ISSN 0021-3640, JETP Letters, 2016, Vol. 103, No. 3, pp. 167–170. © Pleiades Publishing, Inc., 2016. Original Russian Text © A.A. Lanin, A.M. Zheltikov, 2016, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2016, Vol. 103, No. 3, pp. 184–188.
OPTICS AND LASER PHYSICS
Octave Phase Matching for Optical Parametric Amplification of Single-Cycle Pulses in the Mid-Infrared Range A. A. Lanina, b and A. M. Zheltikova–d* a
Faculty of Physics and International Laser Center, Moscow State University, Moscow, 119992 Russia b Russian Quantum Center, Skolkovo, 143025 Russia c Texas A&M University, College Station TX 77843, USA d National Research Centre Kurchatov Institute, Moscow, 123098 Russia *e-mail:
[email protected] Received December 18, 2015
Analysis of optical properties of mid-infrared-transparent nonlinear crystals reveals octave phase matching for a highly efficient optical parametric amplification of single-cycle electromagnetic field waveforms within the 3- to 12-μm wavelength range, recently demonstrated in experiments. DOI: 10.1134/S0021364016030103
Extremely short waveforms of electromagnetic radiation with a pulse width close to the field cycle provide a new powerful tool for time-resolved studies of ultrafast processes [1–6]. The electronic response of matter to such pulses is highly sensitive to the carrier–envelope phase [7], suggesting new ways to control a vast class of physical and chemical phenomena [8]. Single-cycle and subcycle waveforms (SCWs) of electromagnetic radiation find growing applications for the generation of attosecond pulses [9], timeresolved studies and coherent control of attosecond electron dynamics [8, 10–12], tomography of molecular orbitals [13], and coherent X-ray generation [14]. Advanced laser technologies enable SCW generation in the visible and near-infrared (near-IR) spectral ranges [1, 2]. Until recently, however, mid-infrared (mid-IR) SCWs were observed only in two-frequency ultrashort-pulse laser filaments [15]. Although this regime of SCW generation provides important information on the physics behind two-frequency laser filamentation, it does not offer a technology for robust mid-IR SCW sources with reliably reproducible parameters. Recent experiments show [16, 17] that such a source can be created in an all-solid format through a sequential optical parametric frequency down-conversion of a short-pulse master-oscillator output in crystals with quadratic optical nonlinearity. This technology enables the generation of microjoule mid-IR SCWs with a wavelength tunability range from 4 to 9 μm. However, physical processes whereby the output energy of such solid-state mid-IR SCW sources could be boosted still need to be identified.
Here, we show that this challenge can be addressed on a platform of optical parametric amplification (OPA) of SCWs in mid-IR-transparent crystals with quadratic nonlinearity. Analysis of optical properties of such crystals presented in this paper suggests the ways to achieve an ultrabroadband phase matching for such an OPA process within a frequency range exceeding an octave. This regime provides a highly efficient OPA of mid-IR SCWs. An all-solid system for the generation of highpeak-power SCWs considered in this work (Fig. 1) consists of a frequency-tunable source of ultrashort microjoule pulses in the mid-IR experimentally demonstrated in [16, 17], a mid-IR pulse compressor, and an SCW amplification stage. The source of ultrashort mid-IR pulses includes a front-end modelocked Ti:sapphire (Ti:S) master oscillator, a multipass amplifier (MPA), an OPA unit based on a BBO crystal, and a system for difference-frequency generation (DFG) using an AGS crystal. In the OPA unit, three-wave mixing ωp = ω1 + ω2 in a nonlinear crystal (BBO) is used to parametrically amplify a broadband radiation (the signal wave at the frequency ω1) generated by the front-end Ti: sapphire laser in a GaAs plate. This Ti: sapphire laser also provides a pump for the three-wave mixing process, generating an idler wave at the frequency ω2. The signal and idler fields generated as a result of this three-wave mixing are then used to produce ultrashort pulses in the mid-IR through DFG ωd = ω1 – ω2 in an AGS crystal. As was shown in [16, 17], this process yields 1– 15 μJ ultrashort pulses with a central wavelength tunable from 3 to 15 μm.
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Fig. 1. (Color online) Optical parametric amplification of single-cycle pulses in the mid-infrared: (Ti:S) modelocked Ti:sapphire oscillator; (MPA) multipass amplifier; (OPA) optical parametric amplification system; (DFG) difference-frequency generation unit; (BBO, AGS, and GaAs) beta barium borate, silver thiogallate, and gallium arsenide crystals, respectively; (LPF) low-pass filter; (BFP and BFL) barium fluoride plate and lens, respectively.
Depending on its central wavelength, the shortpulse mid-IR DFG output either experiences spectral broadening in the regime of normal dispersion or undergoes anomalous-dispersion-assisted spectral– temporal transformations in a thin GaAs plate in the pulse-compressor unit. The nonlinear phase shift acquired by mid-IR pulses in this plate is then compensated with a stack of thin plates of suitable materials, chosen for the highest accuracy of phase correction. As a suitable OPA solution for SCWs in the midIR, we consider three-wave mixing ω2 = ωd + ω3 in a crystal with a quadratic nonlinearity in the regime of ultrabroadband phase matching. An amplified ω2 field, which served as an idler wave at the previous OPA stage and was used then to generate the DFG output, is now used as a pump. This wave can be amplified with the use of Ho:YAG [18–20], Cr:ZnSe, Cr:ZnS [21, 22], or Cr, Er:YSGG [23] laser crystals or thulium-doped fiber amplifiers [24, 25]. These laser media provide a sufficiently high gain at around 2.05, 2.3–2.5, 2.65–2.80, and 1.95 μm, covering most of the tunability range of the ω2 wave. For a field waveform to be shorter than the field cycle, its spectrum has to be broader than an octave. An ultrabroadband phase matching, providing OPA within the entire octave-spanning spectrum of an SCW, is thus one of the key criteria in the search for
nonlinear materials for a parametric amplification of SCWs. In Fig. 2, we examine phase matching for a variety of available nonlinear materials, such as CdSe, LiGaTe2 (LGT), ZnGeP2 (ZGP), GaSe, and HgS (HS), that could potentially serve for a parametric amplification of SCWs in the mid-IR. Figure 2 presents maps of the phase-matching factor F = [sin(ΔkL/2)]2/(ΔkL/2)2 (where L is the crystal thickness, and Δk = |k2 – kd – k3| is the wave-vector mismatch for the type-I ω2 = ωd + ω3 three-wave mixing process, that is, e–oo for GaSe and o–ee for CdSe, LGT, ZGP, and HS) as a function of the pump wavelength λ2 = 2πc/ω2, as well as the wavelengths of the signal and idler fields, λd, 3 = 2πc/ωd, 3, for different angles φ between the wave vectors k2 and kd. As can be seen from these calculations, the considered class of nonlinear-optical materials can support an octave phase matching, needed for an OPA of SCWs. Moreover, an octave phase matching can be achieved with these materials for different schemes of ω2 pump amplification. The dashed lines in Figs. 2a–2j show the wavelength of this field when it is amplified with Ho:YAG, Cr:ZnSe, Cr, Er:YSGG, or Tm [18–25]. Figures 2k–2o present the profiles of the F factor plotted as a function of the wavelength λ and obtained as one-dimensional cuts of the F maps in Figs. 2a–2j. Gray shading in Figs. 2k–2o shows the spectrum of mid-IR SCWs generated in recent experiments [17]. Comparison of the profile of the F factor and the SCW spectrum suggests that phase matching can be achieved within the entire bandwidth needed for a highly efficient parametric amplification of this SCW. As can be seen from Fig. 2, the broadest band of parametric gain with minimum gain modulation is achieved for collinear (φ = 0) OPA in a CdSe crystal with a pump field centered at λ2 = 2.8 μm amplified in a Cr:Er:YSGG laser crystal (Fig. 2a and the violet dashed line in Fig. 2k). As can be seen from Fig. 2, this regime of parametric amplification becomes possible owing to an accurate matching of a nonlinear optical material used for OPA and a laser material (Fig. 1), amplifying the λ2 pump field. The OPA gain band in this regime features a sharp high-frequency edge at about 3.6 μm and a gently sloping roll-off in the wavelength range from 10.5 to 11.8 μm. Such a broad OPA gain band enables a highly efficient OPA of mid-IR waveforms with a pulse width much shorter than the field cycle. As can be seen from Figs. 2a–2j, the parametric gain band can be finely tuned to match the spectra of the ω2 and ωd pump and mid-IR signal fields at a cost of some loss of parametric gain uniformity by varying the φ angle. To summarize, analysis of optical properties of mid-IR-transparent nonlinear crystals reveals octave phase matching for a highly efficient optical parametric amplification of electromagnetic field SCWs within the wavelength range from 3 to 12 μm. JETP LETTERS
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Fig. 2. (Color online) Maps of the OPA gain factor F plotted as a function of the pump wavelength (x axis), as well as signal and idler wavelengths (y axis) for φ = (a–e) 0°, (f) 1.1°, (g) 0.85°, (h) 0.6°, (i) 1.4°, and (j) 1.33° for (a, f) CdSe, (b, g) LGT, (c, h) ZGP, (d, i) GaSe, and (e, j) HS. (k–o) Profiles of the F factor for (k) CdSe, (l) LGT, (m) ZGP, (n) GaSe, and (o) HS with a pump field amplified with (blue line) a Cr:ZnSe crystal at the wavelength λ2 = (k–m) 2.5 and (o) 2.4 μm, (violet line) Cr : Er : YSGG crystal at the wavelength of (k) 2.8 and (l, m) 2.65 μm, (green line) Ho : YAG crystal at the wavelength of (n, o) 2.05 μm, and (red line) Tm-doped fiber at the wavelength of (n) 1.95 μm. Gray shading shows the spectrum of mid-IR SCWs generated in experiments [17]. The vertical dashed lines in panels (a) through (j) show the central wavelength of the gain band in a laser crystal used for the amplification of the pump field. The thickness of nonlinear crystals in all the calculations is 5 mm.
This work was partially supported by the Russian Foundation for Basic Research (project nos. 14-2907182, 16-02-00843, and 15-02-07820) and the Welch JETP LETTERS
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Foundation (grant no. A-1801). Study of nonlinear optics in the mid-infrared range was supported by the Russian Science Foundation (project no. 14-12-00772).
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Translated by A. Zheltikov
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