1. Introduction

The development of ultrahigh-peak-power lasers has reached a new level, where several 10-PW systems have been built and other facilities with tens of PW capabilities are either in the planning stage or under construction. When combined with large-aperture nonlinear crystals such as partially deuterated KDP (DKDP), optical parametric chirped-pulse amplification (OPCPA) provides the most viable route for the development of tens to hundreds of PW laser systems [1,2]. Growing large-aperture DKDP crystals is a mature technology that allows for energy scaling, originally supported by the need for nonlinear frequency conversion of high-energy nanosecond lasers [3]. DKDP supports the deuteration-dependent ultra-broadband phase matching in parametric amplifiers [4], therefore enabling the generation of sub-20-fs pulses. It has been demonstrated that the DKDP-based PW-level OPCPA can achieve high energy-conversion efficiency up to 37% [5].

The temporal contrast of the ultrahigh-peak-power pulses becomes critically important for laser–matter interaction. Understanding the origins of contrast degradation and maximizing the temporal contrast therefore become essential for the development of laser facilities. Several mechanisms that degrade the temporal contrast have been identified in chirped-pulse–amplification systems. Some of them, such as spectral phase modulation due to the surface roughness of stretcher and compressor optics [6,7] or post-to-prepulse generation via nonlinear coupling [8], are common to Ti:sapphire and OPCPA-based high-power systems. Unique to OPCPA systems, the pump temporal modulation can degrade the temporal contrast of the recompressed signal because it induces high-frequency spectral modulation on the chirped signal during parametric amplification [9]. The pump temporal modulation is commonly introduced from the interferometric beating between the main pump pulse and the amplified spontaneous emission (ASE). Analytical and numerical studies have revealed the underlying physics, showing that the pump-induced contrast degradation depends on the temporal characteristics of the pump modulation and the parametric amplifier’s operating regime [10,11]. Narrowband spectral filtering of the pump pulse has been demonstrated as an effective way to reduce the pump-induced contrast degradation [12].

In OPCPA systems, it is common to use a single laser to pump several optical parametric amplification (OPA) stages [13,14] to reduce experimental complexity and cost. In such a system, the signal amplified in the first stage carries the pump modulations, and amplification in the second stage occurs with a pump pulse having the same modulations. This results in an amplified signal with temporal modulations that depend not only on the operating regime of the optical parametric amplifiers and the pump temporal modulation, but also on the difference in pump-seed delay in different stages. A corollary of this configuration is that the temporal contrast of the recompressed signal depends on these parameters.

We investigate, for the first time to our knowledge, the pump-to-signal noise transfer in a two-stage ultra-broadband OPCPA and show the dependence of signal noise, characterized both before and after pulse compression, on the pump-seed delay and amplifier operating regime. With both amplifiers operating in the linear amplification regime, an up-to-15-dB reduction of the pump-induced contrast degradation via pump-seed delay optimization has been experimentally observed and confirmed by simulations. Gain saturation reduces the pump-induced contrast degradation. However, even in a system where amplifiers operate at saturation with a pump having a flattop beam profile and flat-in-time pulse shape, the edges of the pulse and the beam experience unsaturated amplification. As a result, the pump-induced contrast degradation is delay-dependent even when both amplifiers are operated in saturation, thereby making the pump-seed delay a simple and effective tool in minimizing the pump-induced contrast degradation in multi-stage OPCPA. The results presented in this work will support the design and development of OPCPA-based ultrahigh-peak-power systems. They are also applicable to the hybrid OPCPA/laser-power-amplifier systems [15,16], in which an OPCPA front end provides broadband, high signal-to-noise ratio seed pulses to the high-energy laser amplifiers.

This article is organized as follows: Section 2 describes the experimental setup and presents details on pump pulse generation and signal pulse amplification, as well as the characterization of pump and signal intensity noise. Section 3 provides a general description of the numerical modeling used in this work. Section 4 discusses the results obtained in a single-stage OPCPA, i.e., the first stage of a two-stage system. Section 5 presents the experimental and simulation results detailing the pump-to-signal noise transfer in two-stage ultra-broadband OPCPA. Some final remarks are included in Sec. 6.

2. Experimental setup

2.1 Overall layout

The experiments were performed in a two-stage ultra-broadband OPCPA system [Fig. 1(a)], which is a subsystem of the Multi-Terawatt‒pumped optical parametric amplifier line (MTW-OPAL), i.e., a 0.5-PW, 20-fs, all-OPCPA system [17]. The subsystem consists of an ultra-broadband front end (UFE) providing the seed, two noncollinear optical parametric amplifiers (NOPA4a and NOPA4b), a single pump laser for pumping both NOPA stages, and a grating compressor.

 

Fig. 1. (a) Experimental layout of the two-stage ultra-broadband OPCPA together with the illustrative pump and signal pulses propagating through the system; UFE: ultra-broadband front end; NOPA: noncollinear optical parametric amplification; ET: energy throttle; DL: delay line. (b) Schematic layout of the pump laser system. SLMO: single-longitudinal-mode oscillator; CLARA: crystal large-aperture ring amplifier; SHG: second-harmonic generation. The dashed items SLMO #2 and fiber splitter have been added to combine with SLMO #1 so that a controllable amount of sinusoidal intensity modulation can be introduced when needed.

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2.2 Pump-pulse generation and intensity-modulation characterization

The pump laser shown in Fig. 1(b) is very similar to the one reported in [18]. It is electronically synchronized with the UFE and composed of four main stages: a fiber front end, an Nd:YLF regenerative amplifier, an Nd:YLF crystal large-aperture ring amplifier (CLARA), and a second-harmonic generation (SHG) stage. The fiber front end temporally shapes the wavelength- and power-tunable, continuous-wave, 1053-nm seed from a single-longitudinal-mode oscillator (SLMO #1). The pulse-shaping system consists of a sequence of two Mach–Zehnder modulators, driven at a 300-Hz repetition rate. The first one generates a flat-in-time 1.6-ns pulse, and the second one driven by an arbitrary waveform generator (10 GS/s) introduces a positive ramp in the pulse to precompensate square-pulse distortion in the subsequent amplifiers. The shaped pulse is amplified by an Yb-doped fiber amplifier to tens of picojoules before seeding the Nd:YLF amplifiers.

In this work, a sinusoidal modulation is intentionally introduced on the pump pulse to facilitate the identification and control of the pump-to-signal noise transfer as part of the study. A second co-polarized single-longitudinal-mode oscillator (SLMO #2) is incorporated in the system via the 10% port of an added fiber splitter with 90/10 splitting ratio. The power loss to the main seed from the fiber splitter is compensated by operating the main seed source at higher power. The wavelength of SLMO #2 is detuned from that of SLMO #1 to create a sinusoidal modulation on the pump pulse. The modulation depth is controlled by varying the output power of the added seed. In our experiments, a 3 × 10⁻³ power ratio between SLMO #2 and SLMO #1 has been chosen to introduce ∼10% peak-to-mean modulation on the pump pulse. This sinusoidal modulation is maintained after fiber amplification and can be clearly seen in the pulse waveform [Fig. 2(a)] measured with a high-bandwidth InGaAs photodiode (DSC10, Discovery Semiconductors) and a 70-GHz oscilloscope (DPO77002SX, Tektronix). As will be discussed in Sec. 4, the 10% peak-to-mean modulation depth is chosen in order to have an observable impact of pump sinusoidal modulation on the compressed pulse contrast. Larger pump modulation depths, while potentially leading to more observable effects, have not been used to avoid damage in the high-energy laser amplifiers. For baseline measurements, the pump sinusoidal modulation is removed by turning off SLMO #2, leaving the pump pulse with only ASE modulation. Due to the negligible relative power of SLMO #2, turning it on and off (and, consequently, the sinusoidal modulation on the pump pulse) has negligible impact on the pump-laser energy performance.

 

Fig. 2. Measured single-shot pulse waveforms from (a) fiber amplifier and (c) CLARA with and without the 30-GHz sinusoidal modulation; [(b) and (d)] the corresponding rf spectra calculated from the waveforms in (a) and (c). A strong rf peak at 30 GHz exists when the sinusoidal modulation is introduced on the pump pulse.

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The shaped and modulated pulse from the fiber front end is amplified to a few millijoules at 5 Hz in a diode-pumped Nd:YLF regenerative amplifier. The Gaussian output beam is then shaped to a square super-Gaussian beam using a binary pixelated apodizer [19]. This defines a reference plane that is re-imaged at each round-trip in the CLARA cavity. The CLARA contains two 25-mm-diam, flash-lamp–pumped Nd:YLF heads operating at 5 Hz and boosts the pulse energy to as high as 2 J after four round-trips. The output beam is image relayed onto an 8-mm-long lithium triborate (LBO) crystal for SHG to 526.5 nm, with up to 70% conversion efficiency. That beam is then split into two beams that are independently image relayed to pump the NOPA4a and NOPA4b stages. The pump energy for each stage is controlled independently by an energy throttle, i.e., a half-wave plate combined with a thin-film polarizer.

The CLARA pulses at 1053 nm are spatially sampled in the near field using a single-mode fiber and characterized with the same high-bandwidth InGaAs photodiode and the 70-GHz oscilloscope used for the fiber front-end output pulses. The sinusoidal modulation is not distinguishable from the broadband noise due to ASE [Fig. 2(c)], but it can be clearly identified in the calculated rf spectrum as a strong peak at 30 GHz together with the broadband modulation [see Fig. 2(d)]. The broadband modulation is the result of the interferometric beating between laser and the ASE and is introduced mainly from the high-gain regenerative amplifier. This is confirmed by the rf spectra of the regenerative amplifier seed pulses, which show negligible broadband modulation [Fig. 2(b)]. The energy ratio between ASE and the main monochromatic pulse can be estimated at ∼10⁻³ based on the temporal modulations.

The 30-GHz modulation frequency is chosen for two reasons: First, the frequency detuning needs to be small such that the added seed source is within the spectral gain bandwidth of the Nd:YLF regenerative amplifier, which is about 40-GHz full width at half maximum (FWHM) [12]. This ensures that the sinusoidal modulation can be maintained after laser amplification. Secondly, as explained in [10], a sinusoidal modulation of the pump pulse introduces pre- and postpulses in the compressed signal pulse, with their delays from the main pulse proportional to the pump modulation frequency. A relatively large frequency detuning is therefore required to separate the pre- and postpulses from the main peak.

The broadband modulation due to ASE and the single-frequency modulation due to interference between the two SLMO’s fluctuate shot-to-shot because the interference among the multiple waves has varying phase. Because of this, the envelope of a collection of multiple rf spectra or the average of multiple pulses is presented, unless otherwise specified, to show the collective effect of pump-to-signal noise transfer.

2.3 Signal-pulse amplification and intensity-modulation characterization

The two-stage OPCPA system consists of two noncollinear optical parametric amplifiers: NOPA4a and NOPA4b. These stages use type-I phase-matched BBO crystals with a thickness of 10 mm and 5.5 mm, respectively. The seed originates from a white-light continuum seeded UFE. The UFE contains three NOPA stages that deliver 5-mJ, few-picosecond pulses with a >200-nm bandwidth centered around 920 nm. The seed pulse is stretched to >1.6 ns to match the pump pulse duration with a cylindrical Offner stretcher. More details about UFE can be found in [17].

After pulse stretching, the 100-μJ seed pulse is amplified to 20 mJ in NOPA4a with 70 mJ of pump energy. The pump-seed delay at NOPA4a is adjusted using an electronic timing system and optimized, together with phase-matching optimization, for maximum output bandwidth and pulse energy. The amplified signal beam (2.7 × 2.7 mm²) from NOPA4a is image relayed to NOPA4b with an up-collimation factor of 2.6. At NOPA4b, the pump-to-signal noise transfer depends not only on the amplifier operating regime and the pump temporal modulation characteristics, but also on the difference in pump-seed delay in the two stages. An optical delay line [see Fig. 1(a)] controls the pump-seed delay τ with <50-fs temporal resolution. The signal energy is boosted up to 180 mJ with 450-mJ pump energy in NOPA4b. The amplified signal beam is 6.7 × 6.7 mm², which is defined by the pump beam size. The pump peak intensity for both stages is close to 1 GW/cm², only half of the design value. The pump intensity is currently lowered to avoid damage to out-of-imaging plane transport optics. The spatial profile on these optics is highly modulated because of the high-order super-Gaussian beam profile and wavefront static and dynamic modulations. Because of this, both amplifiers operate away from the complete saturation, as shown in Fig. 3, where NOPA4a partially saturates and NOPA4b operates in the linear regime.

 

Fig. 3. Amplified signal output energy (a) after NOPA4a and (b) after NOPA4b. In (b), the NOPA4b output energies are obtained with two different seed energies (i.e., 10 mJ and 20 mJ) obtained from NOPA4a.

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The amplified signal pulse after NOPA4b is recompressed using a double-pass grating compressor with 70% throughput. An acousto-optic programmable dispersive filter (DAZZLER, Fastlite) installed in the UFE manages the fine dispersion control to allow near-transform-limited pulse compression. Compressed pulses with 19.8-fs mean duration (18.5-fs Fourier transform limit) and 1-fs rms over 1000 shots have been measured using a SPIDER device [20]. The optical spectrum is acquired using a multichannel spectrometer, which has ∼1.5-nm spectral resolution at 920 nm. The representative NOPA4b spectrum, obtained at full energy and near-zero pump-seed delay, is plotted in Fig. 4(a).

 

Fig. 4. (a) Representative single-shot spectrum measured after NOPA4b at 180-mJ output; (b) a collection of 50 rf spectra of the NOPA4b chirped pulses. The thick red curve represents the envelope of the 50-rf spectra.

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The modulation in signal spectrum is linked to the pump-intensity modulation and can be evaluated by analyzing the rf spectrum of the chirped signal pulse. The rf spectrum is obtained by first converting the measured optical spectrum to a time-domain representation of the chirped pulse using the stretcher’s group delay. The obtained pulse is then further transformed to the rf spectrum using a Fourier transform. Figure 4(b) shows a collection of 50 rf spectra of the NOPA4b chirped signal pulses, obtained when only ASE modulation is present in the pump. The thick red curve represents the envelope of the 50 rf spectra. Intensity modulation in the signal spectrum leads to the contrast degradation of the recompressed pulse, which is characterized using a high-dynamic-range scanning third-order cross correlator (SEQUOIA, Amplitude Technologies), as detailed in Secs. 4 and 5. A small portion (up to 5 × 5 mm²) from the center of the signal beam (35 × 35 mm²) after the pulse compressor is sampled by the cross-correlator for pulse-contrast characterization.

3. General description of numerical modeling

The two-stage ultra-broadband OPCPA system is simulated by including the following processes: pulse stretching, two-stage optical parametric amplification and pulse compression, as well as the third-order cross-correlation for pulse contrast characterization. Pulse stretching is accounted for by using the stretcher’s group delay to convert a spectral-modulation-free seed spectrum (tenth-order super-Gaussian with 210-nm FWHM centered at 920 nm) into a chirped seed pulse. The signal chirp introduced by the cylindrical Offner stretcher is nonlinear with second-order [group-delay dispersion (GDD)] and third-order dispersion (TOD) of the order of 3.4 ps² and −0.008 ps³, respectively, at the 920-nm center wavelength. The mapping from frequency to time and vice versa are used in the simulations to convert field representations between these two domains.

The optical parametric amplification is simulated following the approach described in [21]. The pump, signal, and idler waves are represented in the time domain by the scalar values of their electric field. Spatial effects such as diffraction and spatial walk-off are neglected because they are not significant for collimated beams with a size of a few millimeters. The temporal step size, and therefore the resolution of pump-seed delay, is set to be 1 ps. The phase mismatch $\mathrm{\Delta }k$ among three waves at each time step is calculated based on the corresponding spectral components of the three waves and the experimental phase-matching conditions. More specifically, a pump angle θ_p of 23.84° and a noncollinear angle α of 2.245° are used to achieve broadband amplification in BBO, where both angles follow the definition used in [22]. The NOPA4a seed intensity (0.5 MW/cm²) and the pump intensities for both stages are chosen to closely match the experimental values. The pump temporal modulation is introduced by adding ASE and/or a second monochromatic light, both with random phase, on the main monochromatic pulse. The ASE is assumed to have a Gaussian spectral distribution with 40-GHz FWHM bandwidth and an energy ratio of ∼10⁻³ to the main pulse. The electric-field amplitudes of the pump, signal, and idler at each time step are then evaluated using Jacobi elliptic integrals to account for the nonlinear interaction. After amplification, the time-domain pulse is calculated via Fourier transformation with the assumption of a flat residual phase consistent with the measured near-transform-limited pulse.

The third-order cross-correlation process is also simulated in order to compare the temporal contrast obtained from measurements and simulations. It has been found that the spectral bandwidth limitation of the cross-correlator in both second-harmonic generation (SHG) for 2ω probe-pulse generation and third-harmonic generation (THG) for contrast characterization must be taken into account to better match measurements and simulations. Due to the limited spectral acceptance of the THG process, any noise from the portion of signal spectrum (e.g., both sides) that is not phase matched is not measured. As will be discussed in Sec. 5.3, the cross-correlation measurements cannot reveal the contrast improvement via pump-seed delay optimization, when amplifiers are operated near or in saturation, in which case the contrast noise is mainly from the edges of the signal pulse/spectrum.

4. Pump-to-signal noise transfer in single-stage OPCPA

Pump-to-signal noise transfer and the resulting contrast degradation at NOPA4a have been investigated in two operating regimes, i.e., linear versus partially saturated regime, in which the pump energies are 45 mJ and 70 mJ, respectively, and the corresponding output signal energies are 10 mJ and 20 mJ [see Fig. 3(a)].

Figures 5(a)–5(c) show the rf envelope of the pump pulse at 1053 nm, the input seed pulse, and the amplified signal pulse, respectively. The input pulse has negligible high-frequency modulations, as shown in Fig. 5(b), when compared to the pump pulse and the amplified signal pulse. As plotted in Fig. 5(c), when NOPA4a is operated in the linear regime, both ASE and sinusoidal modulations in the pump pulse are transferred to the amplified signal pulse. However, operation of NOPA4a near saturation strongly suppresses both modulations.

 

Fig. 5. The rf envelope of (a) the NOPA4a pump pulse at 1053 nm with both ASE and sinusoidal modulations; (b) the chirped seed pulse to NOPA4a showing negligible modulations; and (c) the amplified signal pulse after NOPA4a, when the stage is operated in the linear or the partially saturated regimes.

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After pulse compression, the measured temporal contrast shows a similar dependence on the amplifier operating regime. For instance, the prepulse introduced by the 30-GHz pump sinusoidal modulation is present in the measured cross-correlation signal in the temporal range from –1 ps to –0.5 ps [Fig. 6(a)], when NOPA4a is operated in the linear regime. We note that the 10% peak-to-mean modulation on the pump pulse after the fiber amplifier [see Fig. 2(a)] has been chosen to induce an observable impact of pump sinusoidal modulation on the pulse contrast, i.e., to generate well-identified pre-/postpulses after compression. The introduction of pre- and postpulse in the compressed signal by the pump sinusoidal modulation and its dependence on the signal chirp are discussed in detail in Appendix A. The prepulse does not appear in the cross-correlation signal when NOPA4a is operated near saturation [Fig. 6(b)]. This agrees well with the previous observation that the sinusoidal modulation on the signal is strongly suppressed by amplifier saturation [see Fig. 5(c)]. The broad pulse pedestal is introduced by the broadband ASE modulation and other contrast degradation sources such as high-frequency phase modulation from the stretcher optics.

 

Fig. 6. Measured cross-correlation signals with and without the 30-GHz pump sinusoidal modulation, when NOPA4a is operated (a) in the linear regime and (b) in the partially saturated regime.

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5. Pump-to-signal noise transfer in two-stage OPCPA

In OPCPA, the pump-seed delay has great influence on the amplified signal spectrum [23,24] as well as on the contrast degradation due to the amplification of parametric fluorescence [23,25–27]. Several methods have been used to determine the pump-seed delay, relying on either a direct photodiode measurement [28] or a contrast measurement [23]. In this section, we first present a new method for determining the delay between nanosecond pump and seed pulses with high precision (i.e., ±2 ps for a 1.6-ns pump pulse) in multi-stage OPCPA. With the excellent knowledge and control of the pump-seed delay, we then demonstrate precise control of the pump-induced contrast degradation at NOPA4b. Finally, the dependence of pump-induced contrast degradation on the NOPA4b operating regime is also discussed.

5.1 Dependence of pump-noise transfer on pump-seed delay and its application for in-situ pump-seed delay determination

The pump-to-signal noise transfer at NOPA4b shows strong dependence on the pump-seed delay when both NOPA4a and NOPA4b are operated in the linear regime, where NOPA4a outputs 10 mJ with 45 mJ of pump energy, and NOPA4b outputs 120 mJ with 450 mJ of pump energy (see Fig. 3). Different from the NOPA4a rf spectrum [Fig. 7(a)] that gradually decays at a higher frequency, the NOPA4b rf spectrum [Fig. 7(c)] exhibits clear modulation with peaks and nulls. The frequencies of these peaks and nulls vary as the NOPA4b pump-seed delay changes.

 

Fig. 7. The rf envelope of the chirped pulses (a) measured after NOPA4a, (b) simulated after NOPA4a, (c) measured after NOPA4b, and (d) simulated after NOPA4b, when both NOPA4a and NOPA4b are operated in the linear regime. The NOPA4b rf modulation is dependent on the pump-seed delay.

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The formation of the nulls is explained by the strong suppression of modulation frequencies at $f_n^{\textrm{null}} = {{({n - {1 / 2}} )} / \tau },$ where n = 1,2,3,…, for which the pump-seed delay τ equals to (n–1/2) period of the corresponding modulation. For these combinations of frequency and delay, modulations in the pulse amplified by NOPA4a are out of phase with respect to the pump modulations in NOPA4b and therefore get suppressed via parametric amplification. The lowest suppressed frequency is $f_1^{\textrm{null}} = {1 / {({2\tau } )}}.$ The rf modulation is strongly suppressed when NOPA4a and NOPA4b are operated in the saturation regime. The frequencies of the first three nulls can be identified from Fig. 7(c) as 6.89GHz, 18.94 GHz, and 31.43 GHz, respectively. The pump-seed delay determined as an average of the delays obtained from the second and third null is 79.4 ps. The pump-seed delay obtained from the first null is ignored because it is significantly different from the other two delays obtained from the second and third null. An explanation about the uncertainty in determining pump-seed delay using the first null is given below.

The dependence of pump-noise transfer on the pump-seed delay at NOPA4b is confirmed by the simulations, in which a 79-ps pump-seed delay is used. As shown in Fig. 7(d), the simulated NOPA4b rf modulation is consistent with the measured modulation, demonstrating that the rf modulation feature can be employed to characterize the pump-seed delay. The simulated NOPA4b rf spectrum [Fig. 7(d)] represents the case where the null frequencies can be well identified and all the nulls are linked to the same pump-seed delay.

In practice, several factors reduce the reliability in determining the null frequencies and their corresponding pump-seed delay. The first null is found to be less reliable for retrieving the pump-seed delay when its frequency is below 10 GHz. This is likely because the low-frequency rf components from the pulse envelope vary shot to shot due to the variation of the pump envelope, therefore introducing large variation to the first null frequency. Secondly, the nulls at high frequencies are too shallow to define their frequencies accurately. This limitation can be mitigated by normalizing the modulated rf spectrum to the one obtained with near-zero pump-seed delay, i.e., the one without clear modulation, that greatly enhances the ability to identify the null frequency. Finally, the ripples in the rf spectrum could also introduce error. Smoothing the curve using a moving average is found to be effective in reducing such error.

Figure 8(a) displays the smoothed rf spectra obtained at pump-seed delays, which are sampled every 10 ps using the delay stage. The moving average span for the smoothing is 15 points. The retrieved mean pump-seed delays at each delay setting as well as a linear fit to the delay scan are plotted in Fig. 8(b). The zero delay for the delay scan in Figs. 8(a) and 8(b) was determined by the linear fit. It is worth emphasizing that the pump-seed delays retrieved from different null frequencies at each delay setting vary within ±2 ps and that the retrieved mean delay is also within 2 ps of the delay from the linear fit. This indicates that an in-situ pump-seed delay characterization with high precision can be achieved. Note that the precise determination of zero pump-seed delay can benefit the optimization of temporal contrast when parametric-fluorescence–induced contrast degradation is concerned.

 

Fig. 8. (a) The rf spectra obtained at different pump-seed delays by scanning the delay stage; (b) the mean pump-seed delays at each delay setting retrieved from the rf spectra presented in (a) and a linear fit to the delay scan. The five rf spectra that exhibit clear null(s) are used to retrieve the pump-seed delays.

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5.2 Dependence of pulse-contrast degradation on pump-seed delay in the linear amplification regime

The contrast degradation has a strong dependence on the pump-seed delay when both amplifiers are operated in the linear regime. Figure 9 presents the cross-correlation signals of the compressed NOPA4b pulses measured at different pump-seed delays. In the case of a pump pulse with both ASE and sinusoidal modulations [Fig. 9(a)], the stretched prepulse, which is introduced by the sinusoidal modulation, exists when the pump-seed delay is equal to zero or the full sinusoidal modulation period T. Throughout this article, T is equal to 33.3 ps (corresponding to a modulation frequency equal to 30 GHz) unless otherwise specified. When the pump-seed delay is set to be half of the modulation period (i.e., 1/2 T = 16.7 ps), the prepulse is strongly suppressed, resulting in the reduction of contrast degradation up to 15 dB. For a pump pulse with ASE modulation only [Fig. 9(b)], the contrast degradation also shows a strong dependence on the pump-seed delay. Up to 10-dB reduction of contrast degradation in the temporal region between –1 and –0.3 ps is observed, when the pump-seed delay is changed from 0 ps to 16.7 ps. In both cases, the contrast degradation has been confirmed to show a similar dependence on the negative pump-seed delays as expected (data not shown).

 

Fig. 9. Measured cross-correlation signals of the compressed NOPA4b pulses at different pump-seed delays, when both NOPA4a and NOPA4b are operated in the linear regime. T = 33.3 ps corresponding to a modulation frequency equal to 30 GHz. (a) The case of a pump pulse with both ASE and 30-GHz sinusoidal modulations; (b) the case of a pump pulse with ASE modulation only.

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Figure 10(a) compares the two cross-correlation signals measured at a 16.7-ps pump-seed delay (i.e., τ = 1/2T), with and without pump sinusoidal modulation. There is no clear difference between the two signals, indicating no significant impact of the 30-GHz sinusoidal modulation on the pump when operating the two amplifiers. This is confirmed by the fact that the two corresponding rf spectra are similar and show no signature of the 30-GHz modulation [Fig. 10(b)]. This demonstrates that the pump-seed delay can serve as a tool to minimize the pump-induced contrast degradation in multi-stage OPCPA. This demonstration also confirms the very high precision achieved when determining the pump-seed delay as presented above.

 

Fig. 10. (a) The two cross-correlation signals measured at τ = 1/2 T or 16.7-ps pump-seed delay with and without sinusoidal pump modulation [identical to those plotted in Figs. 9(a) and 9(b)]; (b) the corresponding rf spectra of the uncompressed NOPA4b pulses.

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The dependence of contrast degradation on the pump-seed delay has been simulated. The input parameters for the simulations are closely matched to experimental values. Both NOPA4a and NOPA4b are operated in the linear regime. Figure 11 displays the simulated cross-correlation signals of the compressed NOPA4b pulses obtained at three different pump-seed delays, with pump ASE and sinusoidal modulations [Fig. 11(a)] or with pump ASE modulation only [Fig. 11(b)]. After taking into account the spectral bandwidth limitation of the cross-correlator, the simulated cross-correlation signals (Fig. 11) are in agreement with the measured ones (Fig. 9) not only for the dependence of contrast degradation on the pump-seed delay but also for some detailed features such as the widths of the stretched prepulse and the main pulse. The impact of the limited spectral bandwidth of the cross-correlator on the cross-correlation signal is discussed in Appendix B.

 

Fig. 11. Simulated cross-correlation signals of the compressed NOPA4b pulses at three different pump-seed delays, when NOPA4a and NOPA4b are operated in the linear regime. (a) The case of pump pulse with both ASE and 30-GHz sinusoidal modulations; (b) the case of pump pulse with ASE modulation only.

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The measured pulse contrast (Fig. 9) is lower than the simulated one (Fig. 11), especially in the temporal region that is farther away from the main peak. This discrepancy can be attributed to the contribution of other contrast degradation sources in the experiment. One contrast-degradation source is the signal spectral phase modulation induced by the surface roughness of the stretcher and compressor optics [6,7,29]. The spectral phase-modulation − induced contrast degradation is independent of pump-seed delay and therefore not studied in this work.

5.3 Dependence of pulse-contrast degradation on pump-seed delay in the saturation regime

When NOPA4a and NOPA4b are operated at their nominal conditions, i.e., closer to saturation, the measured pulse contrast shows no clear dependence on the pump-seed delay with [Fig. 12(a)] or without [Fig. 12(b)] pump sinusoidal modulation. This is in part because the gain saturation reduces the pump-induced contrast degradation. The saturation-assisted contrast improvement is clearly identified by comparing the measured pulse contrasts from Figs. 9(b) and 12(b) in the case of zero pump-seed delay (i.e., τ = 0) and with pump ASE modulation only. At –2 ps, the measured contrasts are comparable at about –47 dB. The contrast difference gradually increases to 10 dB in the region between –1 and –0.5 ps, and then gradually decreases and diminishes at –0.3 ps. The contrast degradation depends on the pump-seed delay between –1.5 and –0.3 ps as demonstrated in Fig. 9(b), and the pump-induced contrast degradation, as compared to other contrast degradation mechanisms such as parametric fluorescence and spectral phase modulation, is the only one that has pump-seed delay dependence. We therefore conclude that the pump-induced contrast degradation dominates in the temporal range between –1.5 and –0.3 ps. The pump-induced contrast degradation could become an even more dominant feature if contrast degradation caused by other mechanisms is reduced. A recent study by Ranc et al. [29] has demonstrated that the contrast degradation caused by spectral phase modulation, one of the dominant contrast degradation mechanisms, can indeed be reduced significantly via using high-quality stretcher optics. Therefore, it is necessary to understand all contrast degradation mechanisms even if one mechanism does not dominate in a specific OPCPA system.

 

Fig. 12. Measured cross-correlation signals of the compressed NOPA4b pulses at different pump-seed delays, when NOPA4a and NOPA4b are operated close to saturation. (a) The case of the pump pulse with both ASE and 30-GHz sinusoidal modulations; (b) the case of the pump pulse with ASE modulation only.

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Another important reason that explains the negligible dependence of contrast degradation on the pump-seed delay in the saturation regime is the limited spectral acceptance of the cross-correlator. One interesting feature, which is not revealed by the cross-correlation measurements, has been observed in both simulated pulses [Fig. 13(a)] and pulses calculated from the measured spectra [see Fig. 13(b)]. Due to the limited spectral resolution of the spectrometer, the calculated pulse has an effective time window from –1.2 ps to 1.2 ps, beyond which the displayed signal is detection noise. In both simulated and calculated pulses, the stretched prepulse that is previously observed in the linear regime case becomes two short prepulses, as shown by the dashed vertical lines, when pump-seed delay equals zero or T. This can be explained as follows: While the sinusoidal modulation inside the flattop part of the signal pulse is strongly suppressed by the gain saturation, the modulations on the rising and trailing edges of the chirped signal pulse are maintained since the amplification of these two regions is not saturated. As discussed in detail in Appendix A, sinusoidal modulations in these two regions of the signal spectrum contribute to the two sides of the stretched prepulse. This results in the suppression of the middle part of the stretched prepulse while maintaining the two sides to form two relatively short prepulses, where the earlier (later) prepulse originates from the modulations on the rising (trailing) edge of the chirped signal pulse or the long-(short-) wavelength side of the signal spectrum. The location of the newly formed side peaks in the simulated pulses is in good agreement with that in the calculated pulses. The contrast between the side peak and the broad pedestal is higher in the simulated pulse than in the measured pulse. This could be due to the slight difference in sinusoidal and ASE modulation depth and/or the level of saturation between simulations and the experiments. These side peaks, even when with high contrast, cannot be captured by the cross-correlator because of its limited spectral bandwidth (see Appendix B for more details). As shown in Figs. 13(a) and 13(b), the side peaks can be suppressed when the delay is tuned to half of the sinusoidal modulation period, leading to the higher temporal contrast.

 

Fig. 13. Compressed NOPA4b pulses that are (a) obtained from simulations and (b) calculated from the spectra measured under the same conditions as these for the cross-correlation measurements presented in Fig. 12(a). Two peaks are present in the prepulse of both simulated and calculated pulses, when pump-seed delay is equal to zero or T. The side peaks are suppressed at the pump-seed delay of 1/2 T. The dashed vertical lines are aligned with the peaks of interest for easier identification.

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The limitation of the cross-correlator in measuring contrast difference and the effectiveness of the control of pump-induced contrast degradation via pump-seed delay have been confirmed by simulations when the two amplifiers are operated either near or in saturation and with pump ASE modulation only:

These simulations confirm that, in the absence of spectral bandwidth limitation from the cross-correlator, the cross-correlation signals can reveal the delay-dependent contrast effect (simulations not shown). (One delay-independent effect by saturation has also been observed as the broadened pulse pedestal near the main pulse due to the more sharpened edges of the signal spectrum). Although gain saturation reduces pump-induced contrast degradation, even in a system where amplifiers operate at saturation with a pump having a flattop beam profile and flat-in-time pulse shape, both the edges of the pulse and that of the beam experience unsaturated amplification. As a result, the pump-induced contrast degradation can become significant especially when the high-power beam is focused to interact with the target. The results presented in this work have revealed that, in a multi-stage OPCPA, pump-seed delay can serve as a simple and cost-effective tool to minimize the pump-induced contrast degradation even when parametric amplifiers are operated in saturation.

 

Fig. 14. Simulation of (a) cross-correlation (CC) signals and (b) compressed NOPA4b pulses at two different pump-seed delays when both amplifiers operate close to saturation corresponding to the experiment condition. (c) Compressed NOPA4b pulses simulated with the same conditions as (b) except that the pump ASE to laser energy ratio is reduced from ∼10⁻³ to 10⁻⁵. (d) Compressed NOPA4b pulses simulated with the same conditions as (c) except both NOPA4a and NOPA4b operate in complete saturation. In (a), the spectral bandwidth limitation of the cross-correlator is included so that the simulations can be compared to the measurements shown in Fig. 12(b). Note that simulations with only two pump-seed delays are presented for easier visualization of the delay-dependent contrast effect.

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6. Conclusions

Pump-to-signal noise transfer in a two-stage ultra-broadband OPCPA system has been investigated. The pump-induced signal noise has been characterized both before and after pulse compression and quantified by the rf spectrum of the chirped signal pulse and the temporal contrast of the compressed signal pulse, respectively. A new method for in-situ pump-seed delay determination with high precision (i.e., ±2 ps for a 1.6-ns pump pulse) has been demonstrated, based on the strong dependence of rf spectral modulation of the two-stage output on the pump-seed delay. The precise pump-seed delay determination has facilitated the demonstration of up to 15-dB reduction of the pump-induced contrast degradation via pump-seed delay optimization. It will also benefit the fine control of the parametric-fluorescence‒induced contrast degradation. Experiments and simulations have shown that the pump-seed delay can be utilized to minimize the pump-induced contrast degradation, even when parametric amplifiers are operated in saturation. Therefore, these results are widely applicable to support the design and development of any high-power systems that employ two or more stages of OPCPA pumped by a single laser, including the all OPCPA-based systems and the hybrid OPCPA/laser-power-amplifier systems for which maximizing the temporal contrast is a high priority.

Appendix A

In this appendix, the dependence of pump-induced contrast degradation on the signal chirp and pump temporal modulation is described. The impact of pump sinusoidal modulation on the compressed signal pulse contrast in OPCPA has been investigated both analytically and numerically for a signal with linear chirp [10,30]. For completeness and to provide immediate access, a similar analytical treatment following [10,11] is presented to provide semi-quantitative assessment of the impact of pump noise on the compressed signal pulse contrast. The sinusoidally modulated pump intensity can be expressed as:

(1)$${I_{\textrm{pump}}}(t )= I_{\textrm{pump}}^{(0 )}[{1 + \alpha \cos ({{{2\pi t} / T}} )} ]$$

where $I_{\textrm{pump}}^{(\textrm{0} )}$ is the intensity distribution without modulation, α is the peak-to-mean modulation depth, and T is the modulation period. By starting with Eq. (3) in [10], performing Taylor expansion to first order, and following the same treatment therein, one can develop the compressed signal intensity as:

(2)$${I_{\textrm{signal}}}(t )= I_{\textrm{signal}}^{(0 )}(t )+ \frac{{{\alpha ^2}{f^2}}}{{16}}\left[ {I_{\textrm{signal}}^{(0 )}\left( {t - \frac{{2\pi {\varphi_2}}}{T}} \right) + I_{\textrm{signal}}^{(\textrm{0} )}\left( {t + \frac{{2\pi {\varphi_2}}}{T}} \right)} \right]$$

where φ₂ represents the signal GDD. The parameter ${{f = ({{{\Delta {I_{\textrm{signal}}}} / {{I_{\textrm{signal}}}}}} )} / {({{{\Delta {I_{\textrm{pump}}}} / {{I_{\textrm{pump}}}}}} )}}$ has the same definition as ${f_{({1,N} )}}$ in [10] and f_OPA in [11]. This parameter quantifies the noise transfer from pump to signal. It depends on the small-signal-gain and operating regime of the parametric amplifier, where $f \gg 1$ for a high small-signal-gain amplifier operating away from saturation and f = 0 when parametric amplifier is in saturation independent of its gain characteristic.

Equation (2) shows that the compressed signal is composed of the main pulse at t = 0 and two replicas of this main pulse located symmetrically at times ${{ \pm 2\pi {\varphi _2}} / T}.$ (Note that Taylor expansion of Eq. (3) in [10] can be developed to higher order, leading to more replicas of the main pulse located at ${{ \pm N(2\pi {\varphi _2}} / T})$ with $N = 2,3,4\ldots $ representing the order of Taylor expansion.) The normalized intensity of the first-order prepulse is α²f²/16, showing the impact of the pump modulation depth on the compressed pulse contrast. To quantify the contrast degradation from this prepulse, one needs to evaluate f across the pump and chirped-signal pulses due to the intensity variation within both pulses. Instead, one can also estimate f from the energy scan such as the one shown in Fig. 3 (i.e., temporally and spatially integrated intensity) to account for overall contribution. The parameter f, in the case of amplifier operating in saturation, needs to be treated differently from the case of unsaturated amplification. If both pump and signal have constant intensities (i.e., continuous-wave case), f = 0 when the amplifier is in saturation. However, because of the intensity variation within both pump and signal pulses and the nonuniform phase matching across the broadband signal spectrum, a large portion of the chirped-signal pulse experiences unsaturated amplification. Therefore, f ∼ 1 can be assumed when the amplifier energy is saturated [11].

Figure 15(a) plots the simulated compressed NOPA4a pulses obtained from the linear and saturated amplification, with the corresponding pump energies of 45 mJ and 95 mJ. In the simulation, a pump pulse with 30-GHz sinusoidal modulation of 5% peak-to-mean depth and a linear signal chirp of 3.4 ps² is used. The first-order prepulse is located at −0.641 ps, the value predicted by ${{ - 2\pi {\varphi _2}} / T}.$ The normalized peak intensities of this prepulse are −28.5 dB and −39.8 dB in the case of linear and saturated amplification, respectively. The corresponding values predicted by α²f²/16, are −28 dB and −38.1 dB, for f = 3.18 and f = 1, respectively. The value f = 3.18 is obtained from the energy scan from simulation for the linear amplification case. The predicted peak intensities from this simple analytic expression are in good agreement with simulations.

 

Fig. 15. Simulated NOPA4a compressed pulses from either linear or saturated amplification, with different initial conditions. (a) A pump pulse with 30-GHz sinusoidal modulation of 5% peak-to-mean depth and a signal pulse with linear chirp of 3.4 ps²; (b) same initial conditions as used in (a) except that a TOD of –0.004 ps³ is added in the signal chirp; (c) same initial conditions as used in (b) except that additional ASE modulation is included in the pump pulse. An ASE to laser energy ratio of 10⁻³ is used. In (b) and (c), only pulses obtained from the linear amplification are presented.

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Replicas of the main pulse are introduced from pump sinusoidal modulation as pre- and postpulses in the case of linear signal chirp. In practice, the pulse stretcher introduces a nonlinear chirp (nonzero TOD and higher-order terms), which reduces the linearity of the time-to-frequency mapping in the broadband chirped signal. With TOD, the signal spectrum modulation inherited from pump sinusoidal modulation is not a sinusoidal function of the optical frequency, i.e., its period varies continuously across the signal spectrum. Because of the continuous range of frequency modulations, the previously observed side peak, which has the same duration as the main pulse, is temporally stretched after a TOD of –0.004 ps³ is added to the stretcher dispersion [Fig. 15(b)]. ASE on the pump pulse introduces a broad pedestal in the compressed pulse [9–11]. Figure 15(c) shows the simulated NOPA4a pulse when both sinusoidal and ASE modulations are included on the pump pulse.

The duration of the stretched pre-/postpulse is mainly defined by the ratio of TOD to GDD. The smaller TOD used in this case leads to a prepulse [Fig. 15(c)] narrower than the one [Fig. 16(a)] obtained with about the same GDD and twice the TOD (i.e., –0.008 ps³). The TOD sign also plays a role. In the case of negative TOD combined with positive GDD, the modulation frequency is higher at the long-wavelength side, leading to expansion toward a large delay. Similarly, the portion of the stretched pre- or postpulse that is close to the main pulse is contributed by the spectral modulation on the short-wavelength side. As will be discussed in Appendix B, the measured duration of the stretched prepulse can be reduced by the limited spectral bandwidth of THG process in the cross-correlator.

 

Fig. 16. Simulated NOPA4b cross-correlation signals at three pump-seed delays that correspond to the ones presented in Fig. 9(a). Both ASE and sinusoidal modulations are included in the pump pulse. Different properties of the cross-correlator are taken into account in these simulations. (a) The step size of the cross-correlator delay scan is included, and both SHG and THG accept the full spectral bandwidth; (b) the SHG bandwidth is reduced to generate a 100-fs probe pulse, and other conditions from (a) are kept the same; (c) the THG bandwidth is limited to 90 nm using a tenth-order super-Gaussian spectral filter, and other conditions from (b) are kept the same. This is the same plot as presented in Fig. 11(a).

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Appendix B

Besides the discrepancy in contrast magnitude that has been explained in Secs. 5.2 and 5.3, two other major discrepancies have been found between the NOPA4b cross-correlation signals simulated without including the spectral bandwidth limitation of the cross-correlator [Fig. 16(a)] and the measured ones [Fig. 9(a)]. First, the main peak from the measured cross-correlation signal is much broader than the one from simulation. This is due to the limited spectral bandwidth of the SHG process in the cross-correlator, which leads to a broader probe pulse and therefore a broader main peak in the cross-correlation signal. Figure 16(b) shows the simulated cross-correlation signals when the SHG bandwidth is narrowed to generate a 100-fs probe pulse and other conditions are maintained.

The second major difference is that the width of the pre- and postpulse from the measurement is significantly narrower than that from the simulation. This difference can be attributed to the limited spectral bandwidth of the THG process in the cross-correlator. Figure 16(c) presents the simulated cross-correlation signals where the THG bandwidth is limited to 90-nm FWHM using a tenth-order super-Gaussian spectral filter. When the THG spectral bandwidth is reduced further, the simulated pre- or postpulse becomes even narrower and more like the postpulse in the measured cross-correlation signal [Fig. 9(a)]. It is likely that the THG spectral bandwidth decreases as the stage scans to the postpulse range. The reduction of the THG spectral bandwidth could be due to the change of the scanning beam’s pointing, which results in a change in phase-matching condition.

Funding

National Nuclear Security Administration (DE-NA0003856); University of Rochester; New York State Energy Research and Development Authority.

Acknowledgments

The authors thank S.-W. Bahk, I. A. Begishev, and M. Spilatro from the MTW-OPAL team for helpful discussions. This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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