Optical parametric amplification at critical wavelength degeneracy&#x2014;a proposed approach for 100-PW class femtosecond laser development

Razvan Dabu

doi:10.1364/OSAC.416451

1. Introduction

In the last years, there has been significant progress in developing femtosecond high-power laser systems by using the chirped pulse amplification (CPA) [1] in laser media with broad emission spectral bandwidth and the optical parametric chirped pulse amplification (OPCPA) [2] in nonlinear crystals with broad parametric gain bandwidth. Petawatt (PW)-class femtosecond laser systems have been reported, based on CPA [3,4] and OPCPA [5,6] techniques. For preserving a large spectral bandwidth of amplified pulses and for improving the intensity contrast after temporal compression of amplified stretched pulses, hybrid femtosecond laser systems were developed [7–9]. These hybrid systems combine the low energy OPCPA in beta-barium borate (BBO) crystals in the Front-End with the high energy CPA in large aperture Ti:sapphire crystals.

A couple of 100-PW class femtosecond laser system projects are currently worldwide in progress [10,11]. They are based on non-collinear (NC) optical parametric chirped pulse amplification (OPCPA) in large size potassium dihydrogen phosphate (KDP) and deuterated KDP (DKDP) crystals pumped by nanosecond green lasers, using the broad parametric gain bandwidth (BGB) around the 900 nm signal phase-matching wavelength. Chinese and Russian projects rely on the temporal overlapping of some multi-PW fs laser beams to get more than 100-PW total power [10], whereas the American project consists in a “single beam” 75 PW laser [11]. Another proposed solution is to enhance the peak power of PW lasers by spectral broadening through non-linear self-phase modulation and post-compression of ultrashort pulses in thin plastic films [12].

In this paper, I propose an approach for 100 PW class femtosecond lasers development, based on the SBGBs obtained by OPCPA near CWD in large size P-DKDP crystals, pumped by nanosecond green lasers. In Section 2, I describe the conditions for the generation of super-broad parametric gain-bandwidths in nonlinear-crystals at critical wavelength degeneracy. In Section 3, the possibility to obtain a SBGB in partially deuterated KDP (P-DKDP) crystals, pumped by some of the available high energy nanosecond green lasers, is presented. Small-angle noncollinear OPCPA configurations in P-DKDP crystals near CWD, optimized for the parametric gain bandwidth improvement and the spatial separation of signal and idler laser beams, are described. Technical challenges of a 100-PW class femtosecond laser system are discussed in Section 4.

2. Super-broad gain-bandwidth in nonlinear-crystals at critical wavelength degeneracy (CWD)

The wave-vectors mismatch Δk around the exact phase-matching condition is given by a Taylor series expansion

(1)$$\begin{aligned}&\Delta k = \Delta {k^{(0)}} + {\left( {\frac{{\partial \Delta k}}{{\partial {\omega_s}}}} \right)_{{\omega _{s0}}}}d{\omega _s} + \frac{1}{{2!}}{\left( {\frac{{{\partial^2}\Delta k}}{{\partial \omega_s^2}}} \right)_{{\omega _{s0}}}}{({d{\omega_s}} )^2} + \frac{1}{{3!}}{\left( {\frac{{{\partial^3}\Delta k}}{{\partial \omega_s^3}}} \right)_{{\omega _{s0}}}}\\&{({d{\omega_s}} )^3} + \frac{1}{{4!}}{\left( {\frac{{{\partial^4}\Delta k}}{{\partial \omega_s^4}}} \right)_{{\omega _{s0}}}}{({d{\omega_s}} )^4} + \ldots \approx \\ &\Delta {k^{(0)}} - \left( {\frac{{\partial {k_s}}}{{\partial {\omega_s}}} - \frac{{\partial {k_i}}}{{\partial {\omega_i}}}} \right)\Delta \omega - \frac{1}{{2!}}\left( {\frac{{{\partial^2}{k_s}}}{{\partial \omega_s^2}} + \frac{{{\partial^2}{k_i}}}{{\partial \omega_i^2}}} \right){(\Delta \omega )^2} - \frac{1}{{3!}}\left( {\frac{{{\partial^3}{k_s}}}{{\partial \omega_s^3}} - \frac{{{\partial^3}{k_i}}}{{\partial \omega_i^3}}} \right)\\&{(\Delta \omega )^3} - \frac{1}{{4!}}\left( {\frac{{{\partial^4}{k_s}}}{{\partial \omega_s^4}} + \frac{{{\partial^4}{k_i}}}{{\partial \omega_i^4}}} \right){(\Delta \omega )^4}\ldots = \\ &\Delta {k^{(0)}} + \Delta {k^{(1)}} + \Delta {k^{(2)}} + \Delta {k^{(3)}} + \Delta {k^{(4)}} + \ldots \end{aligned}$$

Quanta energy conservation and phase matching condition are fulfilled for the ω_p monochromatic pump frequency, and the signal and idler frequencies ω_s0 and ω_i0

(2)$$\begin{array}{l} {\omega _p} - {\omega _{s0}} - {\omega _{i0}} = 0\\ {k_p}({\omega _p}) - {k_s}({\omega _{s0}}) - {k_i}({\omega _{i0}}) = \Delta {k^{(0)}} = 0 \end{array}$$

For the Δω signal frequency variation around the exact phase-matching frequency ω_s0

(3)$$\begin{array}{l} {\omega _s} = {\omega _{s0}} + \Delta \omega ,\,\,\,\,{\omega _i} = {\omega _{i0}} - \Delta \omega \,\,\, \Rightarrow \,\,\Delta k \ne 0\\ \partial {\omega _s} ={-} \partial {\omega _i} \end{array}$$

Six parameters are involved in a non-collinear parametric amplification: wavelengths (frequencies) of interacting waves, λ_p, λ_s, λ_i (ω_p, ω_s, ω_i), and interaction angles inside crystal: θ, α, β (Fig. 1). The phase-matching condition, Δk⁽⁰⁾ = 0, is represented by the first three equations of the (4) equations system.

Fig. 1. Non-collinear optical parametric amplification.

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A broad band gain bandwidth can be obtained if the phase mismatch slowly increases with the signal variation around the exact phase-matching signal wavelength. To get a broad-band phase-matching bandwidth, the first and second order mismatch terms, Δk⁽¹⁾ and Δk⁽²⁾, must be cancelled. The 4^th and 5^th equations of the (4) system are inferred as the result of this cancellation condition [13,14]. These equations represent the required relations between signal group velocity, v_gs, and idler group velocity, v_gi, and signal group velocity dispersion, GVD_s, and idler group velocity dispersion, GVD_i, respectively, at the phase matching signal wavelength. In this case, only one parameter, among the six parameters involved in the non-collinear parametric process, can be chosen. The practical choice is the pump wavelength, λ_p, which must correspond to the available pump lasers, like frequency doubled Nd:YAG (532 nm), Nd:glass (527 nm), and Yb:YAG (515 nm) lasers.

(4)$$\begin{array}{l} \frac{1}{{{\lambda _p}}} = \frac{1}{{{\lambda _s}}} + \frac{1}{{{\lambda _i}}}\\ \frac{{{n_p}({\lambda _p},\theta )}}{{{\lambda _p}}}\sin \alpha - \frac{{{n_i}({\lambda _i})}}{{{\lambda _i}}}\sin \beta = 0\\ \frac{{{n_p}({\lambda _p},\theta )}}{{{\lambda _p}}}\cos \alpha - \frac{{{n_s}({\lambda _s})}}{{{\lambda _s}}} - \frac{{{n_i}({\lambda _i})}}{{{\lambda _i}}}\cos \beta = 0\\ {\nu _{gs}} = {v_{gi}}\cos \beta \\ \frac{{{\partial ^2}{k_s}}}{{\partial \omega _s^2}}\cos \beta + \frac{{{\partial ^2}{k_i}}}{{\partial \omega _i^2}} - \frac{{{{\sin }^2}\beta }}{{v_{gs}^2{k_i}}} = 0\\ \frac{{{\partial ^3}{k_s}}}{{\partial \omega _s^3}}\cos \beta - \frac{{{\partial ^3}{k_i}}}{{\partial \omega _i^3}} + 3\frac{{{{\tan }^2}\beta }}{{{k_i}}}\frac{{\partial {k_i}}}{{\partial {\omega _i}}}\left[ {\frac{{{\partial^2}{k_i}}}{{\partial \omega_i^2}} - \frac{1}{{{{\cos }^2}\alpha }}{{\left( {\frac{{\partial {k_i}}}{{\partial {\omega_i}}}} \right)}^2}} \right] = 0 \end{array}$$

I considered two frequently used nonlinear crystals, BBO and DKDP, and pump laser wavelengths (PLW) of frequency doubled Nd:YAG and Nd:glass, respectively. By using Sellmeier equations of refractive indexes [15], under the conditions required by a broad parametric gain bandwidth (BGB), for a type I optical parametric amplification, the phase-matching signal wavelength (λ_s0), the crystal orientation versus optical axis (θ angle) and in the xy crystallographic plane (ϕ angle), and the non-collinear interaction geometry (α angle), were calculated (Table 1).

Table 1. Parameters of the BGB parametric amplification in some nonlinear crystals. The ϕ angle was calculated for the maximization of effective nonlinear coefficient.

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Parametric gain bandwidths calculated for NC OPCPA in BBO and DKDP crystals, at 1 GW/cm² pump intensity, in the 800 nm signal spectral range, as well as the BGB in the 900 nm spectral range in a DKDP crystal, are shown in the Fig. 2. To get similar peak parametric gain, appropriate crystal lengths of 6 mm and 47 mm were considered for BBO and DKDP crystals, respectively.

Fig. 2. Parametric gain bandwidths calculated for NC OPCPA in a BBO crystal (blue line 1) and in a DKDP crystal (green line 2) for the signal pulse amplification in the 800 nm spectral range. The red line 3 represents the BGB for NC OPCPA in a DKDP crystal, optimized for the signal pulse amplification in the 900 nm spectral range. Pump intensity 1 GW/cm², 532 nm pump laser wavelength.

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All gain bandwidths were calculated under the condition of parametric amplification with uniform pump wave intensity, small initial signal wave amplitude, no initial idler wave, and negligible pump wave depletion, using the gain equation from [14,16] references. Conservative values of 1 GW/cm² pump intensity for nanosecond pump lasers and 25 GW/cm² for picosecond pump lasers were considered.

Around 810 nm phase-matching signal wavelength, a BGB of ∼170 nm was obtained for the BBO crystal, able to support the amplification of broad-band femtosecond laser pulses generated by Ti:sapphire femtosecond oscillators. In the same spectral range, the DKDP crystal has only ∼50 nm gain bandwidth, whereas in the 900 nm spectral range the DKDP crystal has a gain bandwidth of ∼150 nm, able to support the amplification of ultra-short pulses too. DKDP crystals can be grown up to half-meter diameter aperture, required for kJ pulse energy amplification of stretched nanosecond pulses in multi-PW femtosecond laser systems. In this case, a 900 nm broad-band signal wave must be generated by shifting the spectral range of the 800 nm laser pulses generated by femtosecond oscillators [13] or by white-light generation in crystals [11].

A SBGB would be obtained in nonlinear crystals if the third order phase-mismatch term, Δk⁽³⁾, could be cancelled too. In this case, all parameters of the parametric amplification process are inferred by solving the six-equations system (4). The result is a collinear OPCPA geometry (α = 0) at critical wavelength (CW) and degeneracy, where the pump laser wavelength, PLW_CWD, is two times shorter than the critical wavelength of the crystal, λ_CW [14]. At CW, the group velocity dispersion of the signal pulse in crystal is canceled. In a type I parametric process, the critical wavelength can be calculated using the equation

(5)$$GVD = \frac{{{\partial ^2}k}}{{\partial {\omega ^2}}} = \frac{{{\lambda ^3}}}{{2\pi {c^2}}}\frac{{{\partial ^2}{n_o}(\lambda )}}{{\partial {\lambda ^2}}} = 0$$

where n₀(λ) is the Sellmeier equation for the ordinary refractive index [15].

I calculated the spectral profile of the SBGB at CWD in BBO and DKDP crystals, considering 1 GW/cm² and 25 GW/cm² uniform spatial intensity profile of the pump laser pulses. The crystal lengths were chosen to get a similar small signal parametric gain, G₀ ≈ 90 in both crystals (Fig. 3). The main parameters at the CWD parametric amplification for both crystals are given in the Table 2.

Fig. 3. Gain bandwidths for a virtual optical parametric amplification at CWD in a collinear geometry. (a) BBO crystal: blue line 1, 1 GW/cm² pump intensity, 8 mm crystal length; cyan line 2, 25 GW/cm², 1.6 mm crystal length. (b) DKDP crystal: blue line 1, 1 GW/cm² pump intensity, 50 mm crystal length; cyan line 2, 25 GW/cm², 10 mm crystal length.

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Table 2. SBGB₁(1 GW/cm²) and SBGB₂₅(25 GW/cm²), at CWD of BBO and DKDP crystals, for a similar small signal gain, G₀ ≈ 90.

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Significantly broader parametric gain bandwidth could be obtained at CWD compared to the non-collinear OPCPA BGB. Because of the lack of high energy pump lasers with the required PLW_CWD pump laser wavelength, OPCPA at CWD in BBO and DKDP crystals can’t be practically realized.

3. SBGBs of P-DKDP crystals pumped by high energy nanosecond green lasers

The ordinary refractive index, n_o(D), of partially deuterated crystals, P-DKDP, can be calculated with the equation [13]

(6)$$n_o^2(\lambda ,D) = n_o^2(1) \times D + n_o^2(0) \times (1 - D)$$

where n_o(1), n_o(0), are the Sellmeier equations of the ordinary refractive indexes of DKDP, KDP crystals, respectively, and D is the deuteration ratio (DR) of the P-DKDP crystal.

Using the Eq. (5), I calculated the required deuteration ratios of P-DKDP crystals to get critical wavelengths corresponding to the wavelengths of the available green nanosecond pump lasers, namely D = 0.64, 0.58, and 0.40 for pumping with frequency doubled 532 nm Nd:YAG, 527 nm Nd:glass, and 515 nm Yb:YAG lasers, respectively.

Gain bandwidths of as broad as 280 nm and 470 nm FWHM were calculated in a 58.3% deuterated P-DKDP crystal at CWD, pumped by 527 nm nanosecond laser pulses at 1 GW/cm² pump intensity, and picosecond laser pulses at 25 GW/cm², respectively (Fig. 4(a)). Crystal lengths of 8 mm and 40 mm were considered to get a similar small signal peak gain, G_p ≈ 60. The SBGB gain bandwidth of 280 nm, which can be obtained in P-DKDP crystals pumped by high energy nanosecond green lasers at CWD, at 1 GW/cm² pump intensity, is significantly broader than the BGB of ∼150 nm, calculated for NC OPCPA in DKDP crystals, under similar pumping conditions and similar peak parametric gain (Fig. 4(b)). This BGB, in the 900 nm spectral range, is currently used for high energy non-collinear OPCPA stages of PW femtosecond lasers. The frequency super-broad gain bandwidth at CWD in P-DKDP crystals can support the amplification of ∼1.4 times shorter femtosecond pulses compared with the frequency broad gain bandwidth in NC OPCPA stages with DKDP crystals. Consequently, higher peak power could be obtained in the same size crystals for a similar amplified signal pulse energy. High-energy amplification of sub-10 fs pulses could be supported by large size P-DKDP crystals at CWD.

Fig. 4. SBGBs in P-DKDP crystals pumped by 527 nm wavelength laser pulses. (a) SBGBs in a P-DKDP crystal at CWD, 58.3% DR, 8 mm crystal length, 25 GW/cm² pump intensity (cyan line 1) and 40 mm crystal length, 1 GW/cm² (blue line 2). (b) Comparison between BGB obtained by NC OPCPA in a DKDP crystal (red line 1) and SBGB in a P-DKDP crystal (blue line 2) at CWD, at 1 GW/cm² pump intensity, for similar 40 mm crystal length.

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The parametric gain curves can be shaped and optimized by a slight variation of the DR around the exact value which corresponds to the CWD condition. Parametric gain curves calculated in a P-DKDP crystal by a slight variation of the deuteration ratio around the 58.3% DR, required for the CWD when pumping by 527 nm laser pulses, are shown in Fig. 5. Gain bandwidths were simulated considering three values of the pump laser intensity: 25 GW/cm², which is suitable for a pump pulse duration in the range of few picosecond; 2 GW/cm² for few-hundred ps pump pulse duration, and 1 GW/cm² for few-ns pump pulse duration. To get a similar peak gain in all cases, P-DKDP crystal lengths of 8 mm, 28.5 mm, and 40 mm have been considered for 25 GW/cm², 2 GW/cm², and 1 GW/cm² pump intensity, respectively. All simulations from Figs. 4–6 were performed for a similar parametric peak gain, G_P ≈ 60. In case of longer P-DKDP crystals, suitable for amplification at 1-2 GW/cm² pump intensity, a more significant change of the gain bandwidth profile, depending on the variation of the deuteration ratio, was observed. For 28-40 mm long P-DKDP crystals, the gain bandwidth shaping in case of only +/- 0.5% deuteration rate variation (Fig. 5(b), c) is more significant than in case of 8 mm long crystals for +/-1.6-1.7% deuteration ratio variation (Fig. 5(a)). By slightly decreasing the deuteration ratio compared to the exact DR value required for the CWD, as broad as 510 nm, 330 nm, and 310 nm FWHM gain bandwidths have been calculated at 25 GW/cm², 2 GW/cm², and 1 GW/cm² pump intensity, respectively (Figs. 5(a),b,c).

Fig. 5. Gain bandwidths for slight variations of DR around the exact value required for OPCPA at CWD in P-DKDP crystals, pumped by a 527 nm wavelength laser. (a) 25 GW/cm² pump intensity, 8 mm crystal length; blue line 1, DR = 58.3%; red line 2, DR = 56.7%. green line 3, DR = 60%. (b) 2 GW/cm² pump intensity, 28.5 mm crystal length; blue line 1, DR = 58.3%; red line 2, DR = 57.8%. green line 3, DR = 58.8%. (c) 1 GW/cm² pump intensity, 40 mm crystal length; blue line 1, DR = 58.3%; red line 2, DR = 57.8%; green line 3, DR = 58.8%.

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Fig. 6. Small angle non-collinear OPCPA in P-DKDP crystals near CWD. (a). Calculated signal-idler GVM in a 58.3% deuterated P-DKDP crystal, 1054 nm signal critical wavelength, pumped by a 527 nm wavelength laser. (b) Small angle non-collinear OPCPA near CWD for ps laser pulses, 25 GW/cm² pump intensity; blue line 1, collinear OPCPA geometry: θ = 38.56⁰, ϕ = 45⁰, α = 0⁰, DR = 58.3%; black line 2: θ = 38.6⁰, ϕ = 45⁰, α = 6 mrad, DR = 58.3%; red line 3: θ = 38.67⁰, ϕ = 45⁰, α = 10.3 mrad, DR = 58.3%; optimized gain bandwidth by DR adjustment, green line 4: θ = 38.67⁰, ϕ = 45⁰, α = 10.3 mrad, DR = 57%. (c), (d) Small angle non-collinear OPCPA near CWD: (c) hundred-ps laser pulses, 2 GW/cm² pump intensity; (d) ns laser pulses, 1 GW/cm² pump intensity. Blue line 1, collinear OPCPA geometry: θ = 38.56⁰, ϕ = 45⁰, α = 0⁰, DR = 58.3%; black line 2: θ = 38.6⁰, ϕ = 45⁰, α = 6 mrad, DR = 58.3%; red line 3: θ = 38.67⁰, ϕ = 45⁰, α = 10.3 mrad, DR = 58.3%; optimized gain bandwidth, green line 4: θ = 38.67⁰, ϕ = 45⁰, α = 10.3 mrad, DR = 57.8%; cyan line 5: θ = 38.74⁰, ϕ = 45⁰, α = 14.4 mrad, DR = 58.3%.

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To separate the signal and idler laser pulses with the same polarization, in a type I nearly degenerated parametric amplification process, a small angle non-collinear OPCPA geometry can be used. Group velocity mismatch (GVM) between signal and idler waves in a P-DKDP crystal is positive for signal wavelengths longer than the critical wavelength, λ_s > λ_CW (Fig. 6(a)). Because non-collinear phase-matching is possible only for GVM > 0, the signal phase-matching wavelengths and SBGBs for small angle non-collinear OPCPA are slightly moved towards longer wavelengths. The signal phase-matching wavelengths of 1140 nm and 1200 nm have been calculated for signal-pump wavevector angles of 6 mrad and 10.3 mrad, respectively.

By optimization of the crystal orientation θ angle and by DR slight variation, with α = 10.3 mrad internal angle between signal and pump wave-vectors, OPCPA gain bandwidths as broad as 490 nm, 285 nm, and 255 nm FWHM were calculated at 25 GW/cm², 2 GW/cm², and 1 GW/cm² pump intensity, respectively (green lines in Figs. 6(b), 6(c), 6(d)).

Stretched pulses of few-ns duration and pump intensities in the range of 1 GW/cm² are suitable for high energy OPCPA stages. I considered a stretched signal pulse with a spectral bandwidth of 300 nm around the 1200 nm central wavelength (1200 nm +/- 150 nm). For 10.3 mrad non-collinearity angle of the OPCPA (Fig. 6(c)), the internal β angle between signal and idler wavevectors is ∼18.2 mrad at 1200 nm phase-matching signal wavelength. The corresponding external angle is more than 27 mrad. The signal/idler wavevector angle varies from 16.7 mrad at 1350 nm to 20.5 mrad at 1050 nm, over an angular spectrum of ∼3.8 mrad. Considering the smallest wave-vectors angle of 16.7 mrad, the angular separation of signal and idler beams out of the P-DKDP crystal would be more than 24 mrad, which corresponds to a spatial separation of 24 mm at 1 m beam propagation distance. A free space propagation distance of signal and idler laser beams in the range of 1 m would be long enough for the spatial separation of signal and idler waves with the beam diameter in the range of 10 mm. For signal waves with a beam diameter in the range of 400 mm, a propagation distance of about 20 meters would be necessary for the full spatial separation of the signal and idler beams.

If we consider an increased noncollinearity angle, α = 14.4 mrad, an internal β angle between signal and idler wavevectors of ∼24.8 mrad can be obtained. The phase-matching wavelength is shifted towards longer wavelengths. At the 1250 nm phase matching signal wavelength, an external angle of as much as 37 mrad between signal and idler wavevectors was calculated. Compared to the OPCPA configuration with a 10.3 mrad noncollinearity angle, the free space propagation distance, required for the spatial signal and idler beams separation, decreases with ∼40%. At the same time, the parametric gain bandwidth (cyan line in Fig. 6(d)), calculated under similar conditions, 1 GW/cm² pump intensity and 40 mm long 58.3% DR P-DKDP crystal, decreases with about 15% compared to the gain bandwidth at 10.3 mrad noncollinearity angle (red line in Fig. 6(d)). If we move away from the amplification condition of critical wavelength degeneracy in a collinear geometry, the available parametric gain bandwidth decreases. A trade-off must be found between the required parametric gain bandwidth and the noncollinearity angle, which determines the size of the high energy OPCPA stage.

4. Technical challenges of a 100-PW class laser system based on OPCPA at CWD in P-DKDP crystals

Some technical difficulties can be encountered in the development of a 100 PW class laser system based on OPCPA near CWD in P-DKDP crystals: generation of white light continuum (WLC) picosecond seed pulses in the near-infrared, around 1.1-1.2 µm central wavelength; green picosecond pump lasers for mJ-energy OPCPA stages; optical synchronization of seed and pump picosecond pulses in the laser system Front-End (FE); development of few-ns pulse duration green pump lasers, with a couple of Hz repetition rate, for Joule-energy OPCPA stages; growing of large size P-DKDP crystals, up to 500 mm clear aperture diameter, with controlled deuteration ratio; multi-kJ green nanosecond pump lasers for kJ-energy parametric amplifiers; large size, broad-band diffraction gratings, with improved laser induced damage threshold (LIDT). Based on the reported scientific results and the technological state of the art, I present some possible solutions to overcome these technical difficulties.

A picosecond Front-End (FE), based on optically synchronized small angle non-collinear OPCPA at CWD degeneracy in P-DKDP crystals, would be appropriate for the SBGB signal pulse amplification near the 1.1-1.2 µm central wavelength. White light continuum (WLC) in the 700-1400 nm spectral range was generated in YAG crystals by focusing µJ femtosecond pulses with the central wavelength of ∼1.5 µm [17]. The WLC, generated by focusing femtosecond laser pulses in crystals, preserves the phase relation in the spectral band. It is re-compressible to femtosecond pulses with the pulse duration determined by its ultra-broad spectral bandwidth [18].

A femtosecond Er:glass fiber oscillator, 1550 nm wavelength, followed by an amplifier, could be a suitable source of few-μJ energy pump pulses required for WLC generation. Before OPCPA stages, the WLC signal pulses should be stretched in a bulk material to about 1 ps pulse duration.

Pump pulses for OPCPA stages can be generated starting from an Yb:YAG femtosecond oscillator at 1030 nm. Afterwards, femtosecond pulses might be stretched to hundred-ps and amplified at 10 Hz repetition rate in an Yb:YAG thin-disk amplifier and booster [19,20]. After pulse compression and frequency doubling, the pump pulses of more than 50 mJ energy, 1-2 ps pulse duration at 515 nm, can be used to pump two-three OPCPA stages with P-DKDP crystals, with DR = 0.40, seeded by the WLC signal pulses.

Temporal overlapping of picosecond signal and pump pulses for parametric amplification can be realized by the synchronization of Er:glass and Yb:YAG femtosecond oscillators, with their repetition rates locked to a suitable radio frequency reference source [21]. An alternative solution for optical synchronization could be the splitting the WLC pulse in two beams, representing the sources of the signal and pump lasers pulses. For the pump laser pulse generation, a 1030 nm pico-Joule pulse, obtained by spectrally filtering of one of the beams, could be used as the Yb:YAG laser amplifier seed.

An acousto-optic programmable dispersion filter, working in the near-infrared spectral domain, would be required for the spectral-phase dispersion correction. By optical parametric amplification of the signal pulse from nJ to 10-mJ energy, an increase of the intensity contrast with about seven orders of magnitude out of the temporal window corresponding to the picosecond pump pulse duration could be expected. FE output picosecond pulses of ∼10 mJ energy, with > 200 nm spectral bandwidth, re-compressible to less than 10-fs can be obtained.

After FE, the signal laser pulses should be stretched in the range of 3 ns duration [11]. Joule-energy amplified signal pulses can be obtained in P-DKDP stages, with DR = 0.64 corresponding to the 1064 nm critical wavelength, pumped by existing commercial high-energy frequency doubled Nd:YAG lasers, specially designed for pumping OPCPA stages [22]. All nanosecond pump lasers can be electronically synchronized with nanosecond signal pulses. By pumping two small-angle non-collinear P-DKDP stages with a couple of ten-J pulse energy, amplified nanosecond signal pulses in the range of few-J energy are expected.

High energy stages, based on OPCPA at 1054 nm CWD, requires large size P-DKDP crystals with DR = 0.58, clear aperture diameter in the range of 100-450 mm [23–25], to amplify the signal pulses to more than 1.5 kJ energy. Single-shot 527 nm wavelength Nd:glass lasers with more than 5 kJ single beam pulse energy, few-ns pulse duration, good quality spatial and temporal intensity profile would be appropriate for pumping these high energy OPCPA stages [6,11].

The availability of meter size diffraction gratings for the temporal compressor, with a spectral bandwidth of more than 200 nm, high diffraction efficiency in the 1.1-1.2 μm spectral range, and high LIDT represents an important technical challenge. Gold gratings [26] and probably hybrid gratings [27] should be a promising solution. Considering an expected ∼70% transmission of the temporal compressor, 100 PW class single-beam laser pulses could be obtained after the 1.5 kJ nanosecond stretched pulses temporal compression down to 10-fs range pulse duration.

5. Conclusions

As broad as 365 nm and 550 nm FWHM parametric gain bandwidths, at 1 GW/cm² and 25 GW/cm² pump intensity, respectively, have been calculated for collinear OPCPA at critical wavelength degeneracy in DKDP crystals. Practically, it is not possible to operate OPCPA stages under these conditions because of the lack of pump lasers with the required wavelength that should be half of the signal critical wavelength.

The critical wavelength of partially deuterated KDP crystals can be adjusted in the range of 1000-1100 nm by changing the deuteration ratio. Critical wavelengths of 1064 nm, 1054 nm, and 1030 nm, corresponding to the emission wavelength of the available high energy pump lasers, such as frequency doubled Nd:YAG, Nd:glass, and Yb:YAG, can be obtained for deuteration ratios of 0.64, 0.58, and 0.40, respectively.

Considering 1 GW/cm² pumping with a frequency doubled nanosecond Nd:glass laser, as broad as 280 nm gain bandwidth was calculated in a 40 mm length P-DKDP crystal. It is significantly larger than the gain bandwidth of 150 nm, which can be obtained for the same parametric peak gain in NC OPCPA stages with DKDP crystals, in the 900 nm wavelength spectral range, which are currently used in multi-PW laser systems. Under these conditions, the SBGB of P-DKDP crystals allows the amplification of ∼1.4 times shorter femtosecond pulses compared to the BGB of DKDP crystals, giving rise to a higher peak power at the same amplified pulse energy.

Large aperture P-DKDP crystals, up to half-meter diameter, would be suitable for the amplification of ultra-broad nanosecond chirped pulses, in the spectral range of 1.1-1.2 μm, up to kJ pulse energy, required by 100 PW class femtosecond lasers.

The spectral profile of the SBGBs can be shaped by slightly adjusting the deuteration ratio near the exact value required by the OPCPA at CWD. To separate the signal and idler laser pulses with the same polarization in a type I optical parametric amplifier, a small-angle non-collinear OPCPA, near CWD, can be used. In this case, for a slight adjustment of the P-DKDP crystal orientation and its deuteration ratio, SBGBs of 490 nm and 255 nm, at 25 GW/cm² and 1 GW/cm², respectively, have been calculated. In case of a small signal-pump wavevectors internal angle of ∼10 mrad, about 20 m free space propagation distance would be necessary for the spatial separation of signal and idler waves with the beam diameter in the range of 400 mm,

There are some technical difficulties in the way towards a 100-PW class femtosecond laser system based on OPCPA at CWD: generation of a stable WLC in the near-infrared spectral range, in crystals irradiated by femtosecond laser pulses; building of picosecond pump lasers for optically synchronized OPCPA stages in the Front-End; growing of large size P-DKDP crystals with a controlled deuteration ratio; building of multi-kJ pulse energy, few-ns pulse duration, green pump lasers; manufacturing of meter-size diffraction gratings with a high LIDT and high diffraction efficiency in a broad spectral bandwidth in the range of 1.1-1.2 μm signal wavelength. Based on the current scientific progress and the technological state of the art of the key laser components, these challenging issues could be solved in the next few years.

Acknowledgments

Portions of this work were presented at the Advanced Solid State Lasers Conference, 13 - 16 October 2020, paper number JTh2A.10-1.

The present work was supported by the Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, which is a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund and the Competitiveness Operational Programme (1/07.07.2016, COP, ID 1334).

Disclosures

The author declares no conflict of interests.

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Crystal	λ_s0(BGB) (nm)	PLW (nm)	α (degrees)	θ (degrees)	ϕ (degrees)
BBO	825	532	2.41	23.87	0
DKDP	900	527	0.92	37.0	45

Crystal	λ_CW (nm)	PLW_CWD (nm)	SBGB₁ (nm)	SBGB₂₅ (nm)	θ (degrees)	BGB (nm)
BBO	1432	716	790	1170	19.9	170
DKDP	1122	561	365	550	36.0	150

Crystal	λ_s0(BGB) (nm)	PLW (nm)	α (degrees)	θ (degrees)	ϕ (degrees)
BBO	825	532	2.41	23.87	0
DKDP	900	527	0.92	37.0	45

Crystal	λ_CW (nm)	PLW_CWD (nm)	SBGB₁ (nm)	SBGB₂₅ (nm)	θ (degrees)	BGB (nm)
BBO	1432	716	790	1170	19.9	170
DKDP	1122	561	365	550	36.0	150

Optical parametric amplification at critical wavelength degeneracy—a proposed approach for 100-PW class femtosecond laser development

Abstract

1. Introduction

2. Super-broad gain-bandwidth in nonlinear-crystals at critical wavelength degeneracy (CWD)

3. SBGBs of P-DKDP crystals pumped by high energy nanosecond green lasers

4. Technical challenges of a 100-PW class laser system based on OPCPA at CWD in P-DKDP crystals

5. Conclusions

Acknowledgments

Disclosures

References

Cited By

Figures (6)

Tables (2)

Equations (6)

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