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Abstract
Optical parametric amplification (OPA) is a powerful tool for the generation of ultrashort light pulses. However, under certain circumstances, it develops spatio-spectral couplings, color dependent aberrations that degrade the pulse properties. In this work, we present a spatio-spectral coupling generated by a non-collimated pump beam and resulting in the change of direction of the amplified signal with respect to the input seed. We experimentally characterize the effect, introduce a theoretical model to explain it as well as reproduce it through numerical simulations. It affects high-gain non-collinear OPA configurations and becomes especially relevant in sequential optical parametric synthesizers. In collinear configuration, however, beyond the direction change, also angular and spatial chirp is produced. We obtain with a synthesizer about 40% decrease in peak intensity in the experiments and local elongation of the pulse duration by more than 25% within the spatial full width at half maximum at the focus. Finally, we present strategies to correct or mitigate the coupling and demonstrate them in two different systems. Our work is important for the development of OPA-based systems as well as few-cycle sequential synthesizers.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Optical parametric amplification (OPA) is a technique to amplify ultrashort light pulses [1,2]. It supports broad amplification bandwidth, spectral tunability, good temporal contrast and high single-pass gain. Furthermore, when implemented in a chirped configuration, known as optical parametric chirped pulse amplification (OPCPA) [3], the approach is able to handle large energy throughputs. These and other features made OPA increasingly popular during the last decades in a variety of fields, particularly in plasma physics and ultrafast optics [4,5]. As the practical implementation of the technique developed, attempts to push the capabilities of OPA-based systems led to the development of optical parametric synthesizers (OPS) [6]. These are systems that coherently combine several OPCPA stages, each of them optimized for the amplification of a different spectral region. They are arranged either in serial (or sequential) [7,8] or in parallel configuration [9], and pumped by a single [8] or multiple [7,10] colors. Despite their design differences, their purpose is common: to produce high-energy optical pulses with broader spectrum and shorter duration than a single amplifier stage provides.
In an ideal pulse structure, the different spectral components propagate in the same direction and overlap in space. In reality, systems producing and/or manipulating light pulses tend to introduce spatio-spectral couplings (SSCs): color-dependent aberrations that can degrade the spatio-temporal structure and the properties of the resulting optical pulse [11]. In most cases, SSCs are developed as a pulse propagates through the different wavelength-dependent optical components of a system, such as lenses or grating compressors [12–14].
However, in OPAs additional SSCs can arise due to the nature and working configuration of the OPA process itself [15]. When an OPA is operated in a non-collinear configuration (NOPA) [16], pulse-front tilt and angular chirp can arise due to the angular dependent nature of the gain curve [17]. This effect can be minimized by working near the “magic” phase matching conditions, where the angular dependency of the spectral gain is smallest. It is also known that the mismatch between the pulse front of the seed and the pump beams, which naturally appears in the non-collinear configuration, is a source of spatial and angular chirp when amplifying temporally chirped pulses [18]. This effect can also be minimized, either by introducing a pulse front tilt in the pump that matches the tilt of the seed, or by matching the pulse durations of the two pulses. Furthermore, numerical investigations concluded that high order distortions can appear when the amplifier is operated in the saturated regime [19]. These can be reduced by the appropriate choice of pump beam profile. It was also reported that aberrations in the pump beam can induce distortions in the amplified signal amplitude and wavefront under certain conditions [20,21]. However, these works did not address the effect of pump wavefront in OPS. It is therefore not yet known if and how the collimation of different pump beams can introduce SSCs. This is especially relevant, considering that many (commercially available) OPS work with focused pump beams [22].
In this article, we report on the observation and characterization of a SSC arising from the lack of collimation of the beam pumping one OPA stage in a sequential OPS. The SSC consisted in the discrete change of direction of the amplified spectral components respect to the input direction of the seed, which manifested as a double foci structure in the far field. In order to better understand this effect, we performed numerical simulations and developed a theoretical model that is consistent with the observations. Finally, we were able to mitigate the SSC thanks to this knowledge.
2. Experimental setup
The spatio-spectral aberration was recognized in the output of a two-color pumped OPS system custom-made by Light Conversion. The system starts with white light generation (WLG) by a Yb:KGW pump laser (1030 nm central wavelength), which is further amplified in an OPA. Then a difference frequency generation stage produces carrier-envelope phase (CEP) stable signal. This undergoes spectral broadening in a second WLG stage to provide the seed, in a similar fashion to the system described in [22]. After that, the seed is sequentially amplified in a total of four NOPA-stages pumped by the third harmonic (3ω, 1st and 3rd stage) and second harmonic (2ω, 2nd and 4th stage) of the pump fundamental. The last two stages are schematically depicted in Fig. 1. The output pulses are generated with a spectrum spanning 580–1050 nm, supporting 5 fs pulses containing about 13 µJ of energy. In the last 2ω pumped stage, where the SSC was found to arise, beam profiles of the seed and pump are Gaussian and have about 1 mm of diameter (1/e2) when propagating through the 2 mm thick beta-barium borate (BBO) NOPA crystal. The 2ω pump energy is 128 µJ and has 170 fs pulse duration. The phase matching of this stage is in Poynting vector walk-off compensation geometry [23].
Fig. 1. Schematic of the spatio-spectral coupling arising as the seed beam undergoes amplification in the 3ω and convergent 2ω-pumped BBO crystals. The light amplified in each stage propagates at a slightly different direction, although they are born from the same seed beam. This effect manifests in the far field as two separate foci. The collimation/wavefront of the pump and seed beams is depicted with dashed lines.
To characterize the output of the laser system we used a simplified version of the INSIGHT technique [24,25], which provides the beam profile and wavefront resolved both spatially and spectrally. The method was implemented using an achromatic lens with 200 mm focal length as focusing optic. The radius of curvature (ROC) of the pump beam at the last amplification stage (NOPA 2ω) was measured with a commercial wavefront sensor (Thorlabs) providing -0.8 ± 0.02 m, while the ROC of the seed at that same stage was measured to be 8 ± 1 m. In this work we use the convention of positive ROC for divergent beams and negative ROC for convergent beams. The seed after the WLG stage was measured to have no angular chirp down to our resolution limit (0.07 mrad).
3. Experimental characterization
We first observed the spatio-spectral aberration when focusing the output of the laser system on a camera with an achromatic lens. The measurement, shown in Fig. 2(a), reveals a double foci structure, with the light in the upper focus mainly originating from the 2ω stage, and the light in the bottom focus from the 3ω stage. We confirmed this fact by blocking either of the pump arms and observing the corresponding focus disappear. To discard artifacts arising from any residual chromatism of the focusing lens, we introduced a band-pass filter (716 nm central wavelength, 10 nm bandwidth) right in front of the detector and readjusted the camera distance to account for the change in focal position along the laser propagation direction. This allowed us to observe a narrow spectral range at the interface between the 2ω and 3ω amplification regions, revealing the same double foci structure. Fig. 2(b) shows the overall output spectrum of the system, with the regions amplified in the 2ω and 3ω stages in green and violet background, respectively, with a certain spectral overlap. We also assessed the severity of the associated spatio-temporal coupling by calculating the spatially resolved Fourier transform limited (FL) pulse duration across the far-field plane. While the calculated FL-duration of the spatially integrated beam is 5.0 ± 0.1 fs, in agreement with the manufacturer specifications, the value becomes 1.3 fs longer (>25%) for parts of the focus still in the spatial full width at half maximum (FWHM) intensity region as shown in Fig. 2(c). Due to the poor overlap between the foci, the peak intensity was estimated to decrease by 40% when compared to a beam with ideal spatio-temporal structure. The spectrum at the center of each focus, plotted in Fig. 2(d), shows similar curves as the spatially integrated spectra, but differently weighted towards shorter or longer wavelengths in each case. This is due to the fact that the spatial intensity distributions of the two foci still partially overlap. Notice that this weighted overlap causes the pulse duration in one end of the profile to become shorter than the spatially integrated FL-duration, as the short wavelength part of the spectrum in that area is stronger.
Fig. 2. Characterization of the spatio-spectral coupling at the focus. (a) Focal plane with the double foci structure. A red and a blue cross indicates the highest intensity point of the light amplified in the 2ω and 3ω stages, respectively. (b) Spatially integrated spectrum of the system, where the green and pink areas denote the 2ω and 3ω amplification regions, with a commonly amplified region in between. (c) Black: intensity line out along the black dashed line in (a) green: Fourier transform limited (FL) duration along the same line. The vertical red and blue dashed lines correspond to the peaks position for each focus, while the FL-duration of the spatially integrated spectrum is shown as a horizontal green dashed line. (d) retrieved spectra at the peak of each focus.
Next, we characterized the spectrally resolved wavefront of the collimated beam before focusing, i.e., the near field. The results show that there is a discrete change in propagation direction across the spectrum taking place around 710 nm, i.e., at the interface between amplification of the 2ω and 3ω stages, as plotted in Fig. 3(a). The difference in propagation direction between the corresponding average of the 2ω and 3ω amplified components is approximately 0.35 ± 0.07 mrad enough to spatially separate the foci to a significant extent as shown in Fig. 2. This is in good agreement with the angular deviation of 0.28 ± 0.02 mrad that is inferred from the separation between the two foci in the far field. The small discrepancy between the measured and inferred values might be due to the asymmetric spatial intensity distribution in the far field (Fig. 2(a)), where we defined the peak as focus position rather than the first moment.
Fig. 3. Characterization of the spectrally resolved wavefront in the near field. (a) Change of propagation direction for each spectral component, with a discrete jump at the interface between the 2ω and 3ω amplification regions. The red and blue dashed lines represent the average of each region, respectively, and the semitransparent background indicates the corresponding standard deviation. The solid blue and red circles correspond to the components shown in (b) and (c), as representative examples of the retrieved wavefront of the beam in each spectral group. Regions with relative intensity below 1/e2 of the maximum have been set to zero.
4. Geometrical model and numerical simulations
The observed shift in propagation direction originates during the amplification process in a NOPA stage with high gain and can be understood through the following geometrical model. Figure 4 shows the overlap between the seed (yellow) and pump (green) pulses as they propagate within the non-linear crystal at two different depths in Z. At the beginning of the crystal (Z = 0) the phase-matching conditions would be optimal at all transverse positions with a flat wavefront. However, because of the finite ROC, the pump wavevector (kP) changes along the beam transversal position (Y). Therefore, each vertical segment has a different pair of phase-matching and non-collinear angles, which fulfill optimal conditions (θ0, α0,) only locally near the center of the beam, and thus amplification gets spectrally narrow and strongly decreases further away from the middle. Notice that this local amplification makes the vertical size of the signal (amplified seed) beam smaller if the gain is large. At certain depth in the crystal (Z = L), the relative transverse overlap between the pulses shifts due to the mismatch between the non-collinear (α0) and the walk-off (β) angles. This fact, combined with a reduced size of the seed, leads to a different pump wavevector (kP1) and corresponding phase-matching and non-collinear angles (α1, θ1), which combination is not optimal for spectral width and gain. Therefore, the signal is gradually naturally shifting to an optimal propagation direction (kA) corresponding to the optimal non-collinear angle (αopt) at the given θ1. In the limit of small shifts, the optimal relation between α and θ can be approximated as a linear function according to Eq. (1),
where δθ is a small deviation with respect to the optimal phase-matching angle for a given configuration and m is a positive proportionality constant in our case. Following geometrical considerations, it can be shown that the angular shift ΔαS between the original seed and final optimal signal wavevector after travelling a distance L through the BBO crystal isFig. 4. Geometrical model describing the change in propagation direction of the amplified beam in a non-linear crystal pumped by a convergent pump beam. θ: phase matching angle, α: non-collinear angle, 0, 1, opt indices of angles: initial, final, and optimal, β: walk-off angle, ΔαS: shift in seed propagation direction, SP: Poynting vector of the pump, kP, S, A: pump, seed, signal (amplified seed) wavevector, and OA: optical axis. The colored solid lines at the perimeter of each pulse represent the intensity profiles and the colored dashed lines inside represent the wavefront. Poynting vector walk-off compensation phase matching geometry is illustrated.
In order to test the described model, we performed numerical simulations of a NOPA process in a single 2ω-pumped OPA stage while introducing different ROCs in the pump beam. The simulation algorithm (chi2D) is based on the split-step method and is described in [26]. Unless otherwise stated, all the simulations were carried out in a walk-off compensation geometry, with a phase-matching angle (θ) of 24.5° and a non-collinear angle (α) of 2.54° (internal). The seed parameters were: Gaussian spatial profile with 1 mm beam diameter (1/e2), peak intensity of 5·104 W/cm2, flat-top spectrum spanning 580 to 1010 nm, and temporal chirp corresponding to group delay dispersion (GDD) of 125 fs2. The pump parameters were: Gaussian spatial profile with 1 mm beam diameter (1/e2), peak intensity of 3·1011 W/cm2 and a spectrum centered at 515 nm with a Fourier limited pulse duration of 170 fs. To maximize the amplified bandwidth, we introduced a group delay (GD) of 75 fs between seed and pump pulses at the beginning of the crystal. The BBO crystal thickness was 2 mm. In order to decouple the conclusions of this study from other already known phase shifting effects due to Kerr lensing [27,28], we switched these off in the simulation software. Moreover, unless otherwise stated, the simulations were performed in the non-saturated regime in order to avoid introducing wavelength-dependent aberrations [19], which we also observed coupling with the shift.
The results, displayed in Fig. 5, show that a shift in propagation direction of the seed indeed occurs when the ROC of the pump has a finite value. Furthermore, the direction in which the amplification is shifted changes with convergent or divergent pump beams, and the magnitude of the shift is inversely proportional to the pump ROC. During the simulations, we observed that the change in direction experienced by the amplified signal did not occur at a certain Z position, but shifted continuously as it propagated through the non-linear crystal, i.e., approximately following a linear relation with the propagation length. Notice that all the previous observations are in good agreement with the predictions of our geometrical model, summarized in Eq. (2). However, the precise value of the proportionality constant m was not derived analytically. It is worth emphasizing that the amplification process does not significantly degrade when the magnitude of the pump ROC changes. For all the cases shown in Fig. 5(b), the unsaturated gain was always in or near the order of 105, and the spectrum stayed similarly broad. Although, a small angular chirp appeared for the most extreme cases that we simulated, shown in Fig. 5(a) (ROCP = 3 cm, divergent pump) and 5c (ROCP = -3 cm, convergent pump), this is smaller than the width of the beam in the propagation direction axis.
Fig. 5. Simulated amplified signal for different collimations of the pump beam. (a) and (c) are examples of the amplification output when using divergent (a) and convergent (c) pump with a ROC of +3 and -3 cm, respectively. These cases are marked with a solid circle in (b). (b) Angular shift versus ROC of pump. The width of the k-space, calculated as the FWHM of the amplified signal in the propagation direction axis, is indicated with a semitransparent color background, while the centroid of the beam corresponds to the circles. The vertical yellow line in (a) and (c) denotes the seed at the beginning of the BBO crystal (isoline at half-maximum of its own intensity). (d) and (e) display the propagation direction of the spectrally integrated signal at different depths of the crystal for the cases of no pump ROC and -3 cm pump ROC, respectively. For better visibility, it was normalized at each point of the crystal. The unsaturated gain experienced by the seed at the end of the crystal was in all cases on the order of ∼105.
We compare the results from these simulations with the experimental characterization of our laser system. Experimentally SSC was found to arise from the last 2ω-pumped NOPA stage and all the spectral components were travelling in the same direction before that stage. Consequently, the observed angular shift (see Fig. 3) was caused only by the ROC of the pump beam in that stage. That ROC was measured to be -0.8 m, which according to Fig. 5(b) should cause a shift of 0.19 mrad in the unsaturated regime at the end of the BBO, in relatively good agreement with the experimental result of 0.35 mrad. The discrepancy between the simulated and experimental values is partly caused by the change in wavefront curvature due to Kerr self-focusing of the pump and possibly by higher order aberrations in the pump beam, both of them were disregarded in the simulations.
Next, we investigated the broadening of the k-space during the amplification process. As shown in Fig. 5(b), the width of the k-space is also dependent on the pump ROC. We carefully checked the k-components of the seed that correspond to the final propagation direction and assessed that before amplification these are negligible, i.e., the ratio of their intensity and the intensity of the original components in 2.54° direction is much lower (10−5) than the OPA gain. Therefore, the k-space not just broadens during the amplification process, but acquires new components. This is best visible in Figs. 5(d) and 5(e), where the evolution of the spectrally integrated signal is shown for the cases without and with ROC (-3 cm) in the pump, respectively. The comparison between these indicates a much larger broadening originating from pump curvature than from pump size (i.e., from the fact that the pump is similar or smaller in diameter than the seed).
To further investigate this effect, we plotted the seed pulse in space as it propagates through the non-linear crystal. The results, shown in Fig. 6, indicate that the size of the seed quickly decreases soon after the amplification process starts. According to our model, this occurs because only a narrow range of α and θ pairs around the optimal α0, θ0 in the center of the beam is initially amplified with significant gain. This spatial shrinking corresponds to new k-components, which are gradually changing and moving away from the original by the changing gain conditions. Notice that smaller pump ROCs mean that the distribution of α and θ pairs with significant gain becomes narrower in space, therefore making the effect stronger. Alternatively, the ROC of the pump corresponds to a finite width in the k-space that generates a certain width of idler with the well-defined seed wavevector. Later, these broad (in k-space) pump and idler beams generate new seed k-vector components defined by the parameter-dependent parametric gain. It is worth mentioning that in the non-collinear configuration used in this simulation, the spatial chirp of the amplified beam is negligible at the end of the crystal (Z = 2.0 mm) as shown in Fig. 6. It is visible considering that in the chirped seed different longitudinal components correspond to different wavelengths, and all of them overlap while propagating in the signal direction. To assess whether the angular shift is dependent on the pump intensity, we simulated the same process but lowered the pump peak intensities down to 2.2·1011, 1·1011, and 5·1010 W/cm2, which led to gains of about 104, 102 and 101. The results show that when compared to the initial pump intensity value (3·1011 W/cm2, gain 105) the shift was reduced by 7%, 20% and 35%, respectively. Therefore the effect is significant at gains above or around 101.
Fig. 6. Spatial evolution of the seed/signal pulse (in color) as it propagates through a 2 mm BBO non-linear crystal in a non-collinear OPA geometry. The contour of the pump beam at 1/e2 in intensity is plotted as a thick black line. The ROC of the pump beam was -3 cm.
For completion, we also investigated if the same SSC appears in a collinear configuration, which is generally known to be less prone to SSC [29]. In this case, the seed has a narrower spectrum (FL duration 20 fs). Figure 7 shows the spatial progression of a seed pulse amplified in an OPA stage when the pump mean k-vector is aligned parallel to that of the seed. The results show that soon after the amplification starts the seed pulse develops a strong pulse-front tilt. This is due to the fact that the non-collinear angle is far from optimum for broadband amplification and the vertically changing phase-matching angle provides high gain for different wavelengths (and a very narrow bandwidth around them) at different Y positions. This signal pulse exhibits temporal and spatial chirp as well as some small angular chirp, where for a pump ROC of -3 cm (see Fig. 7) the spatial chirp is 2.3 µm/nm and the angular chirp is 17.5 µrad/nm. For comparison, the collinear case without ROC in the pump produces no spatial chirp (resolution limit of the simulations of 0.1 µm/nm) and a negligible angular chirp of 0.5 µrad/nm.
Fig. 7. Spatial evolution of the seed/signal pulse (in color) as it propagates through a 2 mm BBO non-linear crystal in a collinear OPA geometry, with an amplified spectrum corresponding to FL-duration of 35 fs. The contour of the pump beam at 1/e2 in intensity is plotted as a thick black line. The propagation direction of each spectral component is plotted in the last graph. The ROC of the pump beam was -3 cm. In this case, the non-collinear angle was 0° and the phase-matching angle was 22.5°
Finally, we used the knowledge acquired from this investigation to correct the described SSC. We did that following two different approaches. The first strategy consisted in changing the phase-matching and the non-collinear angles by tuning the crystal angle and the direction of the pump beam while keeping the seed direction constant. This way, optimal amplification conditions are approximately fulfilled at the end of the crystal, i.e., matching the kA with the kS. Naturally, the phase-matching conditions at the beginning of the crystal were slightly away from optimum and the small signal gain was reduced. However, this was not critical in our case as the amplifier works in the saturated regime, which compensates for the gain decrease. We simulated this solution with the NOPA stage parameters similar to our system in the original and corrected configurations. The results (see Fig. 8(a)) show that the original parameters (α=2.5° and θ=24.5°, in red-yellow) lead to a shift in the beam, while the corrected configuration (α=2.63° and θ=24.45°, in blue-green) leads to negligible overall shift. Notice that using phase matching conditions away from the optimum, i.e., magic angle, leads to small angular chirp [17]. Nevertheless, the results indicate that the coupling can indeed be eliminated with such a strategy. It is important to point out that this strategy only works to correct for mild shifts. When the pump ROC becomes too small, the necessary detuning of the phase-matching conditions that would compensate for the corresponding shift is so far from the optimal that the gain and spectral bandwidth degrade below practical values. We assessed that limit to be somewhere around a pump ROC of 30 cm, with an associated detuning of phase-matching conditions in our configuration that reduced the small signal gain by a factor of 100. Experimentally implementing this method successfully eliminated the double foci in our NOPA synthesizer, as shown in Fig. 8(b).
Fig. 8. Strategies to correct or mitigate the shift in propagation direction. (a) Simulation of the amplification process in a 2ω NOPA stage before (Orig.) and after (Corr.) changing phase-matching conditions to mitigate the shift. The isolines in the red-yellow and blue-green color scales indicate the simulated intensity of the beam profile in the propagation direction vs. wavelength space, for the original and corrected cases. The simulated correction was performed by changing the non-collinear angle from 2.50° to 2.63°, and the phase-matching angle from 24.50° to 24.45°. (b) Experimental focus observation of the overlap between the two foci after implementing the correction. Notice the improvement when compared to Fig. 2(a). (c) Experimental focus observation of the two spectral regions in a different OPS system [7], shown as red and blue, amplified by 2ω and 3ω pumps, respectively. For both (b) and (c) the top row shows the isolines 1/e2 of the focus profile, while the bottom row shows the position of each profile integrated over the Y spatial dimension to highlight the shift in X. The ROC of the pump beam for convergent, collimated and divergent cases in (c) was estimated to be -27 cm, infinite, and 63 cm, respectively. The red and blue ‘x’ marking in (b) indicates the position of the maximum intensity for each case.
The second strategy, arguably the most robust one, consists in carefully collimating the pump beam before the amplification stages. Due to design constraints, this approach could not be implemented in our front end and therefore we demonstrate it here for a different and more flexible system, the LWS20 [7]. The LWS20 is a high-power (16 TW), sub-5 femtosecond OPS system, which sequentially amplifies a spectrally broad seed through a series of 2ω and 3ω pumped stages, in a similar fashion as our front end. In order to induce a shift and demonstrate the correction strategy, we observed the focus of the signal after being amplified in one 2ω and one 3ω stage and changed the pump collimation of the first one. The results (see Fig. 8(c)) show that the spectral region amplified by the 2ω stage (red) shifts with respect of the unchanged 3ω amplified region (blue). Therefore, we demonstrated in a different system that the pump ROC causes a shift in propagation direction and it can be eliminated by controlling the pump collimation.
5. Conclusions and outlook
In this paper we reported on a spatio-spectral coupling, which consists in the change of direction of the amplified signal in a NOPA stage with high gain relative to the input seed. This effect is especially relevant for sequential synthesizers, as the light amplified in different stages will propagate in different directions. We observed and characterized the coupling as a shift in the propagation direction of the spectral components amplified in one NOPA stage corresponding to 0.35 mrad. While seemingly small, it was enough to significantly degrade the spatio-temporal structure of the amplified pulse in a synthesizer, decreasing the peak intensity in the focus by 40%. The degradation of the pulse properties to such an extent can negatively affect the applicability of the laser system in many fields, such as the isolation of attosecond pulses via high-harmonic generation or the generation of plasmas in extreme fields. We have developed a model based on the geometry of the interaction between the seed and the pump pulses, and demonstrated that the coupling originates from the finite radius of curvature of the pump beam. This is especially relevant when considering that many commercially available NOPA-based systems utilize a focused pump beam configuration. We performed numerical simulations to successfully validate our model up to a proportionality constant. Furthermore, the simulations indicated that the coupling is not restricted to the non-collinear configuration, but it also appears in collinear OPA leading to even more serious aberrations including spatial and angular chirp. Finally, we have used the acquired knowledge to experimentally reduce the severity of the coupling from our system to a great extent, while experimentally confirming the approach. It is important to mention that the spatio-spectral coupling described in this paper was observed after performing a routine alignment of the system to optimize for output energy and spectral bandwidth. Since these are arguably the most commonly used parameters for system maintenance and realignment, it is plausible to assume that similar couplings might normally arise in sequential OPS, especially when the spatio-spectral structure is not considered or measured. Furthermore, based on the results of the presented simulations we expect that more severe couplings of the same nature might arise when pump beams with shorter radius of curvature or aberrated wavefronts are used.
Funding
Vetenskapsrådet (2019-02376, 2020-05111); Knut och Alice Wallenbergs Stiftelse (2019.0140); Kempestiftelserna (SMK21-0017); H2020 Marie Skłodowska-Curie Actions (801505).
Acknowledgments
We thank Roushdey Salh for the technical support and Tino Lang for useful discussions and support regarding the simulation algorithm.
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.
References
1. R. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979). [CrossRef]
2. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003). [CrossRef]
3. A. Dubietis, G. Jonušauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4-6), 437–440 (1992). [CrossRef]
4. S. Witte and K. S. E. Eikema, “Ultrafast optical parametric chirped-pulse amplification,” IEEE J. Select. Topics Quantum Electron. 18(1), 296–307 (2012). [CrossRef]
5. L. Veisz, “Optical parametric chirped-pulse amplification,” in Handbook of Laser Technology and Applications: Lasers: Principles and Operations, 2nd ed., S. C. S. Chunlei Guo, ed. (CRC Press, 2020), p. 570.
6. C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015). [CrossRef]
7. D. E. Rivas, A. Borot, D. E. Cardenas, et al., “Next generation driver for attosecond and laser-plasma physics,” Sci. Rep. 7(1), 5224 (2017). [CrossRef]
8. S. Toth, T. Stanislauskas, I. Balciunas, R. Budriunas, J. Adamonis, R. Danilevicius, K. Viskontas, D. Lengvinas, G. Veitas, D. Gadonas, A. Varanavičius, J. Csontos, T. Somoskoi, L. Toth, A. Borzsonyi, and K. Osvay, “SYLOS lasers – the frontier of few-cycle, multi-TW, kHz lasers for ultrafast applications at extreme light infrastructure attosecond light pulse source,” JPhys Photonics 2(4), 045003 (2020). [CrossRef]
9. S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011). [CrossRef]
10. A. Harth, M. Schultze, T. Lang, T. Binhammer, S. Rausch, and U. Morgner, “Two-color pumped OPCPA system emitting spectra spanning 1.5 octaves from VIS to NIR,” Opt. Express 20(3), 3076–3081 (2012). [CrossRef]
11. S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12(9), 093001 (2010). [CrossRef]
12. G. Pariente, V. Gallet, A. Borot, O. Gobert, and F. Quéré, “Space–time characterization of ultra-intense femtosecond laser beams,” Nat. Photonics 10(8), 547–553 (2016). [CrossRef]
13. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14(2), 119–121 (1989). [CrossRef]
14. S. Ranc, G. Chériaux, S. Ferré, J. P. Rousseau, and J. P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70(S1), S181–S187 (2000). [CrossRef]
15. Y. Wang, J. Wang, B. Zhou, J. Ma, P. Yuan, and L. Qian, “Spatiotemporal couplings through a nonlinear phase in broadband optical parametric amplification,” Opt. Lett. 46(22), 5743–5746 (2021). [CrossRef]
16. P. Di Trapani, A. Andreoni, G. P. Banfi, C. Solcia, R. Danielius, A. Piskarskas, P. Foggi, M. Monguzzi, and C. Sozzi, “Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation,” Phys. Rev. A 51(4), 3164–3168 (1995). [CrossRef]
17. J. Bromage, C. Dorrer, and J. D. Zuegel, “Angular-dispersion-induced spatiotemporal aberrations in noncollinear optical parametric amplifiers,” Opt. Lett. 35(13), 2251–2253 (2010). [CrossRef]
18. A. Zaukevičius, V. Jukna, R. Antipenkov, V. Martinėnaitė, A. Varanavičius, A. P. Piskarskas, and G. Valiulis, “Manifestation of spatial chirp in femtosecond noncollinear optical parametric chirped-pulse amplifier,” J. Opt. Soc. Am. B 28(12), 2902–2908 (2011). [CrossRef]
19. A. Giree, M. Mero, G. Arisholm, M. J. J. Vrakking, and F. J. Furch, “Numerical study of spatiotemporal distortions in noncollinear optical parametric chirped-pulse amplifiers,” Opt. Express 25(4), 3104–3121 (2017). [CrossRef]
20. X. Wei, L. Qian, P. Yuan, H. Zhu, and D. Fan, “Optical parametric amplification pumped by a phase-aberrated beam,” Opt. Express 16(12), 8904–8915 (2008). [CrossRef]
21. S. W. Bahk, I. A. Begishev, R. Roides, C. Mileham, R. Cuffney, C. Feng, B. M. Webb, C. Jeon, M. Spilatro, S. Bucht, C. Dorrer, and J. Bromage, “Effect of the pump beam profile and wavefront on the amplified signal wavefront in optical parametric amplifiers,” Opt. Express 30(8), 12995–13008 (2022). [CrossRef]
22. R. Budriūnas, T. Stanislauskas, and A. Varanavičius, “Passively CEP-stabilized frontend for few cycle terawatt OPCPA system,” J. Opt. 17(9), 094008 (2015). [CrossRef]
23. X. Guo, Y. Xu, X. Zou, X. Lu, Y. Li, C. Wang, Y. Leng, and R. Li, “Non-collinear phase-matching geometries in optical parametric chirped-pulse amplification,” Opt. Commun. 330, 24–29 (2014). [CrossRef]
24. A. Borot and F. Quéré, “Spatio-spectral metrology at focus of ultrashort lasers: a phase-retrieval approach,” Opt. Express 26(20), 26444–26461 (2018). [CrossRef]
25. A. De Andres, S. W. Jolly, A. A. Muschet, F. Schnur, F. Quere, and L. Vseisz, “Simple measurement technique for spatio-temporal couplings in few-cycle pulses,” in The International Conference on Ultrafast Phenomena (UP) 2022, Technical Digest Series (Optica Publishing Group, 2022), Tu4A.52.
26. T. Lang, A. Harth, J. Matyschok, T. Binhammer, M. Schultze, and U. Morgner, “Impact of temporal, spatial and cascaded effects on the pulse formation in ultra-broadband parametric amplifiers,” Opt. Express 21(1), 949–959 (2013). [CrossRef]
27. E. Wittmann, H. Hecht, and E. Riedle, “Dramatic beam steering by Kerr lensing in optical parametric amplifiers,” in The European Conference on Lasers and Electro-Optics (Optica Publishing Group, 2017), CF_3_2.
28. E. Wittmann, Taming Optical Parametric Amplification: Stable Few Cycle Pulses at 210 to 10000 nm from Ti: Sapphire and Yb-based Lasers, (Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019).
29. T. Eichner, T. Hülsenbusch, J. Dirkwinkel, T. Lang, L. Winkelmann, G. Palmer, and A. R. Maier, “Spatio-spectral couplings in saturated collinear OPCPA,” Opt. Express 30(3), 3404–3415 (2022). [CrossRef]
