. Comparisons are made between the crystals of LGN, β-BBO and LiNbO3. As shown by the dashed lines in Fig. 5(a), LGN has the smallest phase mismatch across the spectral range from 1.5 μm to 3 μm. On average, the phase mismatches in β-BBO and LiNbO3 are larger than that in LGN by ~6.5 and ~4.5 times, respectively. This implies that LGN can support a much larger gain bandwidth, which is confirmed by the calculations (solid lines in Fig. 5). For a common crystal length of 1 cm, the gain bandwidth [full width at half maximum (FWHM) of the gain spectra] in LGN reaches ~700 nm, nearly two times of those in LiNbO3 and β-BBO [solid lines in Fig. 5(a)]. Compared under the same gain of 1000, the gain bandwidth of LGN is still much larger than those of LiNbO3 and β-BBO [Fig. 5(b)].
Fig. 5 Gain spectra (solid curves) and phase mismatches (dashed curves) for a 2.108 μm degenerate OPA pumped at 1.054 μm. Red, green, and blue curves correspond to LGN, LiNbO3, and β-BBO, respectively. (a) Comparisons under the same crystal length for different crystals, L = 10 mm. (b) Comparisons under the same gain for different crystals, G = 1000. Different crystal lengths are used: LGN, L = 7.96 mm; LiNbO3, L = 4.16 mm; β-BBO, L = 4.40 mm.
Table 1. Calculation parameters for different crystals in the 2.108 μm OPA pumped at 1.054 μm.
For the degenerate Type-I OPA, D2 = 2 × GVDs in Eq. (4). A smaller GVDs means a larger bandwidth. If GVDs = 0, the gain bandwidth will be defined by the fourth-order dispersion (the first and third-order terms are zero at the degeneracy) [29,30]. Further calculations demonstrate that the zero-dispersion wavelengths of LGN, LiNbO3 and β-BBO are located at 1.99 μm, 1.89 μm, and 1.43 μm, respectively. We can see that the zero-dispersion wavelength of LGN is closest to the desired signal wavelength of 2.109 μm, so the LGN OPA has the smallest D2, as shown in Table 1. This is why LGN can support a so much large bandwidth.
Next we move on to the 3.5 μm noncollinear OPA pumped at 1.054 μm. LiNbO3 and KTA are used to compare with LGN. The results are summarized in Fig. 6 and Table 2. In this spectral band, the LGN still exhibit the smallest phase mismatch and thus the largest gain bandwidth. With the same crystal length of 1 cm, the gain bandwidth in LGN is as broad as 660 nm, about 1.5 times larger than those in LiNbO3 and KTA [Fig. 6(a)]. Under the same gain of 1000, the bandwidth gaps between LGN, KTA, and LiNbO3 decrease [Fig. 6(b)], but LGN still has the largest bandwidth. As shown in Fig. 6(a), the phase mismatches are zero at 3.5 μm for all the three crystals. However, in LGN, there is another wavelength (~3.15 μm) that also satisfies ∆k = 0. This phase matching property accounts for a blue shift of the gain spectrum, which greatly enlarges the gain bandwidth of LGN.
Fig. 6 Gain spectra (solid curves) and phase mismatches (dashed curves) for a 3.5 μm nonlinear OPA pumped at 1.054 μm. Red, green, and blue curves correspond to LGN, KTA, and LiNbO3, respectively. (a) Comparisons under the same crystal length for different crystals, L = 10 mm. (b) Comparisons under the same gain for different crystals, G = 1000. Different crystal lengths are used: LGN, L = 8.75 mm; KTA, L = 6.54 mm; LiNbO3, L = 4.34 mm.
Table 2. Calculation parameters for different crystals in the 3.5 μm noncollinear OPA pumped at 1.054 μm.
Another difference between LGN and KTA is that LGN allows directly seeded by mid-IR pulses. In a KTA-based OPA, the group-velocity matching is satisfied only in the case of near-IR seeding, with the mid-IR output as the idler [19]. Near-IR seeding to OPA will inevitably introduce angular dispersion to the newly generated mid-IR pulses [Fig. 7(a)]. However, in a LGN OPA directly seeded by a collimated mid-IR beam, the angular dispersion will be only presented in the newly generated near-IR pulses [Fig. 7(b)], with the amplified mid-IR laser free of angular dispersion. Of course, if such OPA is not correctly aligned, some degrees of angular dispersion will be imposed onto the mid-IR output by the angular-dependent gain in the noncollinear geometry [31].
Fig. 7 Angular dispersion of the newly generated idler in OPAs based on KTA and LGN, both of which are pumped at 1.054 μm. (a) Angular dispersion of the idler at 3.5 μm in a KTA-based OPA seeded by near-IR pulses at 1.508 μm. (b) Angular dispersion of the idler at 1.508 μm in a LGN-based OPA seeded by mid-IR pulses at 3.5 μm.
From above calculations and analysis, we can see that LGN is a superior crystal suitable for broadband mid-IR OPAs. Its tolerance to phase mismatch exceeds other commonly-used crystals. Its zero-dispersion wavelength (~2 μm) enters deeper into the mid-IR region, more promising for a broader gain bandwidth. What’s more, from Table 1 and 2, the spatial walk-off angle in LGN is typically less than 1°, two or three times smaller than those in other crystals.
4. Broadband mid-IR OPCPA in LGN
All above calculations are based on the small-signal approximation. In this section, we try to design broadband mid-IR OPCPAs based on LGN, with the pump depletion included. Thereby, the formulas given in section 2 no longer apply here. To study the gain bandwidth of a highly efficient OPCPA, we numerically solve the standard nonlinear coupled-wave equations by the symmetrized split-step Fourier method [32]. Up to the third-order dispersions are considered in our simulations. Spatial transverse dimensions are excluded as we mainly concern the gain bandwidth. This is also reasonable because 1) all the three waves are assumed to have flat-top beam profiles, and 2) the spatial walk-off in LGN is insignificant. Two types of mid-IR OPCPAs pumped at 1.054 μm are considered in this section, one is the Type-I degenerate OPA at 2.108 μm, and the other is the Type-II collinear OPA at 4.44 μm. In the first case, a LiNbO3-based OPCPA is also simulated as reference. In the simulations, the pump intensity is fixed at 10 GW/cm2 with a 20-order super-Gaussian temporal profile; the seeding is a linearly chirped pulse with a constant spectral intensity across its bandwidth. The total intensity of the seeding mid-IR pulse is 10 kW/cm2 (i.e., Is/Ip = 10‒6). The seeding spectral range is exaggerated to check the ability in gain bandwidth. The pulse durations of both the pump and stretched seeding pulses are 100 ps.
Figure 8 summarizes the simulation results for the Type-I degenerate OPCPA at 2.108 μm. Due to a smaller deff, the needed LGN length for peak conversion is nearly two folds of the LiNbO3 length [Fig. 8(a)]. The positions marked by points A and B are used to carry out the following calculations, which correspond a 15.55-mm-long LGN and an 8.11-mm-long LiNbO3. As expected, the LGN-based OPCPA exhibits an ultra-broad gain bandwidth as large as about 900 nm (FWHM), as shown in Fig. 8(c). By contrast, the gain bandwidth of the LiNbO3-based OPCPA is limited to about 550 nm. For chirped seeding pulse, different spectral components distribute at different temporal positions. Therefore, the larger gain-bandwidth brings about a more efficient signal amplification and a stronger pump depletion, as shown in Figs. 8(a) and 8(b).
Fig. 8 Simulation results for the Type-I degenerate OPCPA pumped at 1.054 μm. (a) Efficiency evolutions along the crystal length in LGN- (red curve) and LiNbO3- (blue curve) based OPCPAs, with the efficiency peak marked by points A and B, respectively. (b) Temporal profiles of the input pump or chirped signal pulses (black solid curve), the residual pump pulses in LGN (red dashed curve) and LiNbO3 (blue dashed curve), and the amplified chirped signal pulses in LGN (red solid curve) and LiNbO3 (blue solid curve). (c) Spectra of the input signal (black solid curve), and the amplified signals in LGN (red solid curve) and LiNbO3 (blue solid curve). The red and blue dashed curves represent the OPP produced in LGN- and LiNbO3-based OPCPAs, respectively. (d) The compressed pulses without (dash dotted curves) and with (solid curves) OPP compensation in LGN-based (red curves) and LiNbO3-based (blue curves) OPCPAs. The dashed curves represent the corresponding Fourier-transform-limited pulses. All the calculations in (b)~(d) are based on the crystal lengths marked by point A for LGN and point B for LiNbO3 in (a).
To compress the amplified broadband chirped pulse to near its Fourier-transform-limit, except for the phase added by the stretcher and that accumulated by linear dispersion in the crystal, it further needs to compensate the additional nonlinear spectral phase produced in the process of parametric amplification, as shown by the dashed lines in Fig. 8(c). This optical parametric phase (OPP) is proportional to the wavelength dependent phase mismatch Δk, and will hamper pulse compression [33,34], as shown in Fig. 8(d). Due to the smaller Δk in LGN [dashed lines in Fig. 5(a)], the OPP in the LGN-based OPCPA is less serious compared with that in the LiNbO3-based OPCPA [dashed lines in Fig. 8(c)]. To obtain the shortest pulse duration, the compensation of OPP is indispensable. In a degenerate OPCPA (the odd-order terms vanish in phase-mismatch), the OPP is dominated by the second-order dispersion, which is simplest for dispersion compensation. As OPP is nearly half the linear crystal dispersion (much smaller than the initial chirp), it can be well controlled by the commonly adopted techniques for dispersion management. For example, the pulse shaper (e.g., an acoustic optical modulator or a liquid-crystal spatial light modulator) that commonly used in few-cycle OPCPA systems can be used to properly compensate the OPP. For the LGN-based OPCPA, a dispersion compensation of 108 fs2 leads to the shortest pulses with a duration of 13.6 fs, very close to its Fourier-transform-limit [Fig. 8(d)]. It is sub-two cycles at 2.108 μm. For the LiNbO3-based OPCPA, the OPP can also be compensated by introducing a larger dispersion of 243 fs2 to achieve the near Fourier-transform-limited pulse duration of 21 fs (three cycles). It should be noted that all the comparisons between LGN and LiNbO3 are made at the same pump intensity of 10 GW/cm2 (for 0.1 ns pulses), which is close to the damage threshold of LGN. In practice, LiNbO3 cannot afford such high pump intensity, so its amplification performance might have been over-estimated.
Another potential advantage of LGN is the extended IR transparent region. In LiNbO3 and KTA, strong absorption will arise for the wavelength beyond 4 μm. In LGN, however, this wavelength limit is pushed to ~6 μm [21]. As shown in Figs. 2 and 3, LGN can support the broadband amplification between 4 and 6 μm. This undoubtedly enlarges the achievable operation range of intense mid-IR OPCPAs. Here, we give one example of the Type-II collinear OPCPA at 4.44 μm, and the calculation results are summarized in Fig. 9. No reference is used because other commonly-used mid-IR crystals have absorption on this waveband. After the compensation of OPP by introducing a dispersion of 140 fs2, a near Fourier-transform-limited pulse duration of 80 fs (~five cycles) at 4.44 μm is obtained in the LGN-based OPCPA.
Fig. 9 Simulation results for the Type-II 4.44 μm collinear OPCPA pumped at 1.054 μm. (a) The efficiency evolution along the crystal length, with the efficiency peak at 25.25 mm. (b) Temporal profiles of the input pump or chirped signal pulses (black solid line), the residual pump pulses (black dashed line), and the amplified chirped signal pulses (red solid line). (c) Spectra of the input signal (black solid line), and the amplified signals (red solid line). The red dashed (black dotted) curve represent the OPP before and after compensation. (d) The compressed pulses by compensating OPP (black solid line). The red dashed curves represent the corresponding Fourier-transform-limited pulses. All the calculations in (b)~(d) are based on the crystal lengths of 25.25 mm.
5. Summary
A theoretical treatment has been presented for the optical properties of LGN crystal with particular reference to its gain bandwidth. The primary aim is to evaluate its potential as the nonlinear crystal for few-cycle mid-IR OPCPA. Its broad transparent region, moderate effective nonlinear coefficient, high damage threshold, small spatial walk-off, large size scalability, and good thermo-mechanical properties make it very promising as a mid-IR nonlinear crystal. And most of all, it can support a much broader gain bandwidth than other commonly used mid-IR crystals, such as β-BBO, LiNbO3, and KTA. Intense mid-IR pulses as short as sub-five cycles are well generated from the LGN-based OPCPAs.
The fundamental cause for the excellent bandwidth performance of LGN lies in the fact that its zero-dispersion wavelength (~2 μm) is the longest among the frequently-used mid-IR crystals. Thus, LGN ensures the smallest phase mismatch for the mid-IR OPCPAs. As a result, its bandwidth is the broadest and its OPP is the minimum, both of which are benefit for enhancing the peak power of the compressed pulses.
In addition to use as a superior optical parametric crystal, LGN also holds promises to be used as a quasi-parametric crystal because it allows doping with various types of rare-earth ions (collectively described by Re3+) [35]. The quasi-parametric amplification based on these Re3+:LGN crystals may combine the ultrahigh efficiency and ultrabroad bandwidth [36]. Besides, Re3+:LGN can support quasi-parametric amplification in an extended spectral range up to 6 μm, which is a significant supplement to the current Re3+-doped yttrium calcium oxyborate crystals.
In conclusion, LGN is a very qualified candidate for the nonlinear crystals of OPA and/or OPCPA aiming to obtain high-peak-power few-cycle mid-IR pulses.
Funding
National Basic Research Program of China (2013CBA01505); China Postdoctoral Science Foundation (2014M560332); Science and Technology Commission of Shanghai (15XD1502100).
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