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Abstract
A compact, femtosecond-pumped noncollinear optical parametric amplifier (NOPA) is presented with a passive spectral shaping technique, employed to produce a flat-top-like ultrabroadband output spectrum. The NOPA is pumped by a dedicated 2 mJ, 120 fs Yb3+-based CPA system, which generates both the second harmonic pump pulse and white light supercontinuum as the signal pulse. A chirped mirror pair pre-compensates the material GVD within the optical path of the signal pulse to produce a near-FTL pulse duration at the OPA crystal output. By optimizing both the pump/signal cross angle and the pump/signal delay, the 40 cm × 40 cm footprint, single-pass, fs-pumped, direct NOPA (non-NOPCPA) system generates a record 20 µJ, 11 fs pulses at 820 nm central wavelength with a bandwidth of 230 nm FWHM, to be used as an ultrashort optical probe pulse for relativistic laser-plasma interactions at the petawatt-class POLARIS laser system.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Noncollinear optical parametric amplification (NOPA) is an effective and demonstrated method for generating high peak and average power laser pulses [1], offering amplification for an ultrabroadband spectrum with a gain exceeding 10$^4$ [2] in millimeter-thin nonlinear crystals. Within the first NOPA pass alone, the µJ-level output energy also enables the application of this nonlinear amplification technique to produce few-cycle optical probe pulses within a compact configuration. Such ultrashort probing systems are valuable tools [3,4] in experiments involving the interaction of high peak power lasers – such as the petawatt-class POLARIS [5] laser at the Friedrich Schiller University and Helmholtz Institute in Jena, Germany – with extreme states of matter (e.g., relativistic laser-plasma interactions), where direct access to the complex, spatio-temporal dynamics is often required to both verify numerical simulations and optimize the laser and target parameters for a further improvement of the experimental yield.
To be successfully applied in relativistic laser-plasma experiments, an NOPA-based probing system must be capable of simultaneously fulfilling the following design criteria. First, the beam diameter must be sufficiently large to illuminate the interaction region with an on-target pulse energy high enough to ensure a measurable signal ($E\geq\!10\,$µJ) on the post-interaction diagnostic setup. To prevent deformation of the experimental target due to ionization, the probe pulse intensity must remain well below 10$^{12}\,$W/cm$^2$. Furthermore, the probe pulse should exhibit an ultrabroadband spectrum ($\Delta \lambda \,>150$ nm FWHM) to enable a few-cycle pulse duration, critical for resolving the ultrafast sub-main pulse temporal dynamics of the interaction involving, e.g., the 98 fs POLARIS [5] pulse with the laser-induced plasma. Additionally, the spectrum should lie between or outside the fundamental (with $\lambda _{\mathrm {L}} = 1030\,$nm) and harmonic wavelengths of the high peak power laser, due to strong plasma scattering and reflection [4,6] within these regions. Finally, the spectrum should be homogenized to prevent the suppression of low energy spectral components below the noise level due to plasma losses, which would otherwise obscure the critical information imprinted within these optical frequencies in spectrally resolved probing schemes [7,8]. Here, a chirped version of the ultrabroadband, spectrally homogeneous probe pulse can be utilized to measure the spatio-temporal evolution of the interaction in a single shot. In the event that further amplification stages are required for high peak power applications, a homogeneous NOPA spectrum for the first pass could also remove the need for gain narrowing compensation within the laser chain. Due to the robust nature of the NOPA process [9], the aforementioned requirements can be readily achieved within a compact, portable setup and installed directly in the target laboratory.
The work within this paper details the development of the ultrashort optical probing system with an emphasis on the optimization of the ultrabroadband NOPA. A dedicated Yb$^{3+}$-based CPA system delivers 2 mJ, 120 fs pulses to pump the NOPA stage. The pre-amplification spectral shaping steps and additional stretcher-compressor that are often required for NOPA systems could be completely replaced by a precise control of the temporal dynamics of the nonlinear amplification process itself, with a record output energy for the first pass of the fs-pumped direct NOPA (non-NOPCPA).
2. Yb$^{3+}$-based, mJ-class ultrashort pump laser for NOPA
To generate the moderate pump intensities ($\approx$ 100 GW/cm$^2$ [2]) necessary for the NOPA process, a Yb$^{3+}$-based CPA system (schematic in Fig. 1) was realized and installed within the POLARIS target laboratory. To reduce the temporal jitter between the POLARIS and probe pulses, the CPA system is seeded by the POLARIS oscillator (MIRA 900, Coherent), in which Kerr-lens mode-locking is employed in Ti:Sapphire to deliver a 75 MHz pulse train of 5 nJ, 85 fs pulses. Birefringent filters are utilized within the cavity to select the spectral region centered at 1030 nm with a 20 nm FWHM bandwidth for the POLARIS laser system. The pulses are then stretched to 20 ps in an Offner-type stretcher [10], comprising a gold grating (1200 lines/mm), a spherical mirror telescope with $f$ = 300 mm and $f$ = -150 mm, and a roof mirror that enables a double-pass through the system. A single stretched pulse is then picked out of the 75 MHz pulse train with a Pockels cell and polarizer and directed through multiple laboratories into a regenerative amplifier in the target laboratory. Here, an automated beam-steering system monitors and corrects seed beam pointing fluctuations generated by air pressure and temperature changes along the beamline.
Fig. 1. Schematic of the ultrashort pump laser system for the NOPA. A seed pulse from the POLARIS oscillator is stretched and amplified with a total gain of 10$^6$ in a Yb:FP15-glass regenerative amplifier. The pulse is then compressed and sent to the upper stage of the two-level system to pump the NOPA.
The p-polarized, 20 ps seed pulse passes through a thin film polarizer (TFP: transmits p-pol., reflects s-pol.), which acts as the input coupler for the regenerative amplifier. The pulse is amplified to 3 mJ in 60 round-trips, each with a double-pass through the diode-pumped active material (Yb:FP15-glass [11]). The amplified pulse then exits the optical cavity through the second TFP and is magnified by a $4\times$ Galilean telescope before compression using a gold grating pair (1200 lines/mm) in a double-pass configuration. The 8.5 cm grating separation compensates for $-5.7\times 10^{5}$ fs$^2$ GDD and $1.5\times 10^{6}$ fs$^3$ TOD, shortening the duration of the amplified chirped pulse from 15 ps – reduced from 20 ps via gain narrowing – to nearly 120 fs. The results are displayed in Fig. 2, with a 1.3 mm 1/$e^2$ diameter Gaussian-like spatial profile at the amplifier output, a spectral bandwidth of 15 nm FWHM, and the compressed pulse duration measurement using a single-shot second order autocorrelator (TOPAG GmbH). The dedicated Yb$^{3+}$-based CPA system delivers 2 mJ, 120 fs pulses with an output intensity of 150 GW/cm$^2$ to generate both the signal and pump pulses for the NOPA.
Fig. 2. Output results of the Yb$^{3+}$-based CPA system, with the amplified beam profile (left, 1.3 mm $1/e^2$ diameter), spectrum (center, 14.7 nm FWHM bandwidth), and compressed temporal profile (right, 121.6 fs FWHM pulse duration) with an image of the single-shot second order autocorrelation measurement in the top left corner.
3. Noncollinear optical parametric amplifier optimization
The mJ-class ultrashort pump pulse enters the NOPA setup via a periscope, which connects the lower (CPA) and upper (NOPA) stages of the compact two-level system. As seen in Fig. 3, a beamsplitter then selects a small fraction of the pulse energy (0.1% – 2 µJ) to generate stable white light supercontinuum (WLC) pulses [12] for seeding the NOPA. Here, the 2 µJ pulse transmitted from the beamsplitter is focused using an $f$ = 50 mm lens ($L$ in Fig. 3) into a 5 mm YAG crystal with a peak power of 6 MW, directly between the two unstable regimes of the white light filamentation process [13], with the first self-focusing event at 4 MW and the subsequent refocusing at 8 MW. The WLC pulse stabilization [14,15] was accomplished with an adjustable iris (AI) and variable neutral density filter (VND) for numerical aperture (NA = 0.02) and input energy (720 nJ) fine-tuning, respectively.
Fig. 3. Schematic of the multi-beam ultrashort optical probing system. The compact setup delivers two mJ-class fundamental (shown in red) and SH (green) pulses along with a few-cycle NOPA (white) pulse, through which ultrabroadband spectral shaping is achieved by a precise control of the temporal dynamics within the nonlinear amplification process. The NOPA phase-matching diagram is given in the bottom center of the figure.
The spectral boundaries of the WLC pulse between the POLARIS fundamental and second harmonic wavelengths were controlled with a combination of a high-pass frequency filter (950 nm cutoff) and the phase-matching process itself within the OPA. For the initial alignment of the WLC beam path as well as for ultrashort temporal synchronization with the POLARIS pulse, the magnetic-mounted YAG crystal along with the spectral filter can be easily removed to allow the higher power pump pulse through the NOPA setup. After collimation using an F/2 90$^{\circ }$ off-axis parabola mounted on a 5-axis stage, the stable WLC pulse, with spatial (2.2 mm $1/e^2$ diameter) and spectral ($\lambda _{\mathrm {L}}$ = 807 nm, $\Delta \lambda$ = 287 nm – the spectrum fills the spectral window of the Ocean Optics Flame-S spectrometer) profiles given in Fig. 4, is directed into a nonlinear crystal for OPA.
Fig. 4. Output spectral (left, $\lambda _{\mathrm {L}}$ = 807 nm, $\Delta \lambda$ = 287 nm measurable within the spectral window of the Ocean Optics Flame-S spectrometer) and spatial (right, 2.2 mm $1/e^2$ diameter) profiles of the collimated stable white light supercontinuum pulse. The spectral range between 700 nm and 950 nm was selected – using both a high-pass filter and the phase-matching process itself – as the NOPA signal.
To enable a high gain over the ultrabroadband spectrum of the WLC pulse, the phase-matching condition [2,16] for the NOPA process must be fulfilled by selecting the appropriate pump wavelength and pump/signal cross angle $\alpha$ within the nonlinear crystal. Here, the nearly 2 mJ, 120 fs pulse reflected by the beamsplitter is converted to the second harmonic (SH, $\lambda _{\mathrm {L}} = 515\,$nm) in a 3 mm KDP crystal (type I SHG, phase-matching angles $\theta _{\mathrm {PM}}$ = 41.2$^{\circ }$, $\phi _{\mathrm {PM}}$ = 45$^{\circ }$) with a conversion efficiency of 65%, matching the predicted results using a dedicated simulation of the SHG process. The final required pump intensity for the NOPA of 200 GW/cm$^2$ was then set with a telescope and by fine-tuning the output SH pulse energy to 1 mJ. The mJ-class, ultrashort pump pulse post-NOPA along with the remaining unconverted fundamental pulse exit the optical probing setup and could, e.g., be employed as dedicated pulses for a controlled excitation of plasma targets in laser-plasma experiments at POLARIS.
Differences in the optical paths between the SH (pump) and WLC (signal) pulses are corrected using a motorized delay stage, such that the two pulses are temporally aligned within a BBO crystal to activate the OPA process. BBO was selected due to its large effective nonlinearity ($d_{\mathrm {eff}}$ = 2.08 pm/V [17]) and capability of broadband phase-matching at a low noncollinear angle. The effect of the large spatial pump/signal walk-off [18] in BBO crystals on the OPA gain can be compensated by using collimated pump and signal beams at a low pump/signal cross angle within a thin crystal. The 2 mm BBO crystal was cut for type I phase-matching ($\theta _{\mathrm {PM}}$ = 24.5$^{\circ }$, $\phi _{\mathrm {PM}}$ = 90$^{\circ }$) and oriented in the tangential phase-matching configuration [19] to prevent parasitic second harmonic generation within the spectral range of the NOPA.
The internal pump/signal cross angle $\alpha _{\mathrm {int}}$ for the NOPA was numerically calculated for the desired spectral regime ($700\,$nm$\,-\,950$ nm) of the WLC pulse. The resulting spectral gain profiles for various $\alpha _{\mathrm {int}}$ configurations are given in Fig. 5, with a value of 2.55$^{\circ }$ producing an ultrabroadband flat-top-like gain profile. Here, however, the amplified spectral profile would be nevertheless inhomogeneous, due to the form of the WLC spectrum in Fig. 4. A flat-top-like output spectrum for the NOPA pulse is critical for spectrally resolved probing of relativistic laser-plasma interactions, where each frequency component carries relevant details [3] of the spatio-temporal dynamics of the interaction. For an inhomogeneous spectrum, the low energy components can be strongly suppressed below a measurable level due to the large losses within the plasma and diagnostic setup, thereby removing access to the desired information.
Fig. 5. Various internal pump/signal cross angle $\alpha _{\mathrm {int}}$ configurations with lineouts of the gain spectra for the ultrabroadband NOPA. A flat-top-like gain spectrum is achievable for $\alpha _{\mathrm {int}}$ = 2.55$^{\circ }$ with slight spectral tuning within $\pm \,0.05^{\circ }$.
In NOPA systems, spectral shaping is accomplished by introducing spectrally dependent losses to the seed, which would, for the case of the WLC pulse, lead to a reduction in the pulse energy by nearly a factor of two. By controlling the temporal dynamics of the NOPA process, however, this inefficient step could be completely bypassed, enabling ultrabroadband spectral shaping with a high output energy. Here, a simulation was constructed to determine the optimum parameters to homogenize the amplified WLC spectrum by solving the coupled wave equations for NOPA:
Due to the ultrashort nature of the fs-NOPA setup and the different group velocities of the pulses ($v_{\mathrm {s}}>v_{\mathrm {p}}$) within the 2 mm BBO crystal, the temporal drift $\tau _{\mathrm {p,s}} = L \cdot \left (v_{\mathrm {g,p}}^{-1} - v_{\mathrm {g,s}}^{-1}\right ) = 100\,$fs between the signal and pump pulses can significantly impact the OPA gain. Using the motorized delay stage (10 µm = 33 fs delay per full step) for the optical path of the SH pulse, however, a pump/signal delay $\tau _{\mathrm {delay}}$ can be introduced to ensure a maximum temporal overlap throughout the crystal length $L$. First, the centers of the signal and pump pulses at the start of the BBO crystal are temporally aligned at the time $t_{\mathrm {c}} = t_0 + \frac {1}{2} \cdot \left (\tau _{\mathrm {p}} + \tau _{\mathrm {s}} \right )$, with the location $t_0$ representing the beginning of the OPA process, where the leading edge of the pump pulse (pulse duration $\tau _{\mathrm {p}}$) coincides with the trailing edge of the signal pulse (pulse duration $\tau _{\mathrm {s}}$). The optimized starting location of the pump pulse with respect to the signal pulse of $\tau _{\mathrm {opt}} = \tau _{\mathrm {c}} + \tau _{\mathrm {p,s}} = 200\,$fs can then be set by the precision delay stage, allowing for a maximum overlap between the two pulses and a preservation of the high gain even at the end of the OPA process, where the largest energy transfer from the pump pulse to the signal pulse occurs.
The temporal alignment of the pump and signal pulses during optical parametric amplification additionally enables a powerful method for ultrabroadband spectral shaping. Due to the GDD compensation via the chirped mirror pair, the WLC pulse at the entrance of the BBO crystal is negatively chirped (pulse duration $\tau _{\mathrm {s}}$ $\approx$100 fs), with the higher frequencies leading the pulse. By temporally delaying the pump pulse slightly before or after the chirped WLC pulse around the gain-optimized location $\tau _{\mathrm {opt}}$, the NOPA spectrum can be tilted to favor certain frequencies. To improve the homogeneity of the amplified WLC spectrum, this technique must be employed simultaneously with the pump/signal cross angle $\alpha$ optimization (various configurations given in Fig. 5). The potential of this ultrabroadband spectral shaping technique is revealed with the results of both the numerical simulation and the measured NOPA spectrum in Fig. 6. By setting the pump/signal delay to $\tau _{\mathrm {opt}}$, a red-shifted NOPA spectrum is produced for the $\alpha _{\mathrm {int}} = 2.65^{\circ }$ given in Fig. 5, confirming the results of the numerical simulation. The compensating blue-shift is then accomplished by adjusting the pump/signal delay to $\tau _{\mathrm {opt}} + 33\,$fs to transform the initially inhomogeneous WLC spectrum into the desired flat-top-like output profile.
Fig. 6. Simulated (left) and experimental (right) confirmation of ultrabroadband spectral shaping for fs-pumped NOPAs. To homogenize the WLC spectrum, a red-shift was induced by setting the pump/signal cross angle $\alpha _{\mathrm {int}}$ to 2.65$^{\circ }$ along with the corresponding blue-shift through a tuning of the pump/signal delay to $\tau _{\mathrm {delay}} = \tau _{\mathrm {opt}} + 33$ fs.
As shown in Fig. 7, the ultrabroadband NOPA pulse ($\lambda _{\mathrm {L}}$ = 820 nm, $\Delta \lambda _{\mathrm {L}}$ = 230 nm FWHM) exits the 2 mm BBO crystal with a nearly Fourier transform limited pulse duration of 11 fs, measured using self-referenced spectral interferometry [21] (WIZZLER, Fastlite), due to the GDD pre-compensation from the chirped mirror pair. The compact, enclosed system operates with a spectral bandwidth fluctuation of less than 1% RMS. The employed passive ultrabroadband spectral shaping technique is capable of controlling the form of the spectral profile while maintaining a high NOPA gain, and the 20 µJ output pulse energy is, to the best of our knowledge, the highest reported for a single-pass broadband fs-pumped direct NOPA – prominent results from other NOPA systems include, e.g., 5 µJ after a double-pass direct NOPA [22], 5 µJ after the first pass of a direct NOPA [23], and 12 µJ after the first pass of an NOPCPA [24].
Fig. 7. NOPA output spatial (top left, 1.8 mm $1/e^2$ diameter), spectral (top center, 230 nm FWHM bandwidth centered at 820 nm), and temporal (top right, 11 fs FWHM pulse duration) profiles at the BBO crystal output. The spectral bandwidth fluctuation was measured to be 0.46% RMS over 1800 consecutive pulses. Spectral pre-shaping of the seed and additional spectral phase control was not required to achieve a flat-top-like ultrabroadband spectrum with a near-FTL pulse duration.
In the presented setup, the use of collimated, mm-size pump and signal beams as well as only a slight detuning of approximately 0.1$^{\circ }$ from the magic angle for spectral shaping were specifically implemented to mitigate the impact of spatio-temporal couplings [25,26] – including spatial chirp, angular dispersion, and pulse-front tilt – in good agreement with the guidelines [27] produced by the work of Giree et al. Furthermore, the pump/signal beam separation of 0.15 mm after the 2 mm thick BBO crystal was compensated by the large pump beam size, thereby maintaining the high quality amplified spatial profile of the 1.8 mm $1/e^2$ diameter NOPA beam, even with the tangential phase matching orientation [19].
The compact NOPA system produces µJ-level, few-cycle pulses with a flat-top-like spectrum that are ideal for probing applications or as a front-end for multi-stage NOPCPAs [24,28]. A direct energy scaling of the presented setup is possible as well, albeit with several limitations. Achieving pulse energies near the 100 µJ-level would require a second stage and a beam size magnification, through which additional spatial chirp and pulse-front tilt compensation methods [26] would have to be employed. A further scaling towards the mJ-level would then require a stretcher-compressor setup with mJ-class, picosecond pump pulses. For this purpose, the seed pulse for the utilized Yb:FP15-based mJ-class pump laser can be further stretched and the amplified beam radius increased to allow for higher output energies after compression. The pulse can then be separated into multiple low and high energy pulses, each for a dedicated NOPA stage.
For the first pass, the 120 fs pump pulse duration offered by the Yb:FP-glass CPA system is critical for a precise control of the temporal NOPA dynamics to achieve passive ultrabroadband spectral shaping without significantly impacting the overall gain. The previously described combination between the slight pre-chirp of the signal pulse and the pump/signal delay strongly shapes the spectrum during the beginning stages of the NOPA process, where only a minimal energy transfer occurs. Afterwards, the spectral shaping is dominated by the pump/signal cross angle setting and, as the dispersion within the BBO crystal corrects for the signal pre-chirp, the signal remains temporally aligned within the pump pulse even at the end of the crystal. Thus, the high NOPA gain – as evident by the experimentally verified 20 µJ output energy – is preserved. Once spectral shaping has been accomplished, subsequent amplification stages can employ higher energy, temporally stretched versions of the pump pulse for, e.g., DC-NOPA schemes [29]. Although the bandwidth of the frequency-doubled pump pulse is negligible in comparison to the signal pulse, the implications of a chirped pump pulse on the total phase-mismatch must be taken into consideration to ensure an ultrabroadband amplification.
While a stabilization of the carrier envelope phase (CEP) was not required for the intended experiments involving the described optical probing system, this could be adapted for phase-sensitive applications by employing, e.g., the fundamental leakage pulse from the SHG (KDP) crystal in Fig. 3 to pump an IR OPA. The resulting CEP-stable idler [30] can then be selected as the seed for the WLC setup. The overall repetition rate of the NOPA was set via the Yb$^{3+}$-based CPA system to 1 Hz, which is largely sufficient for the probing of laser-plasma interactions at the POLARIS laser system operating at 0.02 Hz, as well as for further rep-rated high peak power laser systems.
4. Conclusion
In conclusion, a compact single-pass NOPA system is described with a passive spectral shaping technique that enables an ultrabroadband flat-top-like spectrum and an output pulse duration in the few-cycle regime. The NOPA was pumped by a POLARIS oscillator-seeded, Yb$^{3+}$-based CPA system operating at 1030 nm that produced 2 mJ, 120 fs pulses. The ultrashort pulse was utilized to generate both a stable white light supercontinuum in 5 mm YAG for the NOPA signal and a 200 GW/cm$^2$ NOPA pump pulse operating at 515 nm using second harmonic generation in 3 mm KDP. Both pulses were temporally aligned within a BBO crystal for NOPA using a motorized delay stage.
The ultrabroadband spectral shaping enabled by the simultaneous optimization of the pump/signal cross angle $\alpha$ and the temporal control of the pump/signal dynamics for the fs-pumped direct NOPA (non-NOPCPA) resulted in a flat-top-like output spectrum exhibiting a 230 nm FWHM bandwidth centered at 820 nm with a spectral bandwidth fluctuation of 0.46% RMS measured over 1800 consecutive pulses. The material (5 mm YAG and 2 mm BBO) dispersion pre-compensation using a chirped mirror pair produces similar pump and signal pulse durations at the start of the BBO crystal, as well as a near-FTL pulse duration of 11 fs at the crystal output with a record 20 µJ pulse energy for the single-pass fs-NOPA. With the optimization techniques presented in this paper, a dedicated stretcher-compressor setup or spectral pre-shaping devices for the NOPA were not required, thereby considerably reducing the complexity of the system. The 40 cm $\times$ 40 cm setup fulfills the design criteria for ultrashort optical probing and simultaneously delivers two mJ-class, nearly 100 fs pulses at the POLARIS fundamental and second harmonic to complete the multi-beam probing system for relativistic laser-plasma interactions at the petawatt-class POLARIS laser system.
Funding
LASERLAB-EUROPE (654148); Bundesministerium für Bildung und Forschung (03VNE2068D, 03Z1H531, 05K16SJC, 05K19SJC, 05P15SJFA1, 05P19SJFA1); Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft (2016FE9058).
Disclosures
The authors declare no conflicts of interest.
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