# Multi-mJ Scaling of 5-Optical Cycle, 3 µm OPCPA

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}, LN) [15,16] and potassium titanyl arsenate (KTiOAsO

_{4}, KTA) [20,21] (although in the latter case the output is already closer to 4 µm), clearly evidencing the potential of these crystals in withstanding and operating at high optical intensity levels.

_{3}, MgO:LN), as an ultrabroadband mechanism for the optical parametric amplification of 3 µm pulses from the µJ up to the mJ-level pumped by 1 µm sources. We study a range of configurations and compare their outputs in terms of amplified bandwidth, efficiency, and total gain. We find that by using a single 60 mJ, 6 ps ytterbiumbased pump source at 1030 nm it is possible to obtain an output energy in excess of 5 mJ. We also show that these pulses can be compressed to 5-optical cycles by using compact bulk compression. The numerical model used is a powerful tool that allows the simulation of the relevant nonlinear phenomena involved in the amplification process in the spatial and temporal dimensions [24].

## 2. Choice of Non-Linear Crystals and Simulation Parameters

#### 2.1. Mid-IR Materials for 3 µm Amplification Pumped at 1 µm

^{2}at 740–840 nm, 0.2 ps, 1 kHz [25]), an approximately constant spectral transmission in the range ∼0.5–3.5 µm and moderate non-linear coefficient (d

_{eff}∼2.1 pm/V). Additionally, KTA allows collinear amplification, enabling a simpler design, operation, and less beam aberrations, making it ideal for OPCPA. Potassium titanyl phosphate (KTiOPO

_{4}, KTP) [25] is a material from the same family as KTA showing the same high LIDT. However, its decreasing transmission at 3 µm makes it less desirable for amplification in this region.

_{3}, KN) is a negative biaxial crystal from a different family, for which a LIDT as high as that of KTA has been reported (>200 GW/cm

^{2}at 800 nm, 0.2 ps, 1 kHz [26]), while also exhibiting a high non-linear coefficient (d

_{eff}= 6.0 pm/V) and allowing for a broad phase-matched bandwidth in non-collinear geometries. An experimental study performed with KN crystal for amplification at 3.15 µm with 370 nm bandwidth at 1/e

^{2}has demonstrated its broadband amplification capability while also showing that at intensities larger than 14.4 GW/cm

^{2}for 9.5 ps, 160 kHz, 1064 nm pulses led to optical damage [27]. Furthermore, this material is prone to multi-domain issues due to its structural and ferroelectric properties requiring careful operation.

_{3}, LN), a crystal with negative uniaxial birefringence which when doped with magnesium oxide (MgO) can further reduce the green-induced infrared absorption (GRIIRA) [28]. Its structural type (congruent and stoichiometric) and doping concentration might slightly vary the LIDT of the crystal, but 5 mol% MgO-doped congruent LN was recently reported to have an LIDT comparable to KTA (204 ± 4 GW/cm

^{2}, 10 kHz, 1 ps, 1030 nm) [29]. A recent publication reported that MgO:LN could withstand powers as high as 25 GW/cm

^{2}at 800 nm, 10 Hz, 6.6 ps in an OPCPA configuration [15]. Furthermore, MgO:LN has a high non-linear coefficient (d

_{eff}∼3.9 pm/V) allowing for large phase matching bandwidth which together with its high to moderate LIDT value makes it a very promising crystal for ultrabroadband mJ-level amplification. This material is also used in a periodically poled configuration (PPLN). On the one hand, this brings the advantage of quasi-phase matching (QPM), but on the other hand it has represented so far a challenge for high pumping power, and, therefore, to mJ-scaling, due to parasitic interactions and thermal effects. For this reason, PPLNs are not considered in the present work. Table 1 summarizes the relevant properties of the crystals of interest for high-energy amplification at 3 µm as discussed above, as well as their calculated acceptance bandwidth (assuming a crystal length of $L=2$ mm) for operation at the wavelength in question.

#### 2.2. Amplification Parameters and Numerical Model

^{2}was set to 2.5 mm, which was considered for a compact configuration and well below the current size limit of homogeneous KTA crystals (∼$15\times 15$ mm

^{2}). The pump energy was limited by the maximum radius and pulse duration with respect to the damage threshold of each crystal. Both beams were considered to have spatially Gaussian profiles.

## 3. Results

#### 3.1. Single OPCPA Stage

^{2}(pump energy is 40 mJ). The corresponding optimum phase matching angle and crystal length are $\theta =41.{6}^{\xb0}$, Type II interaction (d

_{eff}= 2.1 pm/V) for a 2.5 mm long crystal. The choice of length stems from a compromise between maximum energy and minimal duration while preserving the beam quality (indicated by the M

^{2}factor), see Figure 1 and Table 2. For these parameters, output pulses with 1.92 mJ, 74 fs at 3130 nm central wavelength were obtained. This represents an overall gain of 38.4 and a 4.8% pump-to-signal conversion efficiency. However, the simple setup comes at the cost of an undesirable pulse broadening factor of 48%, which nevertheless allows compression to just 7-optical cycles. Figure 1 shows the output energy, compressed pulse duration, pulse spectrum and spatiotemporal profile for the parameters studied.

^{2}) used in an OPCPA configuration [15] as stated earlier. This is equivalent to using a maximum pump energy of 16 mJ. For this case, the optimum phase matching angle is 46.7${}^{\xb0}$ for a Type I non-collinear geometry with a 5.1${}^{\xb0}$ angle in the XZ plane, for which we have (d

_{eff}= 3.9 pm/V), and a crystal length of 2.3 mm. For these parameters, output pulses with 1.12 mJ, 51 fs at 3054 nm central wavelength were obtained. This represents a gain of 22.4 and a pump to signal efficiency of 7.0%. It is clear that the non-collinear geometry is highly favorable in terms of bandwidth, with the signal spectrum being preserved, corresponding to a 5-cycle duration. Figure 2 plots the same parameters as above for the case of MgO:LN.

#### 3.2. Multiple OPCPA Stages

^{2}(pump energy 4 mJ), one-tenth of the previously used value. KTA still shows bandwidth narrowing and pulse broadening, with the output energy and spectrum depending strongly on the crystal thickness. For a 2 mm long crystal the spectral width narrows by ∼25% but the energy (69.7 µJ) is not optimal. The maximum energy output (144.4 µJ) is obtained for L = 5.3 mm but with significant bandwidth narrowing. These results make KTA unsuitable for the lower energy amplification stages. The same pump intensity applied to MgO:LN allows preserving the FTL duration (53 fs) with an optimal pump-to-signal conversion efficiency of 7.4%, corresponding to 347.7 µJ, 5 cycles. The optimal crystal length was of 3.6 mm. Figure 3 summarizes these results.

^{2}), this double-stage OPCPA delivers 5-cycle, 2.06 mJ pulses for an optimal crystal length of 2 mm, already at the few-mJ-level, fewcycle regime. In order to scale this output even further to the multi-mJ, a third stage can be added to this setup. Using MgO:LN again would be of interest, provided higher pump intensities could be used. Instead, and keeping with the conservative approach, we consider a high-energy, KTA-based stage. This approach combines efficiently the large phase-matched amplification bandwidth and high non-linear coefficient of MgO:LN in a first non-collinear double-stage and the high LIDT of KTA for the third one in a collinear configuration. Pumping this stage with 40 mJ, yields an optimal crystal length of 1.4 mm, generating 5-cycle, 5 mJ pulses. Figure 4 shows the amplified bandwidth of the proposed design and Table 3 lists the main parameters for each stage. This output energy represents a net gain factor of 100 and 8.4% pump to signal conversion efficiency, for a total pump energy of 60 mJ.

^{2}/mm [30]) than comparable media, such as yttrium aluminium garnet (YAG, −360.50 fs

^{2}/mm [31]) or calcium fluoride (−107.02 fs

^{2}/mm [32]). These materials also have a low non-linear refractive index, which is important when compressing multi-mJ-level pulses to few-cycle duration. A careful compensation of the second and third order dispersions could allow for compression to 53 fs (see Figure 5), close to its FTL duration.

## 4. Analysis and Discussion

^{2}) and same amplification geometry (Type I, $\theta $ = 46.7${}^{\xb0}$ and $\alpha $ = 5.1${}^{\xb0}$) for a crystal length of 2.3 mm. The seed bandwidth was varied to correspond to 40 fs and 30 fs, in order to allow comparing with the previously obtained results for 50 fs (Figure 6). The same conservative approach of having a good quality output profile was maintained. Although the bandwidths of the 50 fs and 40 fs pulses are still fully accepted by the crystal, delivering an output pulse duration (energy) of, respectively, 51 fs (1.12 mJ) and 43 fs (1.09 mJ), the 30 fs pulse is broadened to 36 fs ($20\%$ increase) with an energy of 1.02 mJ. Therefore, for pulses equal or shorter than ∼3-optical cycles a thinner crystal will be required, while also slightly compromising its output energy. Calculating the bandwidth acceptance for this geometry and crystal length yields 430 nm, which reinforces these conclusions.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Results for a single collinear KTA-based amplification stage.

**Top**: output energy and compressed pulse duration vs. (

**left**) phase matching angle $\theta $ for L = 2.5 mm and (

**right**) crystal length L for $\theta =41.{6}^{\xb0}$. The circled points mark the optimum combination of both parameters.

**Bottom left**: Input (

**shaded**) and output (

**blue**) spectra for the optimal parameters.

**Bottom right**: Spatiotemporal profile of the optimized output pulse with 1.92 mJ and 74 fs (FTL).

**Figure 2.**Results for a single non-collinear MgO:LN-based amplification stage. (

**Top**) output energy and compressed pulse duration vs. (

**left**) non-collinear angle $\alpha $ for L = 2.3 mm and (

**right**) crystal length L for $\alpha =5.{1}^{\xb0}$. The circled points mark the optimum combination of both parameters. (

**Bottom left**) Input (

**shaded**) and output (

**blue**) spectra for the optimal parameters. (

**Bottom right**) Spatiotemporal profile of the optimized output pulse with 1.12 mJ and 51 fs (FTL).

**Figure 3.**Output spectra for a 4 mJ pump. Input signal (

**shaded curve**), 2 mm long KTA (

**dashed red**), 5.3 mm long KTA (

**red**), and 3.6 mm long MgO:LN (

**blue**).

**Figure 4.**Spectra and energy output of proposed few-cycle, few-mJ-level OPCPA chain: input (

**shaded**), OPA 1 (

**dotted red**), OPA 2 (

**dashed red**), and OPA 3 (

**blue**). The final 5 mJ output represents a net 8.4% pump to signal conversion efficiency and a net gain of 100×, with an equivalent 52 fs FTL pulse length.

**Figure 5.**Spacetime profile of the optimized final output pulse from the hybrid OPCPA. The top and right lineouts represent the temporal and spatial profiles, respectively.

**Figure 6.**Input (

**shaded**) and output (

**solid line**) spectra for different seed bandwidths in a single MgO:LN-based amplification stage. (

**Top**) 50 fs, (

**Center**) 40 fs; (

**Bottom**) 30 fs pulse durations.

**Figure 7.**Output energy vs. pump input energy and corresponding crystal length with ouput FTL durations of 50 fs in a single MgO:LN-based amplification stage.

**Table 1.**Relevant optical properties of MgO:LN, KN and KTA for high power parametric amplification. The bandwidth shown is calculated for a $L=2$ mm crystal.

Crystal | d_{eff} (pm/V) | LIDT (GW/cm^{2}) | Bandwidth (nm) |
---|---|---|---|

MgO:LN | 3.9 | 204 ± 4 (1030 nm, 10 kHz, 1 ps) [15] | 495 (Type I, $\theta $ = 40.3${}^{\xb0}$, $\alpha $ = 5${}^{\xb0}$) |

KN | 6.0 | >14.4 (1064 nm, 160 kHz, 9.5 ps) [27] | 670 (Type I, $\theta $ = 40.7${}^{\xb0}$, $\alpha $ = 4.5${}^{\xb0}$) |

KTA | 2.1 | >200 (740–840 nm, 1 kHz, 0.2 ps) [25] | 208 (Type II, $\theta $ = 41.6${}^{\xb0}$) |

**Table 2.**Amplification parameters and output values of the proposed single KTA and MgO:LN OPCPA configurations for few-cycle, mJ-level.

Single OPCPA | Stage | |
---|---|---|

Crystal | MgO:LN | KTA |

Pump (mJ) | 16 | 40 |

Radius (mm) | 2.5 | 2.5 |

Length (mm) | 2.3 | 2.5 |

$\theta $ (${}^{\xb0}$) | 46.7 | 41.6 |

$\alpha $ (${}^{\xb0}$) | 5.1 | - |

Out ${\lambda}_{c}$ (nm) | 3054 | 3130 |

Out energy (mJ) | 1.12 | 1.92 |

Out FTL (fs) | 51 | 74 |

Out cycles | 5 | 7 |

Eff conversion (%) | 7.0 | 4.8 |

Gain | 22.4 | 38.4 |

**Table 3.**Amplification parameters and output values of the proposed three OPCPA stage configuration.

Stage | OPA1 | OPA2 | OPA3 |
---|---|---|---|

Crystal | MgO:LN | KTA | |

Crystal length (mm) | 3.6 | 2 | 1.4 |

Phase matching angle $\theta $ | 46.7° | 41.6° | |

Non-collinear angle $\alpha $ | 5.1° | – | |

Pump energy (mJ) | 4 | 16 | 40 |

Output energy (mJ) | 0.35 | 2.06 | 5.01 |

Equivalent FTL duration (fs) | 53 | 47 | 52 |

**Table 4.**Comparative parameters for selected mJ-level laser systems at 3 μm, ordered by output pulse energy. ${\lambda}_{c}$ is the central wavelength, ${E}_{p}$ the pump energy, ${E}_{out}$ the output energy, ${t}_{out}$ the output pulse duration, and RR the pulse repetition rate.

Refs. | ${\mathit{\lambda}}_{\mathit{c}}$ | ${\mathit{E}}_{\mathit{p}}$ (mJ) | ${\mathit{E}}_{\mathbf{out}}$ (mJ) | ${\mathit{t}}_{\mathbf{out}}$ (fs) | RR (kHz) | Medium | Eff. (%) |
---|---|---|---|---|---|---|---|

[15] | 3.3 | 630 | 21 | 70 | 0.01 | MgO:LiNbO_{3} | 3.3 |

[16] | 3.4 | 900 | 13.3 | 111 | 0.01 | LiNbO_{3} | 1.5 |

[17] | 3.0 | 25 | 2.7 | 50 | 10 | PPLN + KTA | 10.8 |

[18] | 3.1 | 27 | 0.85 | 420 | 1 | MgO:PPLN | 3.2 |

[19] | 2.8 | 12 | 0.52 | 100 | 1 | BBO + KTA | 4.4 |

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**MDPI and ACS Style**

Alves, J.; Pires, H.; João, C.P.; Figueira, G.
Multi-mJ Scaling of 5-Optical Cycle, 3 µm OPCPA. *Photonics* **2021**, *8*, 503.
https://doi.org/10.3390/photonics8110503

**AMA Style**

Alves J, Pires H, João CP, Figueira G.
Multi-mJ Scaling of 5-Optical Cycle, 3 µm OPCPA. *Photonics*. 2021; 8(11):503.
https://doi.org/10.3390/photonics8110503

**Chicago/Turabian Style**

Alves, Joana, Hugo Pires, Celso P. João, and Gonçalo Figueira.
2021. "Multi-mJ Scaling of 5-Optical Cycle, 3 µm OPCPA" *Photonics* 8, no. 11: 503.
https://doi.org/10.3390/photonics8110503