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Numerical study on the characteristics of hybrid seeded femtosecond optical parametric amplifier at mid-infrared wavelength
Results in Physics 13 (2019) 102284
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Numerical study on the characteristics of hybrid seeded femtosecond optical parametric amplifier at mid-infrared wavelength ⁎
Yuan Zhoua, Ying Chena,b, , Dongwen Zhangb, Guobao Jianga, Lulu Wanga, Fangrong Hua, a b
T
⁎
School of Electronic Information and Electrical Engineering, Changsha University, Changsha 410003, China Department of Physics, National University of Defense Technology Department, Changsha 410073, China
A B S T R A C T
In the optical parametric amplifier (OPA) process, the phase of the pump is transmitted to the amplified signal due to the spatial walk-off effect and/or a temporal group velocity mismatch (GVM) effect between coherent light waves. As a result, the quality of amplified signal will be reduced by the phase distortion and variation of beam equality of the pump pulse. By using a pair of OPAs, the signal and idler are chosen as seeding lights in the front and back stages, respectively, so that the phase of the amplified signal can be restored, and the influence of phase distortion and beam equality deterioration of pump pulse can be eliminated. The present article also reports other characteristics of this hybrid seeded scheme, including accepted bandwidth, spectral purity, and conversion efficiency.
Introduction The near-infrared femtosecond optical parametric amplifier (OPA) usually incorporates β-barium borate (BBO) crystals [1–3], which the structure were extended from the experience of long pulse pumping OPA, namely using the traditional optical parametric generation (OPG)/OPA structure [4]. The OPA device based on BBO uses the second harmonic pulse of Ti: sapphire laser as the pump laser, and adopts non-collinear phase-matching and white-light seeding methods to obtain ideal and tunable femtosecond pulses in the visible band [5,6]. Currently, BBO-based OPA has been commercialized as a routine method for generating tunable femtosecond lasers from a range of ∼0.45 μm to 2.6 μm. However, for the mid-infrared (MIR) femtosecond OPA system, the conventional OPG device cannot be used directly because its nonlinear crystal is LiNbO3 or KTiOPO4 [7–9]. The conventional OPG device requires higher pump intensity, while MIR crystals such as LiNbO3 have lower damage thresholds than BBO [10]. Therefore, these crystals are subject to serious surface damage and self-focusing problems. Several schemes to improve the reliability of MIR femtosecond OPA have been proposed. One uses a near-infrared femtosecond OPA to generate high intensity signal pulses and seed them into the next stage MIR-OPA device [11]. In this way, tunable MIR idle frequency pulses can be obtained by the difference frequency generation (DFG) between pump and signal. The seeding of high intensity signal pulses reduces the demand for pump intensity in the DFG process, and the conversion efficiency of DFG is relatively high. The DFG method can produce near Fourier-transform limited MIR femtosecond lasers, but because the
⁎
structure of this OPA is very complex and an additional stage OPA is needed, the overall conversion efficiency is limited. Another OPG scheme uses a narrow-band laser as the external seed of the femtosecond OPA to avoid crystal damage [12,13]. The device is compact and efficient. When the external seed is strong enough, even one-stage OPA can achieve high conversion efficiency. Unfortunately, the external seeding process requires adjustment of the wavelength of pump or seed, and of the crystal angle to achieve the wavelength tuning of output signal, which makes the daily operation very inconvenient. In addition, the output femtosecond signal is also attached to the background of narrow-band seeding (i.e., there is a sharp spike in the broad spectrum [14]), and the purity of the spectrum decreases significantly. A hybrid seeded MIR femtosecond OPA scheme was proposed by Luo et al [15]. In the first stage of OPA, an external continuous wave (CW) is seeded at the signal wavelength, plus difference-frequency mixing between the idler and pump in the second stage. Between the two OPA stages, a germanium plate is used to block the amplified CW signal. Compared with the traditional two-stage OPA, the hybrid seeded OPA basically does not introduce additional complexity in the setup, while it generates signal pulses with clean spectra and provides direct wavelength tunability like OPG/OPA scheme. The hybrid seeded femtosecond OPA is free from damage since the external seeding lowers the pump threshold dramatically, and its conversion efficiency has been proved to be as high as that of the conventional seeded OPA in the saturation regime [15]. This so-called hybrid seeded scheme, used in the past to eliminate spectral spikes caused by continuous wave or high-repetition-rate
Corresponding authors. E-mail addresses: [email protected] (Y. Chen), [email protected] (F. Hu).
https://doi.org/10.1016/j.rinp.2019.102284 Received 26 January 2019; Received in revised form 9 April 2019; Accepted 10 April 2019 Available online 12 April 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
and (2). The signal walk-off length Lsps is defined as Lsps = w/ρ, where ρ is the walk-off angle, and Lips = Lsps in the type-I collinear configuration. The ratio of Lsps to crystal length L indicates the practical walk-off magnitude of the OPA process in the nonlinear crystal. The diffraction lengths L2js are defined as L2js = 2πw2/λj and j = s, i, p refers to the signal, idler, and pump waves, respectively. Diffraction involved in the case of large beam size has a minor effect. For example, a beam with waist radius of 2 mm and wavelength 1 μm will have a diffraction length of ∼24 m which is much longer than the typical crystal length used in existing systems. Thus the diffraction effects are ignored in this paper. In the calculations, the initial signal wave is assumed to be a Gaussian beam with phase uniformity, and Δk is set to zero because it primarily affects signal gain and conversion efficiency, which has been thoroughly discussed. Investigation of the walk-off effect in isolation can explicitly clarify its impact on the output signal beam. The standard split-step method and Runge-Kutta algorithm were adopted to solve the nonlinear equations numerically. The coupled wave equations in temporal domain are as follows [20],
Fig. 1. The schematic diagram of two-stage OPA configurations: (a) the traditional walk-off-compensating OPA; (b) the hybrid seeded OPA.
seeding lasers, has been sparsely studied. This article reports a systematic study of the characteristics of the hybrid seeded OPA, and explores more advantages of this scheme.
λp ∂Es (z , t ) L ∂E (z , t ) L ∂2ES (z , t ) + NL s + i NL = −i Ep (z , t ) Ei∗ (z , t ) e−iΔkz 2 λs ∂z Lsp ∂t L2s ∂t
Scheme of hybrid seeded femtosecond OPA and corresponding numerical model
(4)
∂Ei (z , t ) L ∂E (z , t ) + NL i + ∂z Lip ∂t
The hybrid seeded femtosecond OPA scheme uses a two-stage amplification configuration, using seeding lights with different wavelengths, namely signal and idler. Femtosecond OPA often uses twostage or multi-stage amplification configuration [16], which not only optimizes the conversion efficiency by allocating the intensity of pump at all levels, but also helps to minimize the impact of group velocity mismatch (GVM) by using optical delay lines. The principle of the hybrid seeded OPA is shown in Fig. 1(b). The first stage uses a CW signal as external seeding light, which is similar to the traditional OPA device [Fig. 1(a)] [17]. Unlike the traditional OPA device, the signal is blocked after the first stage OPA, leaving only the idler in the second stage. In the second stage of OPA, DFG takes place between idler and pump pulses. Finally, the output signal and idler are clean in both spectral and temporal domains. OPA is the nonlinear process of the interaction of pump, signal, and idler light. The coupled wave equations in the spatial domain are as follows: [18]
= −i
λs
Ep (z , x ) Ei∗ (z , x ) e−iΔkz
∂Ep (z , t ) ∂z
λp λi
∂Ep (z , x ) ∂z
Ep (z , x ) Es∗ (z , x ) e−iΔkz
+i
LNL ∂2Ep (z , x ) = −iEs (z , x ) Ei (z , x ) eiΔkz L2ps ∂ 2x
= −i
λp λi
Ep (z , t ) Es∗ (z , t ) e−iΔkz
+
L ∂2Ep (z , i NL L2p ∂ 2x
t)
= −iEs (z , t ) Ei (z , t ) eiΔkz
(6)
The time variable t is normalized to the Fourier-transform-limitcorresponding duration (τs) of the signal. The wave-vector mismatch Δk and the nonlinear length LNL are the same as that defined in spatial domain. Lipt = τs / GVMip (Lspt = τs / GVMsp) is the GVM length of the idler (signal) with respect to the pump pulse. And the smaller Lipt is, the larger practical GVMip will be. Since most OPCPA systems work near at wavelength degeneracy, we assume equal group velocities of the signal and idler (i.e., GVMsp = GVMip) in this paper. The dispersion effect is characterized by the dispersion length L2jt = 2τs2/GVDj, in which j = s, i, p refers to the signal, idler, and pump waves, respectively. Characteristics of hybrid seeded OPA scheme Recovery effect for signal pulse in presence of pump phase modulation Although hybrid seeded OPA can partially eliminate the effect of pump phase distortion on signal, not all phase distortion can be perfectly compensated [21]. It is assumed that the pump pulse is a Gaussian pulse AP (0, t ) = E0 exp(−t 2 + iϕ (t )) , the phase is a sinusoidal modulation, ϕ (t ) = m sin(2πfm t ), where m and fm are the amplitude and frequency of the modulation. The recovery effect of the signal phase will be worse and worse with the increase of the phase distortion of the pump (Fig. 2), which is consistent with the research conclusions in Ref. [21]. It is stipulated here that if the phase modulation amplitude of the second stage signal is restored to less than 1% of that in the first stage, the phase of the signal is assumed as a well-restored status. According to Fig. 2, if m ⩽ 2 rad , regardless of the value of fm, even if it reaches two orders of magnitude, the phase recovery effect of the output signal is well-restored. If m > 2 rad , the signal phase can be restored to a better situation only when the value of m and fm are both below the curve. Otherwise, the hybrid seeded OPA will lose its advantage of strong recovery. This is because, in the OPA process, with the increase of m and fm of the pump modulation, the amplitude modulation of the signal will become more and more intense, which makes the phase recovery more difficult. In addition, the smaller the GVM (i.e., the larger the Lipt/L), the larger the compensable range of
(1)
∂Ei (z , x ) L ∂E (z , x ) L ∂2Ei (z , x ) + NL i + i NL ∂z Lips ∂x L2is ∂ 2x = −i
t)
(5)
∂Es (z , x ) L ∂E (z , x ) L ∂2ES (z , x ) + i NL + NL s ∂z Lsps ∂x L2ss ∂ 2x λp
L ∂2Ei (z , i NL L2i ∂ 2t
(2)
(3)
where Es(z, x), Ei(z, x) and Ep(z, x) are the envelopes of signal, idler and pump lights, respectively, which are normalized to the input pump field E0. For the sake of simplicity, a one-dimensional transverse model is used in simulations; diffraction effects are ignored due to the large beam aperture. A Gaussian pump beam is assumed throughout this article, although different beam shapes may be involved. The spatial variable x is normalized to the radius of the pump beam waist w; Δk = ks + ki−kp is the wave-vector mismatch among the three waves, where wave vector kj = nωj/c. The nonlinear length is defined by LNL = nλp /(πχ (2) E0) as a measure of the pump intensity [19]. The pump beam is the reference beam; thus, walk-off terms only appear in Eqs. (1) 2
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
Fig. 4. Relationship between Ms2 factors of all stages and the spatial walk-off length, where Mp2 = 10, LNL = 0.25 L, L = 10 mm, Es(0) = 10−6.
Fig. 2. The influence of amplitude and frequency of the pump modulation on the phase recovery effect of the output signal phase in the hybrid seeded OPA scheme, where Es(0) = 10−6 and crystal length L is 10 mm.
curve in the hybrid seeded OPA scheme. The recovery capability for the signal phase when different shapes of the pump phase are adopted is shown in Fig. 3. It is assumed that the phase forms of the pump are ϕ (t ) = (nt )2 and ϕ (t ) = (nt )3 , respectively. Due to the GVM effect, the phase of the signal output at the first stage OPA is modulated (dashed line). In the second stage, the phase of the output signal can almost return to the initial state (solid line) under the hybrid seeded OPA scheme. In addition, the phase shape of the firststage signal is the first-order derivative of that of the initial pump, that is, φs1 ∼ φ′ (t ) .
scheme), then the Ms2 factor of the final output signal will become worse (circle line). If the generated idler is injected as seed source in the second stage (the hybrid seeded OPA scheme), Ms2 factor of the output signal is approximately 1 [i.e., the beam quality of signal is restored to near diffraction limit (square line)]. Additionally, the Ms2 factor of the signal under the traditional OPA scheme is related to the spatial walk-off length Lips, while Lips and Mp2 factor do not affect the output signal beam quality if the hybrid seeded OPA scheme is adopted. Regardless of the Ms2 factor in the first stage, the beam quality of the signal in the second stage is nearly diffractionlimited.
M2 Factor of output signal in spatial domain
Phase reconstruction of signal in temporal domain
The M2 = (c/λ)w0·θ factor is generally used to describe the beam quality, where w0 is the waist width of actual beam and θ is far-field divergence angle [22]. The larger the M2 factor, the worse the beam quality; when M2 = 1, the beam is considered to be an ideal beam (i.e., the beam is diffraction-limited). In this section, the influence of pump beam quality on Ms2 factor of signal and the compensation ability of the hybrid seeded OPA scheme are discussed. The Mp2 factor of pump beam is assumed to be 10. Fig. 4 shows the relationship between Ms2 factors of all stages and the spatial walk-off length. It can be seen from the graph that the Ms2 factor of the first stage signal is greater than 1, and the beam quality is obviously worse (triangle line). If the seed source of the second stage OPA still uses the signal (traditional two-stage OPA
In the birefringent phase-matching scheme, the phase transfer from pump to signal pulse inevitably occurs because of the existence of spatial walk-off or GVM effect in the temporal domain [23]. The phase transfer problem in the spatial domain is usually solved by paired nonlinear crystals [17]. Two-stage OPA processes occur in cascaded crystals sequentially, in which the symbols of space walk-off effect are between the two stages OPA. As a result, the phase of the output signal can be restored to its initial state, thus eliminating the influence of the phase transfer from pump to signal pulse. However, this method cannot be simply applied into the temporal domain, because the symbols of space walk-off effect can be changed by crystal orientation, while the symbols of GVM cannot be changed. The hybrid seeded OPA scheme is
Fig. 3. The phase shape of the signal pulse in the first stage OPA (dashed line) and second stage OPA. The pump phase is adopted as (a) ϕ (t ) = (nt )2 ; (b) ϕ (t ) = (nt )3 , n = 2, where Lipt = Lspt = L, LNL = 0.25 L, L = 10 mm, Es(0) = 10−6. 3
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
Fig. 5. Pulse shape and phase of the signal, solid curve: the first stage OPA; dashed curve: the second stage OPA, where c = 5, Lipt = Lspt = L, LNL = 0.15 L, L = 10 mm, Es(0) = 10−6.
used to solve the problem of phase reconstruction of signal in the temporal domain. Assuming that the pump pulse is a non-Fourier-limited Gaussian pulse AP (0, t ) = E0 exp(− (1 + ic ) T 2/(2T02)) , its linear chirp coefficient c = 5, and the initial signal pulse is a Fourier-limited Gaussian pulse. By using the hybrid seeded OPA scheme (Fig. 5), the signal phase in the first stage is still distorted (solid line), but the output signal phase in the second stage is restored to be near Fourier-transform limited (dashed line). It can be concluded that the hybrid seeded OPA scheme can ensure the optical quality of signal in both spatial and temporal domains in high-energy optical parametric chirped pulse amplification (OPCPA) systems, which provides a new means for optimizing various OPA and OPCPA systems and has a bright prospect in developing high-power laser sources with high optical quality. Accepted bandwidth in OPA system Fig. 6. The spectra of output signal in various OPA systems, the traditional twostage signal seeded scheme (dash-dotted line), the two-stage cascaded-crystals scheme (dotted line) and the hybrid seeded scheme (solid line). (a) Lipt = Lspt = L, LNL = 0.25 L; (b) Lipt = Lspt = 0.3 L, LNL = 0.1 L; L = 10 mm, Es(0) = 10−6.
In order to generate shorter signal pulses, femtosecond OPA devices need a broader accepted bandwidth. A variety of technologies are used to increase the accepted bandwidth of OPA [24,25]; the most typical one is the cascaded-crystals scheme [17]. Next, the output signal spectra for several OPA schemes are compared, including the traditional two-stage signal seeded scheme (dash-dotted line), the two-stage cascaded-crystals scheme (dotted line), and the hybrid seeded scheme (solid line). Fig. 6(a) and (b) correspond to different GVM lengths (i.e., Lip = Lsp = L and Lip = Lsp = 0.3 L, respectively). Obviously, the more serious the GVM effect is, the narrower the spectrum of the output signal is, and the more difficult it is to obtain the ultrashort signal pulse. Compared with the traditional two-stage signal seeded scheme, both the hybrid seeded scheme and the cascaded-crystals scheme increase the accepted bandwidth of OPA. When the GVM effect is not too serious, the accepted bandwidths for the two schemes are the same (solid line and dotted line in Fig. 6(a)). When the GVM effect is relatively serious, the accepted bandwidth for the hybrid seeded scheme is broader, as shown by the solid line in Fig. 6(b), which also demonstrates its advantage in practical applications. Spectral purity of signal
Fig. 7. Spectra of the output signal using continuous wave seeding OPA system, the traditional two-stage signal seeded scheme (solid line), and the hybrid seeded scheme (dashed line), where Lipt = Lspt = 5 L, LNL = 0.35 L, L = 10 mm, Es(0) = 10−6.
In the case of OPA system using CW seeding, the amplified signal is always accompanied by a narrow-band background light [14]. Therefore, the broad spectrum of signal has a sharp spine, and the spectral purity is obviously deteriorated, as shown in the solid line in Fig. 7. If the hybrid seeded OPA scheme is adopted, the spectral component at 4
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
(2018JJ2455), the Scientifc Research Fundation of Hunan Provincial Education Department (17A020). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.rinp.2019.102284. References [1] Greenfield S, Wasielewski M. Near-transform-limited visible and near-IR femtosecond pulses from optical parametric amplification using Type-II β-barium borate. Opt Lett 1995;20:1394–6. [2] Marcinkevičiūtė A, Michailovas K, Butkus R. Generation and parametric amplification of broadband chirped pulses in the near-infrared. Opt Commun 2018;415:70–3. [3] Tamošauskas G, Beresnevičius G, Gadonas D, et al. Transmittance and phase matching of BBO crystal in the 3–5 μm range and its application for the characterization of mid-infrared laser pulses. Opt Mater Express 2018;8:1410–8. [4] Cerullo G, De Silvestri S. Ultrafast optical parametric amplifiers. Rev Sci Instrum 2003;74:1–18. [5] Reed M, Armas M, Steinershepard M, et al. 30-fs pulses tunable across the visible with a 100-kHz Ti:sapphire regenerative amplifier. Opt Lett 1995;20:605–7. [6] Cheng Y, Gao G, Poulin P, et al. Efficient two-stage dual-beam noncollinear optical parametric amplifier. Appl Phys B 2018;124:93. [7] Rotermund F, Petrov V, Noack F, et al. Laser-diode-seeded operation of a femtosecond optical parametric amplifier with MgO: LiNbO3 and generation of 5-cycle pulses near 3 μm. J Opt Soc Am B 1999;16:1539–45. [8] Xu H, Yang F, Chen Y, et al. Millijoule-level picosecond mid-infrared optical parametric amplifier based on MgO-doped periodically poled lithium niobate. Appl Opt 2015;54:2489–94. [9] Baravets Y, Honzatko P, Todorov F, et al. Narrowband widely tunable CW midinfrared generator based on difference frequency generation in periodically poled KTP and KTA crystals. Opt Quant Electron 2016;48:286. [10] Bach F, Mero M, Chou M, et al. Laser induced damage studies of LiNbO3 using 1030nm, ultrashort pulses at 10–1000 kHz. Opt Mater Express 2017;7:240–52. [11] Gale G, Gallot G, Hache F, et al. Generation of intense highly coherent femtosecond pulses in the mid infrared. Opt Lett 1997;22:1253–5. [12] Petrov V, Noack F. Tunable femtosecond optical parametric amplifier in the midinfrared with narrow-band seeding. J Opt Soc Am B 1995;12:2214–21. [13] Pires H, Baudisch M, Sanchez D, et al. Ultrashort pulse generation in the mid-IR. Prog Quantum Electron 2015;43:1–30. [14] Jovanovic I, Barty C, Haefner C, et al. Optical switching and contrast enhancement in intense laser systems by cascaded optical parametric amplification. Opt Lett 2006;31(6):787–9. [15] Luo H, Qian L, Yuan P, et al. Hybrid seeded femtosecond optical parametric amplifier. Opt Express 2005;13(24):9747–52. [16] Stepanenko Y, Radzewicz C. High-gain multipass noncollinear optical parametric chirped pulse amplifier. Appl Phys Lett 2005;86:211120. [17] Armstrong D, Alford W, Raymond T, et al. Parametric amplification and oscillation with walkoff-compensating crystals. J Opt Soc Am B 1997;14:460–74. [18] Chen Y, Zhou Y, Jiang G, et al. Numerical simulations of transfer of spatial beam aberrations in optical parametric chirped-pulse amplification. Adv Cond Matter Phys 2018;5731938. [19] Chen Y, Zhou Y, Wang Z. Improvement of the frequency-doubling efficiency of high-average-power lasers using multicrystal scheme with opposite thermal properties. Results Phys 2017;7:3530–6. [20] Yuan P, Qian LJ, Luo H, Zhu HY, Wen SC. Femtosecond optical parametric amplification with dispersion precompensation. IEEE J Sel Top Quantum Electron 2006;12:181–6. [21] Wei X, Qian L, Yuan P, et al. Optical parametric amplification pumped by a phaseaberrated beam. Opt Express 2008;16:8904–15. [22] Yang H, Zhao D, Lu X, Wang S. Several viewpoints related to the beam quality factor M 2. Chin J Lasers 1997;24:709–14. [23] Forget N, Cotel A, Brambrink E, et al. Pump-noise transfer in optical parametric chirped-pulse amplification. Opt Lett 2005;30:2921–3. [24] Kraemer D, Cowan M, Hua R, et al. High power femosecond infrared laser source based on noncollinear optical parametric chirped pulse amplification. J Opt Soc Am B 2007;24:813–8. [25] Ogawa K, Aoyama M, Akahane Y, et al. Bandwidth enhancement of optical parametric chirped pulse amplification by temporally delayed two pump beams. Jan J Appl Phys 2008;47:4592–4.
Fig. 8. The relationship between conversion efficiency and initial signal energy, the traditional two-stage seeded OPA scheme (solid line), and the hybrid seeded OPA scheme (circle), where Lipt = Lspt = 5 L, LNL = 0.35 L, L = 10 mm.
the signal wavelength is blocked in the first stage, leaving a clean idler in both time domain and frequency domain, which enter into the second stage. Finally, the signal pulse is generated when DFG takes place between the idler and pump pulse in the second stage. Importantly, temporally and spectrally clean pulses at signal wavelength can be obtained, which does not contain the component of continuous wave (dashed line in Fig. 7). Conversion efficiency of OPA system High gain and high conversion efficiency have always been the goal of laser amplification systems. Two-stage or multi-stage OPA has been proved to be a very effective method [16], which also avoids the risk of crystal damage caused by excessive pumping energy. The conversion efficiency of the hybrid seeded OPA scheme is also investigated (Fig. 8). It can be seen that the hybrid seeded scheme can achieve the same conversion efficiency as the traditional two-stage OPA scheme. Therefore, it is not at the expense of conversion efficiency to control the phase transfer from pump to signal in the hybrid seeded OPA scheme. Conclusion We demonstrate that the hybrid seeded OPA scheme can control the phase transfer from pump pulse to signal pulse in both temporal and spectral domains by use of numerical simulation, so that the phase of output signal field is not restricted to the undesirable phase of pump pulse. In addition, the hybrid seeded OPA scheme has many advantages, such as broad accepted bandwidth, clean output spectra at signal and idler wavelength, and high conversion efficiency. This technology will have good prospects in the development of high-power laser sources with high optical quality. Acknowledgements This work was partially supported by NSAF under grant no. U1830206 and the Natural Science Fundation of Hunan Province, China
5
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Numerical study on the characteristics of hybrid seeded femtosecond optical parametric amplifier at mid-infrared wavelength ⁎
Yuan Zhoua, Ying Chena,b, , Dongwen Zhangb, Guobao Jianga, Lulu Wanga, Fangrong Hua, a b
T
⁎
School of Electronic Information and Electrical Engineering, Changsha University, Changsha 410003, China Department of Physics, National University of Defense Technology Department, Changsha 410073, China
A B S T R A C T
In the optical parametric amplifier (OPA) process, the phase of the pump is transmitted to the amplified signal due to the spatial walk-off effect and/or a temporal group velocity mismatch (GVM) effect between coherent light waves. As a result, the quality of amplified signal will be reduced by the phase distortion and variation of beam equality of the pump pulse. By using a pair of OPAs, the signal and idler are chosen as seeding lights in the front and back stages, respectively, so that the phase of the amplified signal can be restored, and the influence of phase distortion and beam equality deterioration of pump pulse can be eliminated. The present article also reports other characteristics of this hybrid seeded scheme, including accepted bandwidth, spectral purity, and conversion efficiency.
Introduction The near-infrared femtosecond optical parametric amplifier (OPA) usually incorporates β-barium borate (BBO) crystals [1–3], which the structure were extended from the experience of long pulse pumping OPA, namely using the traditional optical parametric generation (OPG)/OPA structure [4]. The OPA device based on BBO uses the second harmonic pulse of Ti: sapphire laser as the pump laser, and adopts non-collinear phase-matching and white-light seeding methods to obtain ideal and tunable femtosecond pulses in the visible band [5,6]. Currently, BBO-based OPA has been commercialized as a routine method for generating tunable femtosecond lasers from a range of ∼0.45 μm to 2.6 μm. However, for the mid-infrared (MIR) femtosecond OPA system, the conventional OPG device cannot be used directly because its nonlinear crystal is LiNbO3 or KTiOPO4 [7–9]. The conventional OPG device requires higher pump intensity, while MIR crystals such as LiNbO3 have lower damage thresholds than BBO [10]. Therefore, these crystals are subject to serious surface damage and self-focusing problems. Several schemes to improve the reliability of MIR femtosecond OPA have been proposed. One uses a near-infrared femtosecond OPA to generate high intensity signal pulses and seed them into the next stage MIR-OPA device [11]. In this way, tunable MIR idle frequency pulses can be obtained by the difference frequency generation (DFG) between pump and signal. The seeding of high intensity signal pulses reduces the demand for pump intensity in the DFG process, and the conversion efficiency of DFG is relatively high. The DFG method can produce near Fourier-transform limited MIR femtosecond lasers, but because the
⁎
structure of this OPA is very complex and an additional stage OPA is needed, the overall conversion efficiency is limited. Another OPG scheme uses a narrow-band laser as the external seed of the femtosecond OPA to avoid crystal damage [12,13]. The device is compact and efficient. When the external seed is strong enough, even one-stage OPA can achieve high conversion efficiency. Unfortunately, the external seeding process requires adjustment of the wavelength of pump or seed, and of the crystal angle to achieve the wavelength tuning of output signal, which makes the daily operation very inconvenient. In addition, the output femtosecond signal is also attached to the background of narrow-band seeding (i.e., there is a sharp spike in the broad spectrum [14]), and the purity of the spectrum decreases significantly. A hybrid seeded MIR femtosecond OPA scheme was proposed by Luo et al [15]. In the first stage of OPA, an external continuous wave (CW) is seeded at the signal wavelength, plus difference-frequency mixing between the idler and pump in the second stage. Between the two OPA stages, a germanium plate is used to block the amplified CW signal. Compared with the traditional two-stage OPA, the hybrid seeded OPA basically does not introduce additional complexity in the setup, while it generates signal pulses with clean spectra and provides direct wavelength tunability like OPG/OPA scheme. The hybrid seeded femtosecond OPA is free from damage since the external seeding lowers the pump threshold dramatically, and its conversion efficiency has been proved to be as high as that of the conventional seeded OPA in the saturation regime [15]. This so-called hybrid seeded scheme, used in the past to eliminate spectral spikes caused by continuous wave or high-repetition-rate
Corresponding authors. E-mail addresses: [email protected] (Y. Chen), [email protected] (F. Hu).
https://doi.org/10.1016/j.rinp.2019.102284 Received 26 January 2019; Received in revised form 9 April 2019; Accepted 10 April 2019 Available online 12 April 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
and (2). The signal walk-off length Lsps is defined as Lsps = w/ρ, where ρ is the walk-off angle, and Lips = Lsps in the type-I collinear configuration. The ratio of Lsps to crystal length L indicates the practical walk-off magnitude of the OPA process in the nonlinear crystal. The diffraction lengths L2js are defined as L2js = 2πw2/λj and j = s, i, p refers to the signal, idler, and pump waves, respectively. Diffraction involved in the case of large beam size has a minor effect. For example, a beam with waist radius of 2 mm and wavelength 1 μm will have a diffraction length of ∼24 m which is much longer than the typical crystal length used in existing systems. Thus the diffraction effects are ignored in this paper. In the calculations, the initial signal wave is assumed to be a Gaussian beam with phase uniformity, and Δk is set to zero because it primarily affects signal gain and conversion efficiency, which has been thoroughly discussed. Investigation of the walk-off effect in isolation can explicitly clarify its impact on the output signal beam. The standard split-step method and Runge-Kutta algorithm were adopted to solve the nonlinear equations numerically. The coupled wave equations in temporal domain are as follows [20],
Fig. 1. The schematic diagram of two-stage OPA configurations: (a) the traditional walk-off-compensating OPA; (b) the hybrid seeded OPA.
seeding lasers, has been sparsely studied. This article reports a systematic study of the characteristics of the hybrid seeded OPA, and explores more advantages of this scheme.
λp ∂Es (z , t ) L ∂E (z , t ) L ∂2ES (z , t ) + NL s + i NL = −i Ep (z , t ) Ei∗ (z , t ) e−iΔkz 2 λs ∂z Lsp ∂t L2s ∂t
Scheme of hybrid seeded femtosecond OPA and corresponding numerical model
(4)
∂Ei (z , t ) L ∂E (z , t ) + NL i + ∂z Lip ∂t
The hybrid seeded femtosecond OPA scheme uses a two-stage amplification configuration, using seeding lights with different wavelengths, namely signal and idler. Femtosecond OPA often uses twostage or multi-stage amplification configuration [16], which not only optimizes the conversion efficiency by allocating the intensity of pump at all levels, but also helps to minimize the impact of group velocity mismatch (GVM) by using optical delay lines. The principle of the hybrid seeded OPA is shown in Fig. 1(b). The first stage uses a CW signal as external seeding light, which is similar to the traditional OPA device [Fig. 1(a)] [17]. Unlike the traditional OPA device, the signal is blocked after the first stage OPA, leaving only the idler in the second stage. In the second stage of OPA, DFG takes place between idler and pump pulses. Finally, the output signal and idler are clean in both spectral and temporal domains. OPA is the nonlinear process of the interaction of pump, signal, and idler light. The coupled wave equations in the spatial domain are as follows: [18]
= −i
λs
Ep (z , x ) Ei∗ (z , x ) e−iΔkz
∂Ep (z , t ) ∂z
λp λi
∂Ep (z , x ) ∂z
Ep (z , x ) Es∗ (z , x ) e−iΔkz
+i
LNL ∂2Ep (z , x ) = −iEs (z , x ) Ei (z , x ) eiΔkz L2ps ∂ 2x
= −i
λp λi
Ep (z , t ) Es∗ (z , t ) e−iΔkz
+
L ∂2Ep (z , i NL L2p ∂ 2x
t)
= −iEs (z , t ) Ei (z , t ) eiΔkz
(6)
The time variable t is normalized to the Fourier-transform-limitcorresponding duration (τs) of the signal. The wave-vector mismatch Δk and the nonlinear length LNL are the same as that defined in spatial domain. Lipt = τs / GVMip (Lspt = τs / GVMsp) is the GVM length of the idler (signal) with respect to the pump pulse. And the smaller Lipt is, the larger practical GVMip will be. Since most OPCPA systems work near at wavelength degeneracy, we assume equal group velocities of the signal and idler (i.e., GVMsp = GVMip) in this paper. The dispersion effect is characterized by the dispersion length L2jt = 2τs2/GVDj, in which j = s, i, p refers to the signal, idler, and pump waves, respectively. Characteristics of hybrid seeded OPA scheme Recovery effect for signal pulse in presence of pump phase modulation Although hybrid seeded OPA can partially eliminate the effect of pump phase distortion on signal, not all phase distortion can be perfectly compensated [21]. It is assumed that the pump pulse is a Gaussian pulse AP (0, t ) = E0 exp(−t 2 + iϕ (t )) , the phase is a sinusoidal modulation, ϕ (t ) = m sin(2πfm t ), where m and fm are the amplitude and frequency of the modulation. The recovery effect of the signal phase will be worse and worse with the increase of the phase distortion of the pump (Fig. 2), which is consistent with the research conclusions in Ref. [21]. It is stipulated here that if the phase modulation amplitude of the second stage signal is restored to less than 1% of that in the first stage, the phase of the signal is assumed as a well-restored status. According to Fig. 2, if m ⩽ 2 rad , regardless of the value of fm, even if it reaches two orders of magnitude, the phase recovery effect of the output signal is well-restored. If m > 2 rad , the signal phase can be restored to a better situation only when the value of m and fm are both below the curve. Otherwise, the hybrid seeded OPA will lose its advantage of strong recovery. This is because, in the OPA process, with the increase of m and fm of the pump modulation, the amplitude modulation of the signal will become more and more intense, which makes the phase recovery more difficult. In addition, the smaller the GVM (i.e., the larger the Lipt/L), the larger the compensable range of
(1)
∂Ei (z , x ) L ∂E (z , x ) L ∂2Ei (z , x ) + NL i + i NL ∂z Lips ∂x L2is ∂ 2x = −i
t)
(5)
∂Es (z , x ) L ∂E (z , x ) L ∂2ES (z , x ) + i NL + NL s ∂z Lsps ∂x L2ss ∂ 2x λp
L ∂2Ei (z , i NL L2i ∂ 2t
(2)
(3)
where Es(z, x), Ei(z, x) and Ep(z, x) are the envelopes of signal, idler and pump lights, respectively, which are normalized to the input pump field E0. For the sake of simplicity, a one-dimensional transverse model is used in simulations; diffraction effects are ignored due to the large beam aperture. A Gaussian pump beam is assumed throughout this article, although different beam shapes may be involved. The spatial variable x is normalized to the radius of the pump beam waist w; Δk = ks + ki−kp is the wave-vector mismatch among the three waves, where wave vector kj = nωj/c. The nonlinear length is defined by LNL = nλp /(πχ (2) E0) as a measure of the pump intensity [19]. The pump beam is the reference beam; thus, walk-off terms only appear in Eqs. (1) 2
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
Fig. 4. Relationship between Ms2 factors of all stages and the spatial walk-off length, where Mp2 = 10, LNL = 0.25 L, L = 10 mm, Es(0) = 10−6.
Fig. 2. The influence of amplitude and frequency of the pump modulation on the phase recovery effect of the output signal phase in the hybrid seeded OPA scheme, where Es(0) = 10−6 and crystal length L is 10 mm.
curve in the hybrid seeded OPA scheme. The recovery capability for the signal phase when different shapes of the pump phase are adopted is shown in Fig. 3. It is assumed that the phase forms of the pump are ϕ (t ) = (nt )2 and ϕ (t ) = (nt )3 , respectively. Due to the GVM effect, the phase of the signal output at the first stage OPA is modulated (dashed line). In the second stage, the phase of the output signal can almost return to the initial state (solid line) under the hybrid seeded OPA scheme. In addition, the phase shape of the firststage signal is the first-order derivative of that of the initial pump, that is, φs1 ∼ φ′ (t ) .
scheme), then the Ms2 factor of the final output signal will become worse (circle line). If the generated idler is injected as seed source in the second stage (the hybrid seeded OPA scheme), Ms2 factor of the output signal is approximately 1 [i.e., the beam quality of signal is restored to near diffraction limit (square line)]. Additionally, the Ms2 factor of the signal under the traditional OPA scheme is related to the spatial walk-off length Lips, while Lips and Mp2 factor do not affect the output signal beam quality if the hybrid seeded OPA scheme is adopted. Regardless of the Ms2 factor in the first stage, the beam quality of the signal in the second stage is nearly diffractionlimited.
M2 Factor of output signal in spatial domain
Phase reconstruction of signal in temporal domain
The M2 = (c/λ)w0·θ factor is generally used to describe the beam quality, where w0 is the waist width of actual beam and θ is far-field divergence angle [22]. The larger the M2 factor, the worse the beam quality; when M2 = 1, the beam is considered to be an ideal beam (i.e., the beam is diffraction-limited). In this section, the influence of pump beam quality on Ms2 factor of signal and the compensation ability of the hybrid seeded OPA scheme are discussed. The Mp2 factor of pump beam is assumed to be 10. Fig. 4 shows the relationship between Ms2 factors of all stages and the spatial walk-off length. It can be seen from the graph that the Ms2 factor of the first stage signal is greater than 1, and the beam quality is obviously worse (triangle line). If the seed source of the second stage OPA still uses the signal (traditional two-stage OPA
In the birefringent phase-matching scheme, the phase transfer from pump to signal pulse inevitably occurs because of the existence of spatial walk-off or GVM effect in the temporal domain [23]. The phase transfer problem in the spatial domain is usually solved by paired nonlinear crystals [17]. Two-stage OPA processes occur in cascaded crystals sequentially, in which the symbols of space walk-off effect are between the two stages OPA. As a result, the phase of the output signal can be restored to its initial state, thus eliminating the influence of the phase transfer from pump to signal pulse. However, this method cannot be simply applied into the temporal domain, because the symbols of space walk-off effect can be changed by crystal orientation, while the symbols of GVM cannot be changed. The hybrid seeded OPA scheme is
Fig. 3. The phase shape of the signal pulse in the first stage OPA (dashed line) and second stage OPA. The pump phase is adopted as (a) ϕ (t ) = (nt )2 ; (b) ϕ (t ) = (nt )3 , n = 2, where Lipt = Lspt = L, LNL = 0.25 L, L = 10 mm, Es(0) = 10−6. 3
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
Fig. 5. Pulse shape and phase of the signal, solid curve: the first stage OPA; dashed curve: the second stage OPA, where c = 5, Lipt = Lspt = L, LNL = 0.15 L, L = 10 mm, Es(0) = 10−6.
used to solve the problem of phase reconstruction of signal in the temporal domain. Assuming that the pump pulse is a non-Fourier-limited Gaussian pulse AP (0, t ) = E0 exp(− (1 + ic ) T 2/(2T02)) , its linear chirp coefficient c = 5, and the initial signal pulse is a Fourier-limited Gaussian pulse. By using the hybrid seeded OPA scheme (Fig. 5), the signal phase in the first stage is still distorted (solid line), but the output signal phase in the second stage is restored to be near Fourier-transform limited (dashed line). It can be concluded that the hybrid seeded OPA scheme can ensure the optical quality of signal in both spatial and temporal domains in high-energy optical parametric chirped pulse amplification (OPCPA) systems, which provides a new means for optimizing various OPA and OPCPA systems and has a bright prospect in developing high-power laser sources with high optical quality. Accepted bandwidth in OPA system Fig. 6. The spectra of output signal in various OPA systems, the traditional twostage signal seeded scheme (dash-dotted line), the two-stage cascaded-crystals scheme (dotted line) and the hybrid seeded scheme (solid line). (a) Lipt = Lspt = L, LNL = 0.25 L; (b) Lipt = Lspt = 0.3 L, LNL = 0.1 L; L = 10 mm, Es(0) = 10−6.
In order to generate shorter signal pulses, femtosecond OPA devices need a broader accepted bandwidth. A variety of technologies are used to increase the accepted bandwidth of OPA [24,25]; the most typical one is the cascaded-crystals scheme [17]. Next, the output signal spectra for several OPA schemes are compared, including the traditional two-stage signal seeded scheme (dash-dotted line), the two-stage cascaded-crystals scheme (dotted line), and the hybrid seeded scheme (solid line). Fig. 6(a) and (b) correspond to different GVM lengths (i.e., Lip = Lsp = L and Lip = Lsp = 0.3 L, respectively). Obviously, the more serious the GVM effect is, the narrower the spectrum of the output signal is, and the more difficult it is to obtain the ultrashort signal pulse. Compared with the traditional two-stage signal seeded scheme, both the hybrid seeded scheme and the cascaded-crystals scheme increase the accepted bandwidth of OPA. When the GVM effect is not too serious, the accepted bandwidths for the two schemes are the same (solid line and dotted line in Fig. 6(a)). When the GVM effect is relatively serious, the accepted bandwidth for the hybrid seeded scheme is broader, as shown by the solid line in Fig. 6(b), which also demonstrates its advantage in practical applications. Spectral purity of signal
Fig. 7. Spectra of the output signal using continuous wave seeding OPA system, the traditional two-stage signal seeded scheme (solid line), and the hybrid seeded scheme (dashed line), where Lipt = Lspt = 5 L, LNL = 0.35 L, L = 10 mm, Es(0) = 10−6.
In the case of OPA system using CW seeding, the amplified signal is always accompanied by a narrow-band background light [14]. Therefore, the broad spectrum of signal has a sharp spine, and the spectral purity is obviously deteriorated, as shown in the solid line in Fig. 7. If the hybrid seeded OPA scheme is adopted, the spectral component at 4
Results in Physics 13 (2019) 102284
Y. Zhou, et al.
(2018JJ2455), the Scientifc Research Fundation of Hunan Provincial Education Department (17A020). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.rinp.2019.102284. References [1] Greenfield S, Wasielewski M. Near-transform-limited visible and near-IR femtosecond pulses from optical parametric amplification using Type-II β-barium borate. Opt Lett 1995;20:1394–6. [2] Marcinkevičiūtė A, Michailovas K, Butkus R. Generation and parametric amplification of broadband chirped pulses in the near-infrared. Opt Commun 2018;415:70–3. [3] Tamošauskas G, Beresnevičius G, Gadonas D, et al. Transmittance and phase matching of BBO crystal in the 3–5 μm range and its application for the characterization of mid-infrared laser pulses. Opt Mater Express 2018;8:1410–8. [4] Cerullo G, De Silvestri S. Ultrafast optical parametric amplifiers. Rev Sci Instrum 2003;74:1–18. [5] Reed M, Armas M, Steinershepard M, et al. 30-fs pulses tunable across the visible with a 100-kHz Ti:sapphire regenerative amplifier. Opt Lett 1995;20:605–7. [6] Cheng Y, Gao G, Poulin P, et al. Efficient two-stage dual-beam noncollinear optical parametric amplifier. Appl Phys B 2018;124:93. [7] Rotermund F, Petrov V, Noack F, et al. Laser-diode-seeded operation of a femtosecond optical parametric amplifier with MgO: LiNbO3 and generation of 5-cycle pulses near 3 μm. J Opt Soc Am B 1999;16:1539–45. [8] Xu H, Yang F, Chen Y, et al. Millijoule-level picosecond mid-infrared optical parametric amplifier based on MgO-doped periodically poled lithium niobate. Appl Opt 2015;54:2489–94. [9] Baravets Y, Honzatko P, Todorov F, et al. Narrowband widely tunable CW midinfrared generator based on difference frequency generation in periodically poled KTP and KTA crystals. Opt Quant Electron 2016;48:286. [10] Bach F, Mero M, Chou M, et al. Laser induced damage studies of LiNbO3 using 1030nm, ultrashort pulses at 10–1000 kHz. Opt Mater Express 2017;7:240–52. [11] Gale G, Gallot G, Hache F, et al. Generation of intense highly coherent femtosecond pulses in the mid infrared. Opt Lett 1997;22:1253–5. [12] Petrov V, Noack F. Tunable femtosecond optical parametric amplifier in the midinfrared with narrow-band seeding. J Opt Soc Am B 1995;12:2214–21. [13] Pires H, Baudisch M, Sanchez D, et al. Ultrashort pulse generation in the mid-IR. Prog Quantum Electron 2015;43:1–30. [14] Jovanovic I, Barty C, Haefner C, et al. Optical switching and contrast enhancement in intense laser systems by cascaded optical parametric amplification. Opt Lett 2006;31(6):787–9. [15] Luo H, Qian L, Yuan P, et al. Hybrid seeded femtosecond optical parametric amplifier. Opt Express 2005;13(24):9747–52. [16] Stepanenko Y, Radzewicz C. High-gain multipass noncollinear optical parametric chirped pulse amplifier. Appl Phys Lett 2005;86:211120. [17] Armstrong D, Alford W, Raymond T, et al. Parametric amplification and oscillation with walkoff-compensating crystals. J Opt Soc Am B 1997;14:460–74. [18] Chen Y, Zhou Y, Jiang G, et al. Numerical simulations of transfer of spatial beam aberrations in optical parametric chirped-pulse amplification. Adv Cond Matter Phys 2018;5731938. [19] Chen Y, Zhou Y, Wang Z. Improvement of the frequency-doubling efficiency of high-average-power lasers using multicrystal scheme with opposite thermal properties. Results Phys 2017;7:3530–6. [20] Yuan P, Qian LJ, Luo H, Zhu HY, Wen SC. Femtosecond optical parametric amplification with dispersion precompensation. IEEE J Sel Top Quantum Electron 2006;12:181–6. [21] Wei X, Qian L, Yuan P, et al. Optical parametric amplification pumped by a phaseaberrated beam. Opt Express 2008;16:8904–15. [22] Yang H, Zhao D, Lu X, Wang S. Several viewpoints related to the beam quality factor M 2. Chin J Lasers 1997;24:709–14. [23] Forget N, Cotel A, Brambrink E, et al. Pump-noise transfer in optical parametric chirped-pulse amplification. Opt Lett 2005;30:2921–3. [24] Kraemer D, Cowan M, Hua R, et al. High power femosecond infrared laser source based on noncollinear optical parametric chirped pulse amplification. J Opt Soc Am B 2007;24:813–8. [25] Ogawa K, Aoyama M, Akahane Y, et al. Bandwidth enhancement of optical parametric chirped pulse amplification by temporally delayed two pump beams. Jan J Appl Phys 2008;47:4592–4.
Fig. 8. The relationship between conversion efficiency and initial signal energy, the traditional two-stage seeded OPA scheme (solid line), and the hybrid seeded OPA scheme (circle), where Lipt = Lspt = 5 L, LNL = 0.35 L, L = 10 mm.
the signal wavelength is blocked in the first stage, leaving a clean idler in both time domain and frequency domain, which enter into the second stage. Finally, the signal pulse is generated when DFG takes place between the idler and pump pulse in the second stage. Importantly, temporally and spectrally clean pulses at signal wavelength can be obtained, which does not contain the component of continuous wave (dashed line in Fig. 7). Conversion efficiency of OPA system High gain and high conversion efficiency have always been the goal of laser amplification systems. Two-stage or multi-stage OPA has been proved to be a very effective method [16], which also avoids the risk of crystal damage caused by excessive pumping energy. The conversion efficiency of the hybrid seeded OPA scheme is also investigated (Fig. 8). It can be seen that the hybrid seeded scheme can achieve the same conversion efficiency as the traditional two-stage OPA scheme. Therefore, it is not at the expense of conversion efficiency to control the phase transfer from pump to signal in the hybrid seeded OPA scheme. Conclusion We demonstrate that the hybrid seeded OPA scheme can control the phase transfer from pump pulse to signal pulse in both temporal and spectral domains by use of numerical simulation, so that the phase of output signal field is not restricted to the undesirable phase of pump pulse. In addition, the hybrid seeded OPA scheme has many advantages, such as broad accepted bandwidth, clean output spectra at signal and idler wavelength, and high conversion efficiency. This technology will have good prospects in the development of high-power laser sources with high optical quality. Acknowledgements This work was partially supported by NSAF under grant no. U1830206 and the Natural Science Fundation of Hunan Province, China
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