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For pumping multipetawatt Ti:sapphire laser facilities we developed a compact repetitively pulsed laser based on neodymium phosphate glass with pulse energy of 220 J, pulse repetition rate of 0.02 Hz, beam diameter of 43 mm, aperture fill factor of 0.8, and FWHM pulse duration of 30 ns. The phase distortions of laser radiation were compensated by optical phase conjugation via stimulated Brillouin scattering. The depolarization was reduced to 0.4% using linear compensation methods. The beam quality was 2.5 x diffraction limit (150 µrad).
© 2014 Optical Society of America
1. Introduction
Since the creation of the first ruby laser in 1960, enhancement of laser peak power has been one of the most important tasks in quantum electronics. Petawatt lasers with peak power up to 1015 W are the most powerful lasers to date [1–3]. A relatively low energy of several tens of Joules in these lasers is concentrated in a very short pulse of several tens of femtoseconds. Petawatt facilities are based on the principle of Chirped Pulse Amplification (CPA) implemented in 1985 [4]. CPA is a technique that permits stretching a pulse by a factor of about 104 and more due to linear frequency modulation (chirping), reducing the radiation intensity dramatically. Then, the stretched pulse is amplified in an active medium, undergoes dispersive recompression (the process reverse to chirping), and hence becomes short again, spectrally limited in a perfect case. The resulting intensity is increased by orders of magnitude.
There are several projects worldwide aimed at further enhancement of the peak power of laser radiation and advance to the multipetawatt range (peak power of order 10 PW) [5–11]. These projects may be conventionally classified into 3 types according to the used amplifying medium: i) neodymium glass (Nd:glass); ii) Ti:sapphire (titanium doped corundum Ti:Al2O3); and iii) DKDP crystals (deuterated potassium dihydrophosphate KD2PO4) with the use of the principle of parametric amplification. In systems of the second and third types Ti:sapphire pumping or parametric pumping of DKDP crystals will be performed by the second harmonic radiation of Nd:glass laser (the wavelength of 527 nm). Thus, Nd:glass laser amplifiers are an integral part of all multipetawatt laser facilities under construction.
The principal advantage of Nd:glass as compared to the other known laser media is a possibility to produce active elements with large volume and aperture that combine high optical quality and high level of stored energy. This enables operation at relatively low laser field intensities (below laser damage threshold) up to kilojoule energies in pulses of nanosecond duration. This energy is demanded for implementing multipetawatt projects. However, low heat conductivity of glass and high heat release in the active elements caused by pumping by pulsed flash lamps limit the pulse repetition rate in these systems substantially. In all available Nd:glass lasers with pulse energy of several hundred Joules, the pulse repetition rate is about 1 pulse per hour, which is determined by the time needed for the active elements to be cooled, after which thermally induced effects may be neglected. As a consequence, in all multipetawatt projects the expected pulse repetition rate does not exceed a few pulses per day, which greatly reduces the efficiency of research and limits practical applications of multipetawatt lasers due to the low rate of obtaining experimental data. An increase of pulse repetition rate in such facilities as a result of suppression of thermally induced radiation distortions is a topical problem to date. Ti:sapphire systems are the most promising in this respect, as they are pumped by an Nd:glass laser with the energy much less than in the systems where Nd:glass is used directly for chirped pulse amplification, on the one hand, and pump pulse duration may be much longer than the duration of the pump pulses of a parametric amplifier of chirped pulses, on the other hand. In the latter case there is a strong limitation. As a parametric amplifier does not store energy in the form of population inversion, the pump pulse duration must be comparable with the duration of the amplified chirped pulse – of order 1 ns. In Ti:sapphire systems pump pulse duration may be several tens and even hundreds nanoseconds, which makes development of a repetitively pulsed source of such radiation easier.
It is important to note that in 2012 the researchers at the French company Thales built the Ti:sapphire laser BELLA [12] generated 1 PW pulses with a repetition rate of 1 Hz. The unique pulse repetition rate was obtained thanks to using Nd:YAG crystals instead of Nd:glass. The present day technologies do not permit growing Nd:YAG crystals with a diameter more than 20 mm with high optical quality, thus restricting stored energy in one amplifier to 10-20 J. A great number of such amplifiers placed in parallel is demanded for creation of a petawatt facility (i.e. the BELLA laser uses 12 separate GAIA-HP pump lasers each delivering 16 J at the second harmonic or 24 J at the fundamental; GAIA-HP achieves the output energy by polarization combining of two separate amplifier legs). Thus, further scaling seems almost impossible, because extensive increase of the number of separate channels of Nd:YAG amplifiers is not efficient. Active elements with stored energy of several hundred Joules are demanded. Currently, such elements can be fabricated from neodymium glass only.
Nowadays the development of kilojoule class Nd:glass lasers operating with the 1 shot per 1 minute repetition rate is an urgent problem worldwide. One of the main preferable geometries of active elements is the slab geometry [10]. This is due to the ability to create slabs of almost any size, as well as a large ratio of surface area of the slab to its volume, which greatly increases the efficiency of heat removal from the bulk of the active medium. However, significant disadvantages of slabs are the complexity of the amplifier design, their large size, strong optical distortions of laser radiation, difficulties when aligning several amplifiers. All these points ultimately decrease the scalability of the setup. In our opinion, rod active elements also have good prospects. The optical quality of rods is generally much higher than that of slabs. Rod amplifiers are much more compact and easy to adjust. Recently, Nd:glass rods of a very large size – up to 150 mm in diameter – have become available [13]. Each of such active elements stores more than 500 Joules of energy. But up to date only rods of small diameter (less than 20-25 mm) are used in repetitively pulsed Nd:glass lasers [14,15]. As a consequence, the pulse energy in such systems is low. It is at the level of several tens of Joules at a pulse repetition rate of 0.1 Hz. The possibility of using large aperture (up to 100 mm in diameter and more) Nd:glass rod amplifiers in regimes of 1 shot per 1 minute or less remained unclear for a long time.
A fundamental limitation in increasing pulse repetition rate is fracture of active elements when the threshold of allowed thermally induced elastic stresses is exceeded. At smaller heat loads no breakdown occurs yet, but distortions of polarization and of radiation phase front play a significant role. Such repetitively pulsed regimes of operation of large-aperture Nd:glass rod laser amplifiers were investigated in [16–18]. In particular, in [16,17] it was shown that the amplifiers with neodymium phosphate glass active elements 45 to 100 mm in diameter developed by the team of the Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS) store 110 to 280 J energy in one pump pulse in the form of population inversion and have a fivefold margin to thermomechanical damage for the interval between the pump pulses from 1 to 2.5 minutes, respectively.
The goal of this work was creation of an Nd:glass laser with the pulse energy of several hundred Joules in one channel for pumping high-power Ti:sapphire chirped pulse amplifiers of the multipetawatt facility operating with a record pulse repetition rate of 1 pulse per minute. The preliminary results obtained in the experiments on the built laser were published in [19]. Here we present a more detailed description of the performed research and its results.
2. Laser layout
A schematic diagram of the used laser is shown in Fig. 1(a). It comprised a front end system, a system of formation of space-time radiation structure, and a power amplification cascade. The front end system generated relatively low-energy pulses of high optical quality with a stable space-time structure. An Nd:YLF laser with the radiation wavelength (1053 nm) almost coinciding with the wavelength of Nd:glass amplification (1054 nm) was used for the front end. The laser consisted of a master oscillator based on an Nd:YLF crystal with a diameter of 5 mm and active part length of 75 mm (1% concentration of Nd3+ ions) and a two-pass amplifier containing an Nd:YLF crystal with a diameter of 6 mm and active part length of 60 mm (1% concentration of Nd3+ ions). The laser scheme was described in [20]. The front end provided stable generation of pulses with FWHM (full width at half maximum) duration of 30-35 ns, energy up to 150-170 mJ, and 1 Hz repetition rate. The radiation was fed to the power cascade through the system of beam shaping – the input spatial filter ISF that will be described in section 3 of this paper [a detailed scheme is given in Fig. 1(b)]. After that the beam passed through the Faraday isolator FI consisting of two polarizers, a half-wave plate and a Faraday rotator with a magnetoactive TGG crystal (terbium gallium garnet) 18 mm in diameter. The Faraday isolator transmitted 95% of the radiation of horizontal polarization and removed from the system the backward-directed radiation from the power amplification cascade with the isolation degree of 5⋅103. After the Faraday isolator the beam was expanded by means of a Kepler telescope T, whose lenses had focal distances of 425.6 and 1291.9 mm. A pinhole with a diameter of 0.63 mm (11 diffraction limits) made in aluminium foil was placed in the telescope waist. Note that the focal waist was not in vacuum, it was in air under normal conditions. This peculiarity will be discussed in detail in section 7. On passing the telescope, the beam with a diameter of 43 mm was forwarded to the two-pass four-cascade amplifier (power amplification cascade) with a phase conjugate (PC) mirror (see sections 4-7). The whole laser system occupied only one and a half of an optical table (2700 mm x 1000 mm).
Fig. 1 (a) Schematic diagram of the laser. Nd:YLF – front end, ISF – input spatial filter, FI – Faraday isolator, P – polarizer, M – mirrors, T – telescope, R90 – quartz polarization rotators by 90 degrees, FR – Faraday rotator, SBS – cell providing phase conjugation due to stimulated Brillouin scattering, L – lens, A45 – amplifiers with 45 mm aperture. (b) Scheme of input spatial filter. P1, 2 – polarizers, AD – apodizing diaphragm; focal lengths of the used lenses (F1, 2, 3) and diaphragm diameters (d1, 2, 3, 4) as well as the distances l1, 2, 3 are listed in Table 1.
3. Beam shaping at the power amplification cascade input
The radiation injected into the power amplification cascade must meet definite requirements such as stable propagation direction, invariable phase front (no pronounced divergence fluctuations), preset invariable transverse distribution of optical field intensity. High heat release in active elements of the master oscillator does not allow, as a rule, to fully satisfy these requirements. Radiation with needed space structure at the input of the power Nd:glass amplification cascade built by our team was obtained with the aid of an input spatial filter (ISF) described below in this section. The design of such a filter was developed in [20].
The ISF scheme is presented in Fig. 1(b). The filter consisted of a collecting lens (with a focal length F1), pinhole line (diaphragms d1, d2 and d3), expanding Galilean telescope (lenses F2 and F3) and apodization node which included two polarizers P1 and P2, apodizing diaphragm AD and conventional diaphragm d4. The ISF parameters are listed in Table 1.
Table 1. Parameters of the input spatial filter (dimensions are given in mm)
Lens F1 focused the input radiation into the first pinhole (d1). The pinholes were chosen so that, on the one hand, the beam structure at the output of the pinhole line should be weakly sensitive to fluctuations of intensity and phase distribution in the input beam and, on the other hand, the transmission coefficient of the pinholes should not be too small (of order 0.8). The focal distance F1 was taken to be rather large to exclude “shielding” of the pinholes by plasma that could be formed at their surface if the radiation energy density exceeded a certain threshold value.
The measured dependence of the energy at the output of the pinhole line on the energy at the input for laser pulses with FWHM duration of 30 ns is shown in Fig. 2. The effect of laser radiation shielding by plasma manifested by reduction of the transmission coefficient of the pinhole line was insignificant in the energy range up to 170 mJ (Fig. 2).
The pinhole line suppressed fluctuations of the wave front curvature that were presented in the radiation of the master oscillator. The radiation at the output of the pinhole line had diffraction limited divergence. On passing the pinhole line the radiation propagated through the expanding Galilean telescope and arrived at the apodizing AD and conventional d4 diaphragms located between two polarizers P1 and P2 (Fig. 2). The apodizing diaphragm was a spherical plano-convex lens made of crystalline quartz oriented at an angle of 45 degrees to the direction of polarization orientation. To compensate for the divergence the plano-convex lens had optical contact with the lens of equal optical power made of fused silica. The difference of phase incursions of the ordinary and extraordinary waves on the axis of the apodizing diaphragm was 2π, and π at a given distance rd from the axis (see Table 1). The polarizer P2 converted the polarization modulation to the intensity modulation by the law
where Ta is the transmission coefficient of the apodizing diaphragm-polarizer pair. The diaphragm d4 cut the central circle from the ring structure. In this way the apodization node formed a beam having radius rd with zero field and its derivative at the boundary. The intensity distribution in the beam at the ISF output is shown in Fig. 3(a). The aperture fill factor (the ratio of the beam intensity averaged over the aperture to the peak value) was 0.4. The measured far field distribution of the beam is presented in Fig. 3(b). It is clear from the figure that the beam divergence was close to the diffraction limit equal to ϑdif = 0.85λ/rd = 0.13 mrad in the case under consideration. The total transmission coefficient of the ISF was 10-15%. The ISF decreased fluctuations of the radiation propagation direction of the front end by a factor of 12.Fig. 3 Transverse radiation intensity distributions after the input spatial filter in the near (a) and far (b) fields.
The intensity distribution of laser radiation at the ISF output may be represented analytically by the following formula
where t and r are the temporal and radial coordinates, respectively, I0 is the peak intensity in the laser pulse, t0 is FWHM pulse duration, and 2rd is beam diameter at zero field.4. Nd:glass amplifiers
The power amplification cascade of the laser [see Fig. 1(a)] comprised four two-pass A45 Nd:glass amplifiers placed in series and a nonlinear optical mirror performing optical phase conjugation via stimulated Brillouin scattering (SBS) [21]. Despite the fact that the total small signal gain in the channel after two passes was of order 1.7⋅106, the amplifiers A45 were not self-excited due to the threshold character of the SBS mirror. After two passes through the Faraday rotator FR placed in front of the SBS cell the beam polarization was rotated by 90 degrees as a result of which the radiation was reflected by the polarizer P to the output of the system. The Faraday rotator FR was located in the convergent beam. It was same as the FR used in the optical isolator at the ISF output, the TGG magnetoactive element also had a diameter of 18 mm.
The active elements of the A45 amplifiers were made of phosphate Nd:glass KGSS-1621 (Nd3+ ion concentration 8.6⋅1019 cm–3), shaped as rods with a diameter of 45 mm and length 320 mm (250 mm of which were the pumped region) and cooled by a distilled water flow with the temperature stabilized to an accuracy of 0.2 °C. The flow rate was 1 liter/min, which corresponded to 15 full cycles of water replacement in a tube with active element per 1 minute. The exponential relaxation time of the rod temperature was 5.2 min [17] (this time also characterizes the establishment of steady state temperature distribution). The end surfaces of two active elements closest to the output were made antireflective. The active medium in each amplifier was pumped by six xenon gas-discharge IFP-5000-2 lamps cooled by air. The lamps were arranged along the lateral surfaces of the active elements. The laser heads had involute shaped reflectors [22].
The power supply circuit for the lamps is shown in Fig. 4(a). Each lamp was inside an independent discharge circuit, the parameters of which (capacitance C and inductance L) are also presented in Fig. 4(a). The capacitors were charged to 3.2 kV. The discharge current and active element luminescence pulse shapes are plotted in Fig. 4(b). The small signal gain G0 in one A45 amplifier was equal to 6, its spatial distribution is depicted in Fig. 4(c). The characteristic features of the amplifier operation with a pulse repetition rate of 0.02 Hz and more were described in [17].
Fig. 4 (a) Power supply circuit in A45 amplifiers; (b) oscillograms of luminescence pulse in A45 amplifier and of discharge current in lamps, as well as critically damped current pulse corresponding to the boundary of periodic and aperiodic discharge mode [23]; (c) small signal gain distribution in A45 amplifier (the white curve maps the cross-section).
Figure 4(b) also shows a critically damped current pulse corresponding to the boundary of the periodic and aperiodic discharge (borrowed from the book [23]). This critically damped regime is optimal in terms of lamp resource and efficiency of energy transfer from capacitors. The current pulse oscillogram obtained in experiment was in a fairly good agreement with the optimal curve, indicating a correct choice of discharge circuit parameters. The maximum value of the parameter of lamp load fex = W/Wex (the ratio of the energy W transferred to the lamp to the explosion energy Wex [23]) was 0.306, which gave the lamp endurance N > fex–8.5 ≈23500 bursts [23]. It was quite acceptable for the operation with a pulse repetition period of 1 min.
5. Compensation of phase and polarization distortions
The thermally induced radiation distortions (depolarization and thermal lens) in A45 amplifiers were compensated. The depolarization was compensated for by using quartz polarization rotators by 90 degrees (14 mm thick SiO2 crystals cut normally to the crystallographic Z-axis) placed between the active elements [Fig. 1(a)], as well as a Faraday rotator and a PC-mirror. A Faraday rotator placed in front of an SBS cell is preferable to a quarter-wave plate that ensures decoupling, but does not reduce depolarization in the amplifiers that has not been compensated by the quartz rotators [24]. The integral depolarization factor γ was 25-30% per one pass through one amplifier, 2-3% per one pass through four amplifiers with two 90° rotators, and not more than 0.5% in two passes through four amplifiers, which was an illustrative evidence of the effective usage of both quartz rotators and PC-mirror with Faraday rotator placed in front. (The integral depolarization factor γ is the ratio of the energy of depolarized component to the total energy of laser pulse at the output of the depolarizing optical element.)
The phase distortions were reduced due to optical phase conjugation. The SBS cell was 1 m long and was filled with high purity perfluorooctane (C8F18) studied in [25]. Prospects of using media based on fluorocarbon liquids for SBS of laser radiation with high-energy pulse were first demonstrated in [26]. Later the authors of that work achieved the pump pulse energy of 73 J (FWHM pulse duration of 13 ns), at which phase conjugation at SBS still occurs without pronounced distortions and optical breakdown (see [27]). The advantage of these media as compared to other SBS media is high laser damage threshold, low absorption in the visible and near IR range (given a properly prepared SBS cell), and high threshold of other nonlinear optical effects (Raman scattering and self-focusing). However, for effective realization of these advantages dispersive [26] and dissolved molecular impurities [25] must be removed from such SBS media. The used perfluorooctane was highly purified by an efficient distillation method performed in [25]. The content of solid suspended particles of submicron size didn’t exceed 1 cm–3. The concentration of hydrogen-containing impurities was about 10−5 wt%. It is also worth noting that perfluorinated liquids are safe for users [28].
In our experiments the measured SBS threshold for 30 ns pulses was 5.7 mJ. The radiation was focused into the cell by a lens with a focal distance of 1.7 m. The reflection coefficient of the PC mirror for laser pulses with the energy up to 16.5 J was above 95%.
The theoretical and experimental curves for the laser pulse energy at the input to the PC cell (ESBS) as a function of the energy at the input to the channel with A45 amplifiers (Ein) are plotted in Fig. 5(a). The measured values of the transmission coefficient of the cell (tSBS) are presented in Fig. 5(b). For pulses with the energy > 1 J, the fraction of the radiation passing past the focal waist did not exceed 5%. No laser damage of perfluorooctane was observed despite high energy in the pulses focused into the PC cell. Our estimates predicted the radiation intensity in the focal waist up to 5·1012 W/cm2, whereas the damage threshold is of order 1011 W/cm2 [25]. This controversy is explained by the fact that the laser pulse duration (30 ns) was much longer than the hypersound decay time in the used perfluorooctane C8F18 (0.78 ns [26]), and the SBS threshold was exceeded many times. Consequently, a volumetric acoustic grating rapidly formed at the leading edge of the laser pulse screened the focal waist and a substantial portion (more than 95%) of the laser energy was reflected near the cell input, while the intensity of the radiation that reached the focus did not attain the threshold value. The impact of screening at SBS in fluorocarbon liquids on the damage threshold and its dependence on laser pulse duration was discussed in ample detail in [26].
Fig. 5 (a) Radiation energy at the SBS cell input (ESBS) versus energy at the input to the channel with A45 amplifiers (Ein); (b) experimental curve for the transmission coefficient of radiation passing through SBS cell (tSBS) versus energy at its input.
It is worth noting that in our experiments the screening effect had no significant impact on the temporal pulse shape (see section 6) because the pulse duration was much longer than the time of its propagation in the SBS cell. Thus, the well known condition for SBS pulse compression [29] (L ≥cτp/2, where L is the interaction length in SBS medium, c is the light velocity in vacuum and τp is the FWHM pulse duration) was not satisfied and as a result notable pulse shortening was not observed.
6. Parameters of output laser radiation
The theoretical and experimental curves for the laser pulse energy at the laser output Eout as a function of pulse energy at the front end Ein (at the input of the power Nd:glass cascade) are plotted in Fig. 6. The maximum output energy was 220 J with pulse repetition rate of 0.02 Hz. The intensity distributions of the beam in the near and far fields at the output of the setup are plotted in Figs. 7(a) and 7(b) for vertical laser beam polarization. The beam had a rather flat top, and the aperture fill factor was 0.8. The root mean square fluctuation of the output beam energy was 8%. The propagation direction instability was less than ± 5 µrad.
Fig. 6 Pulse energy at the laser output Eout and integral depolarization factor γ in single shots and in steady state at the pulse repetition rate of 0.02 Hz plotted versus pulse energy at the front end Ein, after the input spatial filter.
Fig. 7 Transverse intensity distribution of the output beam in the near (a) and far (b) fields and intensity distribution of the depolarized component (c). Arbitrary units are different for each plot.
The angular energy distribution function in the beam
is plotted in Fig. 8 (curve 2) by the experimental intensity distribution in the far field [see Fig. 7(b)]. Here EΣ is total laser pulse energy, E(Θ) is the energy of the radiation propagating within dihedral angle Θ with the edge parallel to the electric field vector in the laser beam (direction of the vertical in Fig. 7). This method of determining beam quality is called energy-in-the-basket technique.Fig. 8 Energy distribution function in the beam in dihedral angles of divergence. Curve 1 – beam with plane phase front at the laser output (calculation), curve 2 – experimental beam at the laser output (Fig. 7), curve 3 – beam in the scheme without compensation of thermally induced polarization and phase distortions after one passage through four A45 amplifiers (calculation).
According to the plot in Fig. 8, about 87% of the laser energy is propagated within dihedral diffraction angle 2Θdif of 120 µrad, and 92% of energy within 2.5Θdif (150 µrad). For comparison we present the calculated dependences FE(ΔΘ), one of which (curve 1) corresponds to the beam with measured intensity distribution in the near field [Fig. 7(a)] and a plane phase front (a diffraction limited beam), the other one (curve 3) corresponds to the beam that has passed through four successive A45 amplifies in one direction without compensation of thermally induced radiation distortions. In the latter case, the distributions of thermally induced phase incursions of radially and tangentially polarized eigenwaves presented in [17] were used in the calculations. The parabolic component of thermally induced lens average over two polarizations was subtracted from those distributions. Hence, curve 3 in Fig. 8 corresponds to the minimum possible beam divergence that may be obtained in the laser without compensation of thermally induced polarization and phase distortions of radiation. According to Fig. 8, this divergence is 8.3 diffraction limits (for FE = 92%). Note that astigmatism (the difference in the optical power of thermal lens for radially and tangentially polarized radiation) played a decisive role when plotting theoretical curve 3 in Fig. 8. In the laser scheme presented in Fig. 1(a) this astigmatism is compensated for by means of polarization rotators R90 and FR. Theoretically, it may be 100% compensation; in practice, however, there are many factors that cannot be taken into consideration in theory but which also lead to deterioration of laser radiation quality that is comparable with astigmatism. These include incomplete identity of the used amplifiers, inaccurate rotation of the radiation polarization at different points of the laser beam cross-section, the influence of aberrations introduced by imperfect optical elements, laser beam refraction in heated active elements, and diffraction of radiation. Optical phase conjugation minimizes the influence of the factors enumerated above significantly and provides a rather high-quality laser radiation at the output.
The radiation of depolarized component with the energy of about 0.4% of the output energy Eout (see Fig. 6) was removed from the laser scheme by means of the Faraday isolator [Fig. 1(a)]. The intensity distribution of this beam is shown in Fig. 7(c). The 6-th order azimuthal symmetry stipulated by the use in the laser head of 6 pump lamps is clearly seen in the figure. This imprint is a consequence of the rods illumination non-uniformity together with a small variation of the pump energy from one amplifier to another. As a result the depolarization has not been fully compensated. Note that the integral depolarization factor γ in steady state (Fig. 6) has been measured only in an experiment when Ein was about 5-8 mJ. But the same values could be observed in a whole range of Ein magnitudes because the pump energy of active elements does not change when varying the input energy of laser pulses. Thus the thermal load of active medium stays constant.
The shape of the laser pulse on reflection from the SBS cell (Fig. 9) and amplification in the active elements remained almost unchanged, and was close to the pulse shape of the master oscillator with FWHM duration of 30 ns even at the laser output. Thus, we did not observe shortening of the duration of the output pulse and pronounced sharpening of the leading edge typical for lasers with SBS mirrors and amplifiers operating in a saturated regime [30,31]. According to [32] this is explained by a large ratio of the amplifier saturation energy (50 J) to the SBS threshold energy (5.7 mJ).
The laser radiation after conversion to the second harmonic (the wavelength of 527 nm) may be used for pumping Ti:sapphire crystals in amplifiers of chirped femtosecond pulses. We assessed efficiency of such conversion for the case of a DKDP crystal used as a nonlinear optical crystal for frequency doubling, in which the wave interaction of the first and second harmonic of the first type takes place (ooe phase matching). For frequency doubling of the radiation with the energy of 220 J, beam distribution in the near field, and pulse shape observed in experiment, the doubling efficiency is 80% at exact phase matching (DKDP crystal length being 40 mm). Our estimates show that violation of the phase matching condition associated with laser beam divergence results in a decrease of the doubling efficiency to 64%. If the radiation at the laser output had a plane phase front (the ideal case), then the efficiency would be 76%, i.e., 12% more than for a real laser beam having the quality demonstrated in experiment – see Fig. 7(b). Thus, the radiation divergence at the output of the created laser equal to two and a half diffraction limits slightly constrains the possibility of frequency doubling in a DKDP crystal.
It should be noted that LBO crystals are more suitable for frequency doubling because the nonlinearity in such crystals is about 3 times higher than in DKDP ones. Also, LBO crystals have a higher laser-induced damage threshold and a much broader angular bandwidth. For example, in the case considered above one can achieve the same efficiency of second harmonic generation (80%) at perfect phase matching (neglecting the phase velocity mismatch due to beam divergence) as in 40 mm thick DKDP crystal when using 14 mm long LBO crystal. The angular bandwidth in such a crystal is almost 40 times greater [33]. As a consequence, for a real laser beam the loss in the second harmonic generation efficiency determined by the beam divergence will be only a few tenths of a percent. Modern progress in the growth technology of large aperture LBO crystals [34] opens up great opportunities for their use in the laser systems considered above.
Note that radiation frequency doubling is not a difficult problem if there is a stable source of radiation of high diffraction quality at the fundamental wavelength. The effective (efficiency of order 90%) frequency conversion of neodymium laser radiation to the second harmonic is outside the scope of the present work. In particular, the developed setup had no system for formation of flat-top pulses needed for attaining high-efficiency second harmonic generation. It is worth noting, however, that technically production of such pulses at the output of the system with a duration of several tens of nanoseconds is quite possible and has been successively realized [34].
7. Features of optical isolation of the front end from the power amplification cascade
The Faraday rotators used in the laser had a relatively small aperture of 18 mm. These elements are rather cheap, efficient and available commercially, whereas the rotators intended for transmitting beams with a diameter more than 30 mm are unique and costly [35]. The Faraday isolator is intended to protect optical elements from the depolarized radiation component coming exactly backwards from the power amplification cascade as a result of the phase conjugation. However, because of its small aperture the Faraday isolator itself runs the risk of optical damage. In our experiment, the energy of the depolarized component at the amplifier output was about 1 J (Fig. 6), which with allowance for strongly nonuniform distribution [Fig. 7(c)] may lead to TGG crystal breakdown. To avoid this situation a Kepler telescope T [Fig. 1(a)] was used for additional isolation.
As was mentioned above, the distinctive feature of the Kepler telescope T was that the focal waist was in air at atmospheric pressure. The calculations show that a beam with intensity distribution of the form given by Eq. (2), with diameter 2rd = 13.85 mm, FWHM pulse duration t0 = 30 ns, and energy E = 20 mJ, focused by the input lens of the telescope T with focal distance F = 425.6 mm will have the intensity in the waist at pulse maximum Imax = 3.8⋅1010 W/cm2 [, where λ is a wavelength], which is a little less than air breakdown threshold of order 7⋅1010 W/сm2 under normal conditions [36]. Breakdown in gases is a sharp effect. It occurs abruptly with radiation intensity increasing above a certain value.
When the input energy was increased up to 48 mJ, the pulse energy at the telescope output did not exceed 30-35 mJ due to plasma formation in the focal waste caused by the optical air breakdown and “closing” of the waist for radiation transmission. The effect of partial transmission of a laser pulse by the Kepler telescope is demonstrated in Fig. 10. The value of the maximum energy of 30 ns FWHM pulse that can pass through the Kepler telescope obtained in experiment is in good agreement with the above estimate. Pulses with the energy < 25 mJ passed through the Kepler telescope without losses.
The depolarized radiation component with the energy greatly exceeding 30 mJ (see Fig. 6), was scattered in the plasma formed in the telescope waist (as the intensity distribution in the far field strongly differs for the depolarized component from the corresponding distribution of the basic component, the threshold breakdown energy may differ from that presented here several times). Thus, the Kepler telescope T, in addition to the Faraday isolator FI, protected small-aperture elements, including FI, from the depolarized radiation returning from the power amplification cascade.
8. Conclusion
We have created a compact Nd:glass laser with pulse energy of 220 J, pulse repetition rate of 0.02 Hz, beam diameter of 43 mm, and FWHM pulse duration of 30 ns. The beam divergence at the output of the system was 2.5 diffraction limits (150 µrad) and the thermally induced depolarization was reduced from 25% to 0.4%, which was attained with the aid of optical phase conjugation via stimulated Brillouin scattering and linear methods of compensating thermally induced radiation distortions using a Faraday mirror and quartz 90° polarization rotators between active elements. The beam aperture fill factor was 0.8. According to the estimates, the radiation frequency may be doubled without significant restrictions associated with divergence, which opens up an opportunity of using second harmonic radiation for pumping a powerful chirped pulse amplifier based on a Ti:sapphire crystal in a multipetawatt laser facility.
Acknowledgments
The research was done with support from the program of the Presidium of the Russian Academy of Sciences “Extreme light fields and their applications” and the grant program of the President of the Russian Federation for young scientists and postgraduate students engaged in advanced research and development in priority areas of modernization of the Russian economy. Also this work was supported in part by the Ministry of Education and Science of the Russian Federation under contract No.14.Z50.31.0007.
References and links
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