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Abstract
In this study we demonstrated a compact and cost-effective high energy and average power picosecond laser developed for OPCPA system pumping applications. The system delivered record high pulse energy at 100 W average power level in a hybrid laser architecture based on a fiber seed laser and free-space end-pumped Yb:YAG amplifiers. The output pulses were compressed to 1 ps pulse duration and the output beam featured M2 = 1.3, which was further improved to 1.07 by spatial filtering. A silica glass spatially variable wave plate manufactured by direct laser writing was used to reduce depolarization losses from 12% to 5%.
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1. Introduction
Ytterbium doped yttrium aluminum garnet (Yb:YAG) based laser amplifiers are continuously developed to deliver higher intensity and average power radiation. The progress of high power lasers is especially favorable to a wide variety of scientific and industrial applications, such as pumping of optical parametric chirped pulse amplifiers (OPCPA) [1,2], generation of XUV [3] or THz [4] radiation and high throughput laser processing [5–7] among many others.
The reason for the attractiveness of Yb:YAG as an active medium for laser output power scaling lies in the extensive set of its excellent properties. These laser crystals are characterized by high emission cross section, relatively long excited state lifetime, low quantum defect and high thermal conductivity [8,9] that enable high signal gain and facilitate the solution of thermal management problem therefore allowing high energy and average power operation. The use of these advantages in high pulse energy ultrafast lasers improves the productivity, efficiency and complexity of parallel laser-driven machining. This can be achieved by either distribution of laser radiation over a large sample area or beam division, both of which are usually implemented by the use of diffractive optical element and spatial light modulator technologies [10,11]. Furthermore, such amplifiers support sub-ps to few ps pulse durations that are optimal to achieve high pulse contrast in optical parametric amplifiers, a necessary requirement for driving pulses of relativistic light-matter interactions [1,12].
Consequently, the challenge of energy and average power scaling attracts much interest and several distinct high power amplifier geometries are being continuously improved within the modern day laser community. Current state of the art Yb:YAG based systems feature either thin-disc or slab architectures that are based on multi-pass amplification of large laser beams [13,14]. Alternatively, coherent beam combining technique of fiber amplifier outputs has also been used to bypass limiting factors of high power amplification [15,16]. These systems feature unmatched performance and are capable of delivering millijoule level pulse energies and kW scale average output power [15–18] at the expense of having relatively complex architecture. On the other hand, end-pumped rod-type amplifier systems are attractive due to their optical setup simplicity, cost-effectiveness and ease of implementation. Therefore such systems are also investigated for the possibility of further output parameter scaling and have recently exceeded 100 W average power level [19–22] and 20 mJ pulse energy [23,24].
Regardless of the amplifier geometry, the performance of high intensity lasers is limited by thermally induced stress in the gain medium, depolarization losses, nonlinear phase distortion due to nonlinear Kerr effect and laser induced damage [25]. In the case of end-pumped amplifier systems, these effects manifest in degradation of otherwise near Gaussian beam quality (M2) down to 1,3 - 2 and a substantial increase of depolarization losses [19–21]. Several solutions have been proposed to address these problems such as divided pulse amplification [26], along the side pumping [20], use of thin tapered rod with a spherical active medium input surface [24] or the use of single crystal fibers [27]. Although a significant increase in the average output power is observed, such optical arrangements introduce either asymmetric output beam distortions or significant complexity to the amplifier geometry.
Recent emergence of directly written silica glass optical elements enabled a novel and elegant way to suppress output beam distortions and depolarization in end-pumped amplifiers. It was shown, that under high intensity laser irradiation, the structure of glass transforms into self-organized periodical nanostructures consisting of decomposed material planes [28,29]. Such self-structured pattern can then act as a birefringent material and introduce geometrical phase difference to incident laser radiation [29]. It is claimed that the nanostructures have a virtually unlimited lifetime and in order to measure any observable birefringence decay the temperature of the structure has to be increased to approximately 900 $^{\circ }$C [30]. Therefore the technology, based on nanostructure inscription, allowed to produce a variety of optical phase-shifting elements that feature high laser induced damage threshold and good thermal stability [29,31]. In the case of optical amplifiers, the phase difference that is introduced to the beam in a thermally stressed active medium can be reproduced in a spatially variable waveplate (SVWP). SVWP acts as a standard wave plate that features varying retardance as function of the beam radius. Such optical element can be used in the amplifier to reduce depolarization losses and output beam distortions [19,21].
There are several methods that can be applied to compensate depolarization of a thermally stressed gain medium. For example, an intracavity quarter wave plate (QWP) [32] or Faraday rotator can be used to significantly reduce the depolarization level [33,34]. Also, a two crystal amplifier with polarization rotation between the crystals and identical pumping conditions can be designed to cancel out the phase difference induced by an individual active element [34]. However, depolarization compensation by using a SVWP has several advantages over the other approaches. Firstly, a SVWP theoretically allows to achieve complete compensation of depolarization losses at high average power levels and it was also experimentally demonstrated that reduction of losses below 2% is possible [19]. Secondly, a SVWP is as compact as a QWP and more compact than the other two approaches, while at the same time allows to reach better compensation results. Thirdly, when compared to the Faraday rotator approach, the SVWP is less susceptible to nonlinear and thermal effects, as it features lower nonlinear refractive index and lower absorption than commonly used magneto-optic materials [19]. And lastly, a SVWP can be used in a single pass configuration. Nevertheless, there are also some disadvantages to using the discussed compensation method, which have to be taken into account during the design process of the amplifier. A SVWP is a fixed element and has to be matched to the amplifier. This limitation can be mitigated by changing the incident beam diameter or stacking different retardance SVWPs [19]. Moreover, this method of depolarization compensation is more sensitive to misalignment due to the fact that SVWP is a symmetrical element and it has to be aligned at center of the laser beam.
In this study we demonstrate a 1 ps, 100 W class laser system capable of delivering record high pulse energy in an end-pumped, rod-type Yb:YAG amplifier setup. The laser features room temperature operation, novel depolarization compensation method and low spatial and temporal distortions as well as close to ideal beam quality. Theoretical calculation results are presented to support the experimental data and provide insight into optimization of the system output parameters and losses compensation.
2. Experimental setup
The laser system was based on a hybrid approach and consisted of two diode pumped solid state (DPSS) free space Yb:YAG amplifier stages seeded by a high energy fiber laser as shown in Fig. 1. Such system configuration allowed to achieve high energy operation, while retaining near-Gaussian beam quality and excellent stability of the fiber laser. Chirped pulse amplification (CPA) technique was implemented to mitigate the negative effects induced by nonlinearity. The system featured water cooled active medium operated at the room temperature.
Fig. 1. Experimental setup of 100 W class high energy hybrid laser system. YDF – ytterbium doped fiber, CIRC - fiber circulator, CFBG – chirped fiber Bragg grating stretcher, QWP and HWP - quarter-wave and half-wave plates, COL – beam collimator, ISO - optical isolator, POL – thin-film polarizer, DM – dichroic mirror, SM – spherical mirror, HR – high reflectivity mirror, SVWP - spatially variable wave plate, D - beam dump.
SESAM mode-locked fiber oscillator was used to generate ultrashort picosecond pulses at 47.4 MHz pulse repetition rate. The pulses underwent spectral broadening in a silica fiber and then were stretched up to 390 ps pulse duration with a chirped fiber Bragg grating (CFBG). Afterwards the pulse repetition rate was reduced to 10 kHz with a fiber acousto-optic pulse picker and 6 $\mathrm{\mu}$J pulse energy was reached in the final ytterbium doped fiber amplification stage. The output beam quality M2 $\approx$ 1.05 was close to Gaussian.
The free-space amplifier setup consisted of two linear end-pumped Yb:YAG amplifiers. The geometry of both Yb:YAG amplifier stages was based on a two pass configuration, which enabled higher gain without introducing significant complexity. In the first amplifier stage the two-pass configuration was implemented by placing a spherical mirror at the focus of the thermal lens. The spherical mirror optical layout could not be used in the second amplifier stage due to potential of laser induced damage and was changed into a pair of lenses and a flat mirror instead. Radiation outcoupling was performed by using a thin-film polarizer (TFP) combined with polarization rotation by 90$^{\circ }$ with a quarter wave-plate. Seed radiation was imaged to the active medium using 4-f optical setups in order to increase the stability of the whole optical system. Since a lower quantum defect and consequent lower thermal losses were preferable, pumping at zero phonon line (969 nm) was chosen instead of the 940 nm absorption band. 170 W average pump power was used in the first amplifier stage, whereas the second amplifier stage was pumped at 290 W average power enabling amplification up to 22 W and 103 W output signal average power respectively. Both amplifier stages were pumped with fiber coupled laser diodes (nLight) featuring Gaussian output beam and 0.22 NA. The pump diode in the first amplifier stage had 190 W total maximum output power, featured M2 = 38 and was coupled into 105 $\mathrm {\mu }$m core diameter fiber, while in the second amplifier stage a 370 W total maximum output power diode (M2 = 52) coupled into 200 $\mathrm {\mu }$m core diameter fiber was used. The output beam from both diodes was directed to the respective amplifier by a pair of lenses. The active media were mounted in copper housings and were cooled at 18 $^{\circ }$C. A 5$\times$5$\times$15 mm3 size, 3% Yb3+ ion doping concentration and a 4$\times$4$\times$30 mm3 size, 1% Yb3+ ion doping concentration crystals were used for the first and the second amplifier stages respectively. To minimize nonlinear effects and operate at fluence levels below the damage threshold of amplifier optical elements, quite large beam diameters were used: 450 $\mathrm {\mu }$m beam diameter in the first stage and 800 $\mathrm {\mu }$m diameter in the second stage.
The compressor design was based on a single transmission grating aligned at Littrow angle of incidence. Four pass transmission through the grating was realised by folding the beam path twice. The compressor was designed to support 8 nm bandwidth and featured an overall efficiency of $\geq$ 89%.
3. Results and discussion
3.1 Amplification
The high energy laser system operation regime yielded the total maximum pulse energy of 2.2 mJ and 11.7 mJ corresponding to 12.9% (170 W pump power) and 32.3% (290 W pump power) amplification efficiency at the output of the first and the second Yb:YAG amplifier stages respectively. The system featured excellent short term output pulse energy stability $\Delta$E $\leq$ 0.25% RMS, measured over 20 s. The output pulse energy was measured as a function of the input pulse energy at a constant pump power (170 W and 290 W respectively) for both stages and is presented in Fig. 2. The first amplifier stage is operated at low saturation regime yielding high gain, whereas the second amplifier stage is more saturated. While the depolarization losses in the first amplifier stage were moderate ($\approx$ 5%), the Yb:YAG crystal of the second amplifier stage was affected by thermally induced stress more significantly, which resulted in 1.4 mJ (12%) depolarization losses.
Fig. 2. Total output pulse energy dependency on the seed pulse energy in (a) the first amplifier stage and (b) the second amplifier stage. Experimental data compared to numerical simulation data.
Numerical calculations were performed to analyze the prospects for further scaling of the output energy in the end-pumped geometry. The theoretical model is based on a steady state solution of the rate equations for a quasi-three level active medium and semi-analytical solution to the steady-state heat equation [35–37]. Thermal lensing as well as the dependence of absorption and emission cross-sections on crystal temperature were accounted for in the model. The propagation of signal is based on the Fourier transform method whereas pump propagation is described with the ABCD matrix method [37]. To account for depolarization in the second amplifier stage, the signal wave was split into two orthogonal electric field components, which were used during calculations to perform depolarization losses analysis. This theoretical model was previously verified in a similar two pass Yb:YAG amplifier setup operated at 1 MHz pulse repetition rate [37]. The results of numerical simulations match the experimental data reasonably well. The mismatch between experimental and numerical simulation data for the output pulse energy is < 5% for the first amplifier stage and < 15% for the second amplifier stage and can be explained by the discrepancy in parameter values between the model and experiment. Based on the available pump power and accounting for the laser damage threshold, $\approx$ 150 W average power at the output of the second amplifier stage can be reached, which will be the goal of our future experiments.
3.2 Depolarization compensation
A set of spatially variable wave plates (Workshop of Photonics, Lithuania) was used to reduce depolarization losses in the second amplifier stage. The wave plates featured parabolic retardance profile with maximum retardance values of $\mathrm{\lambda}$/2, $\mathrm{\lambda}$/4, $\mathrm{\lambda}$/8, $\mathrm{\lambda}$/16, $\mathrm{\lambda}$/32 at radial coordinate R = 1.5 mm and 1030 nm wavelength (Fig. 3). 3 mm thickness fused silica substrates were used to manufacture the spatially variable wave plates, which were coated with anti-reflective coating at 1030 nm wavelength after the fabrication process.
Fig. 3. (a) Picture of a spatially variable wave plate and (b) retardance profile of a SVWP plotted against the intensity profile of an arbitrary laser beam.
A SVWP having the retardance value of $\mathrm{\delta}$ = $\mathrm{\lambda}$/2 performed with the highest depolarization compensation efficiency and enabled reduction of the losses from 12% to 5% (Fig. 4). The SVWP was placed as close as possible to the input face of the active element between the dichroic mirror and the high reflectivity mirror. This position, which we called the compensation plane, was chosen for several reasons: 1) to avoid affecting or introducing losses to the pump beam by not placing the SVWP in the path of the pump beam, 2) to minimize the effect of diffraction as much as possible and 3) to avoid potential ghost beams generated by reflections from the SVWP if the element was placed too close to the amplifier crystal. The input (measured) and output (calculated) 1/e2 level beam diameters at the compensation plane were $\approx$ 900 $\mathrm{\mu}$m. The placement of the SVWP inside the optical layout is important due the fact that the actual retardance introduced to the beam that is passing through the element depends on the beam diameter. This is advantageous as it allows the experimenter to adapt to changes in the amplifier without making another SVWP element. Taking into account the 900 $\mathrm{\mu}$m beam diameter and the maximum achieved total output pulse energy, F = 3.8 J/cm2 energy density was reached at the compensation plane. This result demonstrates the suitability of directly written optical elements for high energy operation as no apparent degradation of the SVWP element was noticed during the experiment.
Fig. 4. The dependency of depolarized signal energy and depolarized signal fraction on seed pulse energy in the second amplifier stage. The total pump power was fixed at 290 W during the experiment.
Numerical simulation output was similar to the experimental data resulting in 13% uncompensated depolarization losses and 6% losses when using $\mathrm{\lambda}$/2 SVWP. Optimal depolarization compensation in the model was achieved by using a $\mathrm{\lambda}$/3 SVWP, which yielded 0.61% losses. To analyse the compensation mechanism further, we have evaluated birefringence, which was introduced to the signal beam by a single pass through the second amplifier stage as shown in Fig. 5. The birefringence term was evaluated using the theoretical considerations presented in [38]. Firstly, tangential and radial refractive index changes have been calculated using the dependency of the thermal expansion coefficient on temperature reported in [39]. Then, the phase difference between the two orthogonal electric field components can be evaluated according to [34]. In literature it is often estimated that the phase difference has a parabolic distribution over the cross-section of the active medium. However, simulations allowed us to conclude that the retardance can be characterized with higher accuracy by an 8th order parabolic function (odd terms set to zero, Fig. 5), which explains the residual depolarization losses both in simulation and experimental data. This result will allow us to optimize the compensation and achieve near zero depolarization losses in the future.
Fig. 5. Numerically simulated cross section of retardance introduced by (a) the second stage amplifier provided at the crystal output and (b) the compensation plane. Signal beam profiles at respective planes (theoretical model output) and calculated retardance profiles of depolarization compensators (SVWPs) are provided for reference.
3.3 Spectral and temporal characteristics
The spectra of amplified pulses were measured using a high resolution optical spectrum analyzer (Yakogawa AQ6370D). The output pulse spectral width was limited by the gain bandwidth of Yb:YAG active medium. It was reduced to $\Delta \mathrm{\lambda}$FWHM = 1.78 nm after the first amplifier stage and $\Delta \mathrm{\lambda}$FWHM = 1.31 nm after the second amplifier stage at maximum signal output power. The spectra corresponded to 650 fs and 900 fs transform limited pulse duration respectively. After compression, second harmonic frequency resolved optical gating (FROG) method was employed to inspect the output pulses of the second amplifier stage. Compression down to 1 ps was observed with reasonably good pulse contrast of 87.5 % compared to the Fourier transform limited pulse shape characterized by the second stage output spectrum depicted in Fig. 6(a).
Fig. 6. (a) The spectra of the fiber seed laser, the first amplifier stage output signal and the second amplifier stage output signal. (b) Second harmonic FROG measurement result of the second amplifier stage output pulse compared to the Fourier transform limited pulse characterized by the second stage output spectrum in (a).
3.4 Beam quality
Measurements to characterize the output beam quality parameter M2 were performed according to the ISO standard 11146. The output beam quality after the first amplifier stage remained close to ideal M2 = 1.05. However, after the second stage it was affected by thermal stress of the active medium and saturation of amplification. As a result, the beam quality parameter M2 increased to 1.3 (Fig. 7). Simulation of the beam evolution after a focusing lens (f = + 250 mm) at the output of the second amplifier stage was performed and showed good qualitative agreement with the experimental data. (Fig. 8). It is apparent that the thermal effects caused mode distortion and asymmetry (Fig. 8) to the output beam, which is not represented by the beam quality parameter well enough as it retained relatively close to diffraction limited value of 1.3. While a flat-top beam profile combined with relay image transfer could even be beneficial to OPCPA applications due to increased efficiency, Gaussian mode is preferred in many industrial applications, where the ability to clearly define the beam intensity distribution at the focus is highly desirable. Therefore, spatial filtering by using a hard circular aperture was used to reduce the M2 parameter of the second stage to 1.07 with reasonable losses of 8% (Fig. 9). It was also shown that M2 $\approx$ 1.02 can be reached at a cost of higher losses of 18%.
Fig. 7. Beam quality measurement results for (a) the first and (b) the second amplifier stage outputs. Insets - far field beam profiles.
Fig. 8. Qualitative comparison of the system output beam profile evolution after focusing lens. Experimentally measured beam profiles are depicted above the result of numerical simulation. Distance to the focusing lens is provided for reference, the profile size is scaled for convenience.
Fig. 9. Beam quality measurement result after spatial filtering at the second amplifier stage output. Inset - far field beam profile.
4. Summary
We have built a 100 W level CPA based picosecond laser system capable of delivering record high energy in an end-pumped rod-type Yb:YAG amplifier geometry while operating at room temperature. The system delivered 9.1 mJ energy 1 ps duration pulses and 91 W average power at 10 kHz repetition rate at the output of the pulse compressor. It featured beam quality parameter M2 value of 1.3, which was improved to < 1.1 by using a standard spatial filtering technique. This result is a considerable improvement over similar systems that are currently being developed [19,22,24]. The beam quality improvement is facilitated by good thermal management of the active media and pumping at zero phonon line (969 nm), which reduces the overall heat deposited into the amplifier crystal due to smaller quantum defect.
Depolarization compensation by the use of a spatially variable wave plate (SVWP) proved to be a robust method that can successfully be used for both high energy and high power applications. A SVWP was used to reduce the depolarization losses in the second amplifier stage by a factor of 2.4 down to 5%. The experimental results were reproduced with good quantitative and qualitative agreement in a theoretical model of a two-pass end-pumped Yb:YAG amplifier. Further calculations allowed us to determine the necessary conditions for improvement of compensation by optimization of the magnitude and shape of the birefringence pattern of a SVWP. The major advantage of such compensation method is that the losses are returned back to the signal beam rather than filtered out, which leads to increased optical to optical amplifier efficiency. Moreover, the method is not limited to end-pumped rod-type amplifier and can be applied regardless of amplifier geometry or the material used for amplification as long as the birefringence of the amplifier can be accurately described and opens up a path to increase the efficiency of high average power laser systems.
Funding
Mokslo, Inovaciju ir Technologiju Agentura (01.2.1-LVPA-K-856-01-0027).
Acknowledgment
The authors would like to thank Orestas Ulčnas and Workshop of Photonics for the manufacture of spatially variable wave plates.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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