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Abstract
We study and demonstrate the efficient parametric amplification of spectrally incoherent broadband nanosecond pulses to high energies. Signals composed of mutually incoherent monochromatic lines or amplified spontaneous emission are amplified in a sequence of optical parametric amplifiers pumped at 526.5 nm, with the last amplifier set in a collinear geometry. This configuration results in 70% conversion efficiency from the pump to the combined signal and idler, with a combined energy reaching 400 mJ and an optical spectrum extending over 60 nm around 1053 nm. The spatial, spectral, and temporal properties of the amplified waves are investigated. The demonstrated high conversion efficiency, spectral incoherence, and large bandwidth open the way to a new generation of high-energy, solid-state laser drivers that mitigate laser–plasma instabilities and laser-beam imprint via enhanced spectral bandwidth.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction and motivation
Most laser applications require field distributions having a well-defined phase relationship between different temporal or spectral components. Spectral coherence, for example, ensures that, in a chirped-pulse–amplification system, a short, low-energy optical pulse can be temporally stretched before amplification and recompressed at the end of the system [1]. Spectrally incoherent broadband signals with coherence times much shorter than their durations are of great interest, however, in the field of high-energy laser systems. Spectral incoherence can be used in conjunction with spatial incoherence, originating for example from spatial phase modulation or addition of relatively large delays to different parts of the beam, to improve on-target beam uniformity and yield a well-controlled, time-averaged focal spot [2,3]. In this context, nanosecond pulses with short coherence times can be obtained by phase modulation at one or several frequencies, leading to a broadened optical spectrum [4–7], or by carving of spectrally incoherent amplified spontaneous emission [8,9]. The resulting field distributions significantly decrease laser imprint, which seeds Rayleigh − Taylor instabilities [10,11]. Increasing the spectral bandwidth is a path toward reducing laser–plasma instabilities [12–15]. The bandwidth’s effects on the interaction of high-energy laser beams with targets can also be seen in detuning experiments, where relatively narrowband laser beams with different central frequencies can mitigate cross-beam energy transfer [16–18] and control target-implosion symmetry [19,20]. Understanding and mitigating these effects are paramount to efficient laser–energy coupling into the target—for example, for inertial confinement fusion—and require the development of high-energy broadband laser systems capable of generating nanosecond incoherent optical pulses.
Most large-scale, high-energy laser systems are based on amplification in Nd:glass amplifiers operating at around 1053 nm, followed by frequency tripling to 351 nm [21–23]. These are currently the only solid-state systems with sufficient clear aperture to support amplification at the level of 10 kJ in a single beam, but the achievable optical bandwidth is restricted to a few nanometers in the infrared because of gain narrowing. There are other strategies to generate high-energy broadband pulses. Excimer lasers have a broad amplification spectrum in the UV and have been demonstrated at on-target energies of several kilojoules [9]. Stimulated rotational Raman scattering has been used to increase the bandwidth of high-energy laser pulses after amplification, either in the green (second harmonic of a Nd:glass laser) [24] or in the ultraviolet (krypton fluoride laser) [25]. While increasing the bandwidth of the drive pulses is generally seen as a path toward improving the outcome of laser–matter interactions, there is no consensus on the optimal technology. Developing new technical approaches for generating broadband incoherent high-energy pulses, used either directly or in conjunction with other approaches, is therefore very important.
For specific phase-matching conditions, three-wave optical parametric processes are broadband and are used extensively to generate short, coherent, high-energy optical pulses [26–28]. Most applications of optical parametric amplifiers (OPA’s) are based on interactions of spectrally coherent waves, but operation with spectrally incoherent waves has been reported. For example, OPA’s operating with a spectrally incoherent signal have been simulated and demonstrated in the context of polychromatic image amplification and generation of parametric-fluorescence pulses at the microjoule level using femtosecond pump pulses [29,30]. The operation of OPA’s with a spectrally incoherent pump pulse has been described in the context of multiplexing different pump sources [31].
This work is the first demonstration, to the best of our knowledge, of high-energy optical parametric amplification of spectrally incoherent signals, with significant energy transfer from the pump wave to the signal and idler waves. The collinear configuration of the last amplifier, which allows for the amplified signal wave and generated idler wave to be co-propagating, and choice of signal spectrum result in spectrally incoherent distributions with energy reaching 400 mJ and optical spectrum extending over 60 nm, distributed either in a continuous spectral distributions or as a set of discrete monochromatic lines. The spatial coherence of the initial signal is preserved, therefore facilitating subsequent linear propagation and nonlinear frequency conversion. Section 2 presents simulations of the two parametric amplifier stages that support the presented experimental results. Section 3 describes the experimental setup and presents the detailed characterization of the generated waves in terms of energy, spatial properties (near field and far field), and temporal/spectral properties. Section 4 presents general discussions and conclusions pertaining to this work.
2. Theory and simulations
2.1 General considerations
Simulations of the parametric gain in a nonlinear crystal requires propagation of the signal field, idler field, and pump field in the presence of linear and nonlinear effects, for which we follow the approach and notations described by G. Arisholm [32]. The amplifiers we are considering operate with spatially coherent collimated beams having a size larger than a few millimeters; consequently, we ignore the transverse dependence of the fields and related effects such as diffraction and spatial walk-off. We therefore consider the field of the signal, idler, and pump wave as functions of the longitudinal propagation distance z within the crystal and the time variable t, or conversely the optical frequency ω relative to the respective center frequency ωS, ωI, and ωP, with ωP = ωS + ωI. The fields in the time and frequency domain are linked by Fourier transformations, following $A(z,t) = FT{{\kern 1pt} ^{ - 1}}[{\tilde{A}(z,\omega )} ]$ and $\tilde{A}(z,\omega ) = FT[{A(z,t)} ]$.
Linear propagation over a distance z is accounted for by the frequency-dependent phase k(ω)z, where k(ω) = n(ω)ω/c, with n being the refractive index for the crystal axis corresponding to the field’s polarization. For the field $\tilde{A}(z,\omega )$, this corresponds to:
where δk(ω) is the frequency-dependent propagation term relative to the central frequency. This equation can be written using the time-domain representation of the field A(z,t), It is customary to explicitly develop δk in powers of ω, yielding successive derivatives of the temporal field in the right-hand side of Eq. (2), e.g., a first-order and second-order derivative related to the group velocity and second-order dispersion of the crystal. This is, however, not mandatory for numerical resolution, particularly when using a split-step time-frequency technique, which allows for taking into account the dispersion of the medium via Eq. (1).Nonlinear interactions other than the parametric interaction between pump, signal, and idler are neglected: the impact of second-harmonic generation is demonstrated to be negligible later in this section because of phase-matching conditions, while self-phase modulation is negligible considering the propagation at relatively low intensity, ∼1 GW/cm2, in centimeter-long crystals. In these conditions, the only nonlinear driving term that impacts the evolution of one of the fields is proportional to the product of the two other fields (or their complex conjugate) in the time domain. For example, for the signal field, one has
The evolution of the three fields along the longitudinal direction z is obtained by considering the linear [Eqs. (1) and (2)] and nonlinear terms [Eq. (3)], leading to a coupled system of three differential equations that can be written either in the time or frequency domain. Using the time-domain representation, this system is:
For the amplifiers we are describing in this article, the pump is obtained by second-harmonic generation of a laser pulse amplified in Nd:YLF amplifiers operating at 1053 nm and is therefore at 526.5 nm. The signal is at approximately 1053 nm, resulting in an idler at approximately 1053 nm (although for reasons explicated later, the signal and idler are actually at wavelengths slightly lower and slightly higher than that, respectively). Type-I birefringent phase matching is obtained by angular tuning, with the signal and idler waves being ordinary polarized while the pump is polarized along the extraordinary axis of the crystal. It should be noted that collinear operation of an OPA at spectral degeneracy is known to be noncritical with respect to the signal wavelength and angle in a type-I crystal, due to symmetry of the signal and idler waves relative to the pump [34]. Perfectly collinear operation of OPA’s in spectrally degenerate conditions is not practical, however, in many laser applications. For example, in optical parametric chirped-pulse–amplification systems, the signal and idler waves have opposite chirps and therefore cannot be recompressed with the same hardware. Seeding an OPA stage with both the signal and idler waves from a previous stage can lead to a significant reduction in efficiency [35,36]. This reduction is caused by destructive interference of the signal originating from the first crystal with the signal generated in the second crystal, and similar destructive interference of the idler. We therefore consider a sequence of two amplifiers: a preamplifier, composed of 66 mm of lithium triborate (LBO), operated in a slightly noncollinear geometry to allow for idler removal, and a power amplifier, composed of 16.5 mm of LBO, collinearly operated. These parameters are representative of the parametric amplifiers in the OMEGA EP laser and on their prototype, in which this and previous experimental investigations were performed [36–38]. The simulations were typically performed with a step size δz = 1 mm.
2.2 Preamplifier operation
We first show in Fig. 1 the characteristics of the preamplifier when operating with a quasi-monochromatic signal at 1053 nm. When the phase mismatch is zero, which can be ensured by angular tuning, the output signal intensity is a function of the input signal intensity and input pump intensity [Fig. 1(a)]. This intensity map shows that the pump intensity can be set, for a given signal intensity, to reach a maximal amplified signal intensity. The reference input signal intensity Isignal,ref = 0.1 W/cm2 is chosen because it is representative of the typical seed intensity in experiments. For that input seed intensity, the amplified signal intensity reaches a maximum at Ipump,ref = 0.8 GW/cm2, for which the amplified signal intensity is half the pump intensity, 0.4 GW/cm2 [Fig. 1(b)]. Because of energy conservation in the OPA process, the signal intensity is clamped below this maximal signal intensity corresponding to half the pump intensity [Fig. 1(c)]. This operating point is therefore stationary relative to both pump and signal intensity, which decreases the impact of input intensity variations on the amplified output signal intensity in the temporal and spatial domains. This facilitates the generation of a signal with spatially and temporally uniform properties, i.e., a flattop beam profile and flat-in-time instantaneous power. In particular, the amplitude of slowly varying intensity variations in the input signal is significantly decreased in the amplified signal.
Fig. 1. (a) Simulated preamplifier output signal intensity for a monochromatic input signal as a function of the input signal and pump intensities. The open circle indicates the reference operating point at which the output signal intensity is maximized for the reference input signal intensity Isignal,ref. [(b) and (c)] Lineouts of the output signal intensity at the reference operating point as a function of input signal and pump intensity.
The amplification of two types of spectrally incoherent broadband signals is now considered, one with a continuous broadband optical spectrum (tenth-order super-Gaussian shape, 10 nm at half maximum); the other one composed of four monochromatic lines separated by 5 nm and covering the interval from 1030 nm to 1045 nm. These signals correspond to a 300-fs coherence time when estimated simply as 1/Δν = λ2/(cΔλ), where the signal bandwidth is Δν and Δλ in the frequency and wavelength domain, respectively. The amplified spontaneous emission (ASE) field was obtained by allocating random spectral phases to the optical frequencies composing the continuous spectrum, then Fourier transforming the field to the time domain and multiplying by a 2-ns super-Gaussian temporal envelope. Multiplication in the time domain takes into account the temporal pulse carving performed in the front end of high-energy laser systems, typically with Mach–Zehnder modulators, as is done in the experimental demonstration described in Sec. 3. Pulse carving is required because pulses with finite temporal extent, typically less than 10 ns, are used for high-energy laser–matter interaction. Multiplication in the time domain is equivalent to convolution in the frequency domain, which introduces a correlation between frequencies over a range inversely proportional to the duration. Although the resulting field is not strictly speaking spectrally incoherent, the spectral range over which the field’s spectral components are correlated, ∼500 MHz, is extremely small compared to the source’s bandwidth, ∼2.7 THz. The same process was applied to the four lines of the multiline spectrum. The signals at the input of the preamplifier were normalized so that their intensity averaged over a time interval much longer than the coherence time of the incoherent signals is equal to Isignal,ref. All signals are well within the spectral acceptance of the amplifiers, e.g., approximately 100 nm for the preamplifier. The pump pulses in the preamplifier and power amplifier are 2-ns long.
Simulation results are presented for one realization of the ASE signal on Fig. 2. Amplified spontaneous emission arises from thermal light, and the resulting process is expected to be ergodic [39]. The statistical properties of the resulting time-domain field, and in particular its intensity, are therefore expected to be identical when considered at a given time for a large ensemble of realizations or for one realization over a representative time interval much longer than typical temporal variations (e.g., coherence time). Figure 2(a) displays the amplified signal intensity, averaged over 1 ns as a function of the pump intensity. The average intensity of the amplified incoherent signal follows a behavior similar to that of the monochromatic signal, resulting in a maximum output average intensity for a specific pump intensity. The maximal signal intensity and optimal pump intensity are similar to what is obtained for the reference case, with the spectral incoherence leading to an ∼10% efficiency reduction at saturation. Identical amplification behavior was observed for the multiline signal. This shows that a spectrally incoherent signal can be efficiently amplified in this preamplifier. Because the amplified signal energy is a time and space integral of the simulated intensity, similar output energies are predicted for the monochromatic signal and the broadband incoherent signal. The simulations were also run when ignoring temporal walk-off effects, in which case a small additional reduction of the averaged signal intensity is observed. This case does not relate to a physical situation for this particular amplifier, but it highlights the fact that the statistical temporal properties of the signal and temporal walk-off effects are expected to impact the operation of parametric amplifiers with spectrally incoherent signals.
Fig. 2. (a) Temporally averaged signal intensity after the preamplifier as a function of pump intensity for a spectrally incoherent signal (10-nm bandwidth) with and without temporal walk-off (blue and red lines, respectively) and for a monochromatic field (yellow line). (b) Intensity of the amplified fields over a 20-ps temporal range. (c) Probability density function of the intensity normalized to the average intensity for the seed (blue bars) and preamplifier output (red bars), for the spectrally incoherent 10-nm signal in the presence of walk-off.
Close-ups of the time-dependent amplified signal intensity for the monochromatic signal and for the spectrally incoherent signal with and without temporal walk-off are shown in Fig. 2(b). In all cases, the pump intensity was set at 0.8 GW/cm2, which corresponds to the maximization of the amplified signal intensity for the monochromatic field. With temporal walk-off, the amplified signal has large temporal variations, similar to those of the input signal. These variations are clamped to half the pump intensity in the absence of temporal walk-off. In that case, as in the case of a monochromatic signal, there is a one-to-one relation between the signal, idler, and pump intensities at a given time. Because of energy conservation, the output signal intensity close to spectral degeneracy is therefore, at most, half the pump intensity, as observed. In the presence of temporal walk-off, the amplified signal and idler interact with different temporal slices of the pump pulse as the three waves propagate in the nonlinear crystal. The 66-mm LBO crystal has a calculated temporal walk-off of 3 ps between ordinary waves at 1053 nm and the extraordinary wave at 526.5 nm. This is significantly larger than the coherence time of the input signal, i.e., the scale of its temporal variations, resulting in the nonlinear interaction of any short time slice of the signal with many time slices of the pump pulse. This process results in efficient energy transfer from the pump to the signal and idler.
The probability density function of the intensity after amplification is shown in Fig. 2(c). For this particular operation point of the preamplifier, the probability density is broadly distributed between 0 and approximately 3 times the average intensity (∼0.34 GW/cm2), the latter being approximately the mode of the distribution. The probability density function of the initial broadband incoherent seed has been plotted for reference, showing the expected negative-exponential behavior for polarized thermal light [39]. This shows that the amplification process significantly modifies the intensity distribution.
2.3 Power-amplifier operation
The general behavior of the power amplifier is different from that of the preamplifier because of the significant input signal intensity (Fig. 3). For both the spectrally incoherent and quasi-monochromatic cases, the average amplified signal intensity increases approximately linearly with the pump intensity until saturation and reconversion occur [Fig. 3(a)]. The average amplified signal intensity for the spectrally incoherent signal saturates for a slightly higher pump intensity, resulting in an ∼10%-higher average signal intensity. The conversion efficiency (fraction of power-amplifier pump energy that is transferred to the signal) is 35.5% for the monochromatic signal and 34% for the broadband incoherent signal, showing that energy extraction in this amplifier does not depend strongly on the signal’s coherence. Figure 3(b) shows an example of the simulated intensity at a pump intensity of 0.8 GW/cm2, which corresponds to the optimal pump intensity for the spectrally incoherent signal. The incoherent signal intensity varies significantly as a function of time and is not capped by the pump intensity at a given time because the temporal walk-off in the power amplifier (750 fs) is larger than the source’s coherence time. Figure 3(c) displays the probability density function of the amplified intensity normalized to its average value, 0.3 GW/cm2. The power-amplifier output intensity has a broad density function peaked close to its average value, like the preamplifier. Comparison with Fig. 2(c) shows that the distribution is more peaked in the case of the power amplifier, although there are still significant fluctuations leading to intensities at least 3 × higher than the average value.
Fig. 3. (a) Temporally averaged signal intensity after the power amplifier as a function of pump intensity for a spectrally incoherent signal (10-nm bandwidth) (blue line) and for a monochromatic field (yellow line). (b) Intensity of the amplified fields over a 20-ps temporal range. (c) Probability density function of the intensity normalized to the average intensity for the preamplifier seed (blue bars) and power-amplifier output (red bars), for the spectrally incoherent 10-nm signal.
The amplifiers used in this demonstration operate with flat-in-time pump pulses and seeds that are flat-in-time when averaged over time intervals significantly longer than their coherence time. Temporal pulse shaping of the amplified signal, and equivalently idler, can be performed in an OPA by controlling the signal pulse shape and/or the pump pulse shape [38]. While operating an OPA with a shaped seed and a full-intensity pump might not lead to efficient operation, temporal shaping of the amplified signal via pulse shaping of the pump can be an efficient process, as shown by the transfer function of the power amplifier [Fig. 3(a)]. The quasi-linear dependence between the average amplified signal intensity and input pump intensity shows that pump pulse shaping is a potential path toward temporal shaping of the OPAs output into complex pulse shapes with temporal features mostly limited by the temporal resolution of electro-optic pulse shaping systems (<100 ps).
2.4 Additional considerations
The system of Eqs. (4)–(6) in Sec. 2.1 fully takes into account the interaction of the signal and idler waves, but does not contain terms describing the interaction of the signal with itself (proportional to $A_\textrm{S}^\textrm{2}$) and interaction of the idler with itself (proportional to $A_\textrm{I}^\textrm{2}$). If these interactions are phase matched, even for a subset of optical frequencies, the resulting parasitic second-harmonic generation can reduce the overall energy efficiency and modify the amplified spectrum [40,41]. Analysis of the phase-matching conditions for these amplifiers shows that these interactions are not phase matched and therefore do not have a significant impact on the amplification process, which can therefore be simulated by the system of Eqs. (4)–(6).
We consider a 16.5-mm LBO crystal, phase matched for collinear parametric amplification of a signal at 1030 nm with a pump at 526.5 nm in a Type-I configuration. The calculated phase mismatch for parametric amplification, plotted as a function of the signal wavelength in Fig. 4(a), is relatively small. The relative efficiency of the parametric process, in the absence of pump depletion and idler at the crystal input, has been calculated as
Fig. 4. (a) Phase mismatch (left axis) and relative efficiency (right axis) for signal parametric amplification with a pump pulse at 526.5 nm. (b) Phase mismatch (left axis) and relative efficiency (right axis) for sum − frequency generation of a single-frequency signal. (c) Phase-mismatch map for sum–frequency generation of two single-frequency signals. The subset of wavelength combinations leading to zero phase mismatch is shown with a white line and the group of wavelengths corresponding to a signal between 1020 and 1040 nm and the corresponding idler are shown with black squares. The 16.5-mm LBO crystal has been tuned for parametric amplification of a signal at 1030 nm by a pump at 526.5 nm.
3. Experimental results
3.1 Experimental layout
The system layout is shown in Fig. 5. The fiber front end is based on standard polarization-maintaining fiber. A commercial ASE source (BBS-1μm-22-L, MW Technologies) is used as a seed for broadband operation. Four lasers (TLB-6721-P, Newport), tunable between 1030 and 1070 nm, and 2 × 2 combiners are used for multiline operation. A 3-ns flat-in-time pulse was carved using a single LiNbO3 Mach–Zehnder modulator driven by a high-bandwidth arbitrary waveform generator (AWG70001, Tektronix). The pulse was amplified in two Yb-doped fiber amplifiers and then transported by a polarization-maintaining fiber to the launch site. After coarse collimation by a fiber collimator, the size and divergence of the output free-space beam were precisely set by a three-lens zoom. The beam was then steered to two parametric-amplifier stages designed for optical parametric chirped-pulse amplification (OPCPA), originally as a prototype for the OMEGA EP front end [36,37]. The preamplifier is composed of two LBO crystals, set in a spatial walk-off–compensating geometry and totaling 66 mm in thickness. The power amplifier is composed of a single 16.5-mm LBO crystal. All crystals are cut for type-I phase matching, with θ = 90° and φ = 11.8°, and have an antireflection coating at 1053 nm and 526.5 nm on the input and output faces. In the preamplifier, a small noncollinear angle between signal and pump, typically 5 mrad, is used to facilitate idler separation. A similar angle is used in the power-amplifier crystal for OPCPA operation, but the pump and signal were coaligned to support most of the experimental results presented in this article. The input signal and pump are combined with dichroic mirrors. The pump pulse after the preamplifier and power amplifier is removed using dichroic mirrors (not pictured), while the idler pulse after the preamplifier is removed after propagation, owing to the nonzero signal–idler angle in that amplifier. Both stages are pumped with a flat-in-time 2.6-ns pulse at 526.5 nm, obtained from a 5-Hz Nd:YLF laser after frequency conversion [44]. The broadband fiber front end (OPA signal) and the narrowband fiber front end (OPA pump) are synchronized to a laboratory-wide synchronization system, ensuring temporal overlap with precision better than 10 ps. Precise apodization to a square high-order super-Gaussian beam, spatial imaging between the stages, and operation with flat-in-time pulses ensure a high conversion efficiency.
Fig. 5. Experimental layout. The fiber front end generates a flat-in-time broadband pulse by either temporal carving of an ASE source or the combination of up to four discrete spectral lines tunable between 1030 and 1070 nm. A detailed description of the pump laser can be found in Ref. [44]. The first amplification stage is operated in a slightly noncollinear geometry to allow for idler removal in the far field, while the power amplifier was set in a collinear geometry for most of the results presented in this article.
3.2 Front-end characterization
Broadband operation of the front end was characterized by measuring the output energy, optical spectrum, and pulse shape in various conditions. Spectral gain narrowing in the Yb-doped fiber amplifiers modifies the spectral density of the seed source. This is clearly seen in the optical spectra measured after the ASE source and after the fiber amplifiers [Fig. 6(a)]. No attempt was made to decrease spectral gain narrowing in the amplifiers, e.g., by optimizing the design of the fiber amplifiers or shaping the spectral amplitude of the output pulse. The optical spectrum was acceptable for this demonstration, particularly because the system design calls for a signal with spectral density confined below 1053 nm. Examples of temporal properties are shown in Figs. 6(b) and 6(c), with the Mach − Zehnder modulator driven by a linear voltage ramp. This drive signal yields a sinusoidal variation of the optical power. For a single monochromatic laser tuned between 1030 and 1045 nm, it is observed that the output energy depends on the wavelength because of spectral gain variations in the fiber amplifiers. Importantly, the measured temporal shape does not depend significantly on the wavelength and in particular, is similar for the ASE source and for a monochromatic laser. This is important for applications that require an amplified optical pulse with well-defined temporal properties, which is common for target physics with nanosecond pulses. A flat-in-time seed pulse, with 3-ns duration, was used for the remainder of this work.
Fig. 6. Examples of spectral and temporal properties of the front end. (a) The spectral density of the ASE source at its output and after amplification in one and two Yb-doped fiber amplifiers. (b) and (c) The temporal properties of the front-end output pulse when the Mach–Zehnder modulator was driven by a linear voltage ramp for various monochromatic seeds (wavelength at 1030, 1035, 1040 and 1045 nm) and the ASE source.
3.3 Energy characterization
The energy was first measured when only the preamplifier was running [Fig. 7(a)]. The fiber front end was set to deliver either a monochromatic pulse at various wavelengths between 1030 and 1050 nm, a pulse of ASE, or a pulse composed of four monochromatic lines at 1030, 1035, 1040, and 1045 nm. The amplification behavior for all these signals is similar, showing a sharp increase in output energy versus input energy followed by saturation. The spectrally incoherent pulses (ASE and four-line) are amplified similarly and reach saturation for higher pump energy than monochromatic signals at similar wavelengths. This is due to the lower front-end output energy for the spectrally broadband seeds (typically ∼4 × lower). Amplification of a monochromatic signal at 1050 nm, corresponding to similar injected energy than for the broadband seeds, follows the same trend. Amplification at saturation, where the signal energy is maximized, yields similar energies for all configurations, approximately 35 mJ. Note that the conversion efficiency from the pump pulse to the signal pulse is approximately 25%, lower than expected from simulations that do not take into account the transverse spatial domain. This lower efficiency for the preamplifier is consistent with previous observations and could be a result of nonoptimal beam overlap, spatial walk-off in the crystals, angular acceptance, and edge effects for the super-Gaussian pump beam profile, which is not an ideal flattop beam. These processes have more impact in the preamplifier, which is composed of a total of 66 mm of LBO and operates with a 2.5-mm pump beam, than in the power amplifier, which is composed of 16.5 mm of LBO and operates with a 5-mm pump beam.
Fig. 7. Amplified output energy (a) after the preamplifier and [(b) and (c)] after the power amplifier. In (a) and (b), the continuous lines correspond to a monochromatic seed, with wavelength ranging from 1030 nm to 1050 nm; the solid black circles correspond to a spectrally broadband ASE seed; and the solid red squares correspond to a pulse composed of four monochromatic lines at 1030 nm, 1035 nm, 1040 nm, and 1045 nm. In (c) the measured power-amplifier output energy is plotted for the combined signal and idler in collinear and noncollinear geometries (solid blue and red lines, respectively), and for the signal in a noncollinear geometry (solid yellow line). The energy of the combined signal and idler calculated from the signal energy is plotted with solid black circles.
For power-amplifier operation, the preamplifier pump energy was set to reach saturation in each configuration so that the power-amplifier signal input energy is approximately the same. In the collinear geometry, the amplified energy corresponding to the combination of signal and idler waves evolves identically with pump energy in all configurations and reaches approximately 400 mJ for a pump energy of 530 mJ [Fig. 7(b)]. Considering the input signal energy (30 mJ), this corresponds to an extracted energy of 370 mJ going from the power-amplifier pump to the combined signal + idler, i.e., 70%, which is consistent with the previously demonstrated extraction energy for the OPCPA signal [37]. The demonstrated overall gain is higher than 108. The observed rms energy stability is of the order of 1% for all seeding configurations. The results in Fig. 7(c) compare the operation of the power amplifier in collinear and noncollinear operation for the broadband ASE seed. The total energy in the signal and idler was measured by placing a large-aperture energy meter after two dichroic mirrors to capture both beams, even when they were not collinear. The two angular configurations lead to a similar energy evolution. A slight energy decrease is observed at high pump energy for the noncollinear configuration. This might be caused by loss of overlap between the three interacting beams. The signal energy, measured in the noncollinear geometry by spatially blocking the idler beam, was used to calculate the generated idler energy and the total energy around 1053 nm. As can be seen in Fig. 7(c), the calculated energy matches the measured energy very well. This set of results demonstrates efficient operation of the power amplifier without parasitic effects, regardless of the signal–pump collinearity.
3.4 Spectral-domain characterization
The spectral acceptance of the parametric amplifiers can limit the optical spectrum of the amplified output waves. Figure 8(a) displays the spectrum of the parametric fluorescence generated by the sequence of OPA’s in unseeded conditions when pumped at full energy. For this data, there is no signal at the input of the preamplifier, and the parametric fluorescence generated in this amplifier is amplified in the power amplifier. The spectral width of the parametric fluorescence generated in these conditions is approximately 100 nm (consistent with simulations previously presented in Ref. [38]), which ensures that amplification of the front-end signals will not be limited by the spectral acceptance.
Fig. 8. (a) Measured parametric fluorescence at the power-amplifier output in the absence of seed in the preamplifier; (b) input and output spectra of the power amplifier and simulated output spectrum for an ASE signal; (c) measured output spectrum of the power amplifier for a four-line signal.
Because of energy conservation, each pump photon at frequency ωP generates a photon at frequency ωI = ωP–ωS when adding one photon to the signal at frequency ωS. In the absence of spectrally dependent absorption and spectral acceptance limitations in the nonlinear crystals, the idler’s spectrum is therefore expected to be a symmetric version of the signal’s spectrum relative to ωP/2, which corresponds to 1053 nm in this experiment. Figure 8 demonstrates this property for the power amplifier run in a collinear configuration amplifying either an ASE signal or a four-line signal, using a scanning optical spectrum analyzer. In Fig. 8(b), the input and output spectra are shown, with the latter compared to the expected spectrum of the combined signal and idler waves. The expected idler spectrum is calculated by symmetrizing the input signal spectrum relative to ωP and applying spectral correction factors. These factors take into account spectrally dependent loss in the optical path from the power-amplifier crystal to the optical spectrum analyzer and the fact that the idler is generated only in the power amplifier while the signal wave is present at its input. Figure 8(c) shows the power-amplifier output spectrum when the input signal is composed of four monochromatic lines at 1030 nm, 1035 nm, 1040 nm, and 1045 nm, with identification of the four signal lines (below 1053 nm) and the four generated idler lines (above 1053 nm). The frequency of the four generated idler lines is consistent with applying the energy conservation rule to the frequency of the signal lines.
We have studied the spectral stability of the amplified signal using a spectrometer to measure the optical spectrum on each laser shot at 5 Hz. This spectrometer was first used to adjust, in real time and with the two OPA stages operated at full energy, the relative spectral density of the amplified signal. The measured spectrum of the amplified signal was generally quite predictable, e.g., the relative spectral density of a particular line in the output signal was found to increase when the average power of the corresponding monochromatic laser in the fiber front end was increased. This allowed for the generation of an amplified signal with four lines having approximately the same spectral density [Fig. 9(a)]. In the future, the generation of signals having a predetermined optical spectrum will be facilitated by a closed-loop control system directly acting on the relative power of the monochromatic lasers in the fiber front end. A set of 1000 successive spectra was then recorded at 5 Hz, and the spectral density of each signal line was determined for each shot. A subset of the measured relative spectral density over 100 shots, normalized to its average value for each line, shows that the power variations appear to be correlated [Fig. 9(b)]. This is confirmed by Figs. 9(c)–9(h), which show the correlation between the spectral density measured for different lines. A clearly positive correlation is observed, and the determined correlation coefficients between nonidentical lines range from 0.81 (between 1040 and 1045 nm) and 0.40 (between 1030 and 1040 nm). This set of data is somewhat noisy (the rms variation of the different spectral densities is of the order of 5%, much larger than the rms energy variation, which is of the order of 1%). This is attributed to the limited dynamic range of the spectrometer and possible coupling issues into the single-mode fiber feeding the spectrometer, the latter being a possible explanation for the observed positive correlation coefficients since all lines would be identically impacted by coupling issues. The data are, however, useful because they show that the amplified spectrum is stable over several minutes and that there is no strong gain competition between lines.
Fig. 9. Statistical study of amplification of a four-line signal over 1000 shots. (a) Average spectral density of amplified signal; (b) on-shot spectral density at each line plotted over 100 successive shots; [(c)–(h)] correlation plots of spectral density of two different lines.
3.5 Time-domain characterization
The time-resolved waveform of the power-amplifier output has been measured using a single-mode fiber in the beam near field connected to a high-bandwidth photodiode (DSC10, Discovery Semiconductors). The photodiode signal is acquired in a single shot by a 70-GHz real-time oscilloscope (DPO77002SX, Tektronix). The impulse response of this temporal diagnostic (including the photodiode and oscilloscope), characterized using a subpicosecond pulse at 1053 nm, has a duration of the order of 12 ps. Temporal oscillations shorter than that are temporally averaged; therefore the waveforms do not represent the behavior of the actual instantaneous power but are useful for assessing the impact of power variations on physical processes with response times longer than 10 ps.
The properties of the parametric amplifiers are first highlighted in Fig. 10 with a signal composed of two discrete spectral lines originating from two uncorrelated monochromatic lasers in the fiber front end. The optical frequency difference between the two lasers was set to δν = 11.3 GHz, so that the resulting interference beating and its first few harmonics were well within the photodetection frequency response. The resulting instantaneous power, measured in a single shot, oscillates with a period equal to 88.5 ps, which is much longer than the temporal walk-off in the parametric amplifiers. In the absence of saturation, i.e., at relatively low pump energies, the signal is not distorted and maintains its sinusoidal oscillation, resulting in a Fourier spectrum that is mostly composed of a single sideband at δν [Figs. 10(a) and 10(d)]. At higher pump energy [Figs. 10(b) and 10(e)], depletion of the pump occurs, but the amplified signal and idler intensities are limited by the pump intensity available in a particular time slice because the temporal walk-off is much smaller than the power-oscillation period. This results in saturation of the achievable signal intensity, i.e., the amplified intensity reaches a maximum at which a quadratic behavior of the amplified intensity relative to the input signal intensity is obtained. This leads to a reduction of power in the fundamental sideband at δν and an increase of power in the harmonic sideband at 2δν, as is clearly seen in Fig. 10(e). When the preamplifier is run at this pump-energy setting, operation of the power amplifier at full pump energy leads to a further reduction of the modulations observed on the amplified waveform [Figs. 10(c) and 10(f)]. The initial seed is composed of only two monochromatic lines (with similar, but not identical amplitude), and such signal yields a sinusoidal temporal modulation. It was found via simulation that parametric amplification of such signal at saturation, which significantly decreases the modulation amplitude, is accompanied by changes in the spectral domain, in particular, modification of the relative spectral density of the two lines and generation of new discrete lines at a spacing δν from the original lines.
Fig. 10. Measured temporal waveform (first row) and calculated rf power (second row) with [(a),(d)] preamplifier pumped at 125 mJ, [(b),(e)] preamplifier pumped at 145 mJ, and [(c),(f)] with preamplifier pumped at 145 mJ and power amplifier pumped at 500 mJ. The red dashed line corresponds to δν = 11.3 GHz.
Figure 11(a) displays waveforms measured after the power amplifier when the signal is composed of two monochromatic lines separated by a frequency much larger than the photodetection frequency range, namely 330 GHz. As expected, the resulting temporal oscillations are not resolved. The measured waveforms are also free of any low-frequency oscillations when operating with the ASE seed [Figs. 11(b) and 11(c)]. Although the realization of the ASE field is different for each laser shot, the measured output waveform is very stable. This is attributed to the fact that the coherence time of the seed source is significantly shorter than the photodetection response time, therefore effectively leading to a stable low-frequency output.
Fig. 11. Waveforms measured after the power amplifier for (a) a signal composed of two monochromatic lines separated by 330 GHz and [(b),(c)] a signal composed of an ASE pulse. (a) and (b) represent the waveforms measured on a single laser shot, while (c) corresponds to waveform measurements over 100 successive ASE pulses.
3.6 Near-field characterization
Representative near fields of the amplified beam are shown in Fig. 12 for amplification of a monochromatic signal at 1030 nm and incoherent signals. Figure 12(a) displays the near field of a 1030-nm signal when the power amplifier is set in a noncollinear geometry. The square shape of the amplified beam is due to apodization of the pump beam to a high-order super-Gaussian profile. Although the signal beam is Gaussian at the input of the preamplifier, strong saturation leads, in principle, to a flattop amplified beam. Spatial modulations of the amplified beams result from modulations of the pump beam on this particular laser system, but better control of the pump near field will lead to a more-uniform fluence profile. The amplified beams when the power amplifier is set in a collinear geometry are shown in Figs. 12(b) and 12(c) for the spectrally incoherent signals (note that the measured fluence corresponds to the sum of the signal and idler waves).
Fig. 12. Beam near field after amplification in the power amplifier. (a) Noncollinear operation with a signal at 1030 nm; (b)–(f) Collinear operation. [(b),(c)] The signal is a broadband ASE pulse and a multiline pulse, respectively. [(d)–(f)] Collinear operation with a signal at 1030 nm for (d) the signal and idler beams, (e) the signal beam, and (f) the idler beam.
This mode of operation yields an amplified beam with similar properties. The figures on the second row of Fig. 12 confirm that the signal and idler have similar spatial properties in the near field. Operation of the power amplifier with a 1030-nm monochromatic signal yields an amplified signal and idler at 1030 nm and 1077 nm, respectively. The near field of the combined signal and idler is shown in Fig. 12(d). Dielectric spectral filters were then used in front of the camera to provide independent measurements of the signal and idler beams [Figs. 12(e) and 12(f), respectively]. This data set confirms that the signal and idler beams of the collinear power amplifier have similar properties in the near field, as expected from energy conservation.
3.7 Far-field characterization
The far field of the amplified signal when the OPA’s are run with a monochromatic seed and with a broadband ASE seed are shown in Figs. 13(a) and 13(b). For this data set, the power amplifier is run in a noncollinear geometry. In both cases, the amplified signal is spatially coherent and close to diffraction limited, and the far field does not depend on the spectral coherence because the seed originates from a single-mode fiber and the parametric amplification process does not modify the signal’s phase. These far fields can be compared to the far field of the spectrally and spatially incoherent field that is generated by the OPA’s running in unseeded conditions [Figs. 13(c) and 13(d)]. Without an input seed, the sequence of OPA’s generates spatially and spectrally incoherent parametric fluorescence, with properties that depend on the phase-matching conditions in the nonlinear crystals. In particular, the range of output wave vectors is much larger than in seeded conditions with a spatially coherent field, resulting in the typical arc pattern centered on the pump beam, as can be seen in Fig. 13(d).
Fig. 13. Far fields measured after the power amplifier set in a noncollinear geometry. Seeded conditions with a signal composed of (a) broadband ASE and (b) a monochromatic signal at 1053 nm; [(c),(d)] The entire sequence of OPA’s running at full pump energy without a seed in the preamplifier. The plots in (a)–(c) correspond to the same field of view, while the plot in (d) corresponds to a field of view 4 × larger.
The far fields of the signal, pump, and idler when the power amplifier is operated in a collinear geometry are shown in Fig. 14. For this data set, the seed was a monochromatic signal at 1030 nm, leading to an idler at 1077 nm, in order to allow independent observation of the resulting far fields using two dielectric spectral filters. The pump’s far field was observed on the same camera after blocking the input signal. The signal’s far field [Fig. 14(a)] is, as expected, similar to that shown in Fig. 13(a). The idler’s far field is different, showing significant elongation in the horizontal direction [Fig. 14(b)]. This is explained by the wavefront of the idler beam, which is related to the wavefront of the pump beam. The far field of the pump beam, shown in Fig. 14(c), is extended similarly to the idler’s far field, but with a 2 × reduction in scale. In an OPA that has a signal wave and pump wave at its input, but no idler wave, the phase of the generated idler wave is φI = φP–φS+π/2, following Eq. (5). Considering a signal that is close to diffraction limited (flat spatial phase), the wavefront of the idler beam is therefore dominated by the wavefront of the pump beam. In terms of far-field angle θ (the unit chosen for the plots on Figs. 13 and 14), one has θx = (λ/2π) (∂φ/∂x), which explains that the idler far field is approximately twice as extended as the pump far field close to spectral degeneracy. This observation is consistent with the phase-matching condition, which imposes that the relative angle between signal and idler is twice the angle between signal and pump for phase matching at (or close to) degeneracy. The amplified signal and idler waves therefore have different spatial phases (including a piston term that is related to the pump’s phase, and is, in this particular system, different for every laser shot). The impact of the pump’s wavefront in the last OPA therefore extends beyond that amplifier. For example, it can lead to reduced efficiency in subsequent nonlinear interactions such as frequency conversion because of limited angular acceptance, or nonoptimal on-target focal spot, although the latter effect will be significantly alleviated when using devices such as phase plates to decrease spatial coherence [2]. These effects and the extent to which the resulting signal and idler waves can both be used are highly dependent on the application and are therefore not discussed further in this article.
Fig. 14. Far fields measured after the power amplifier set in a noncollinear geometry for the (a) signal, (b) idler, and (c) pump.
4. General discussions and conclusions
We have studied and demonstrated the high-energy amplification of spectrally incoherent signals in a sequence of two optical parametric amplifiers. Simulations and experiments show efficient energy transfer from the monochromatic pump pulse at 526.5 nm to various spatially coherent signal and idler waves around 1053 nm, despite their highly modulated instantaneous power resulting from spectral incoherence. Various nanosecond incoherent signal pulses with optical spectrum extending over more than 10-nm (∼300-fs coherence time) are amplified to 200 mJ. Simulations demonstrate that the temporal walk-off between the pump at 526.5 nm and the signal/idler around 1053 nm plays a significant role in the OPA operation, resulting in the experimentally validated observation that signals with short coherence times can be amplified with an efficiency similar to that for monochromatic signals. The collinear interaction geometry, where pump, signal, and idler are collinear in the last parametric amplifier, has been investigated as a means to significantly increase the output energy and bandwidth in the infrared when both signal and idler waves are combined. This resulted in the generation of a 400-mJ optical pulse with spectrally incoherent spectrum extending over 60 nm.
These simulations and experiments demonstrate the concept of a high-energy, solid-state spectrally incoherent laser driver based on nonlinear parametric amplification with frequency-doubled lasers based on Neodymium-doped materials. This approach builds on the technological maturity and the existence of multiple high-energy laser facilities based on Nd:glass. High-energy OPA operation can be supported by large-aperture nonlinear crystals (KDP and partially deuterated KDP) originally developed for doubling and tripling of ignition-scale laser systems [45]. The high-frequency temporal modulations observed on simulated signals and those resulting from the interference of the signal and idler wave in the last OPA depend on the parameters of the OPA stages and interacting waves; consequently, these parameters will require optimization to reduce the modulation amplitude and decrease the probability of damage. When the temporal walk-off is small compared to the coherence time, the output signal intensity is clamped to a fraction of the pump intensity, therefore providing a potential strategy for decreasing fluctuations on the signal intensity. Although there is extensive knowledge of laser-induced damage of optical components for coherent pulses with duration either in the nanosecond regime or in the subpicosecond regime, there are no available data for spectrally incoherent nanosecond pulses with subpicosecond coherence time, and dedicated studies will be required. Because laser–target interaction in the context of ignition improves at lower wavelengths, frequency-conversion schemes of the OPA output will most likely need to be implemented. Frequency doubling from 1053 nm to 526.5 nm is broadband in partially deuterated KDP with low deuteration levels around 12% [46]. Reaching the UV, e.g., 351 nm, requires nonlinear mixing of the OPA output either with its own second harmonic or with another source, which will require broadband phase matching implemented, for example, via angular dispersion and/or a noncollinear geometry, as is used for frequency tripling and parametric amplification [26,47].
Funding
National Nuclear Security Administration (DE-NA0003856); New York State Energy Research and Development Authority.
Acknowledgments
The authors thank J. Bromage, R. K. Follett, D. H. Froula, and J. P. Palastro for fruitful technical discussions and I. A. Begishev for technical assistance. The support of DOE does not constitute an endorsement by DOE of the views expressed in this article. 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.
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