In this talk, we propose and demonstrate the process-oriented adaptive optics (AO) wavefront control method, for optimizing the beam quality in the multi-pass amplifiers. Different from the conventional target-oriented wavefront control approach, the novel method divides the aberration correction process into several steps, to optimize the wavefront quality in time during the courses of the beam's transport and amplification. The experimental results show that the proposed method can effectively prevent the beam quality from worsening and ensure the successful reality of multi-pass amplification, so it has obvious advantages both in efficiency and accuracy over the traditional target-oriented method
© 2017 Optical Society of America
Relay-imaged multi-pass amplifiers have been widely used in laser facilities [1–4], generally speaking, they often work as key power amplifiers in order to realize high gain and efficiency amplification. Relay-imaging achieved with the confocal lens pairs is a distinctive and significative property in high power laser amplifiers. It is used to increase reliability of the amplifiers by minimizing intensity modulations that would increase the probability of optical damage. This kind of amplifiers has a number of advantages: (1) the beam is not restricted by mode volume, the huge energy gain and the desired energy output (joule-level or higher) can be attained; (2) the amplifying process can well preserve the mode of input seed laser, without influenced by mode molding or diffraction effect. However, losing the help of oscillator cavity's mode selection, in the relay-imaged multi-pass amplifiers, static aberrations of optical elements, especially dynamic thermal aberrations of active mediums, can deteriorate the beam quality and prevent the reality of beam transmission and amplification.
In order to compensate for the aberrations, adaptive optics (AO) systems are widely used in the multi-pass amplifiers [5–10]. The AO systems are composed by wavefront sensors, deformable mirrors and controllers. Generally speaking, the wavefront sensors are placed beyond the amplifiers, and the deformable mirrors are installed in the amplifiers [5–7]. In fact, at the beginning, the deformable mirrors are placed outside of the amplifiers , to compensate for optical distortions accumulated in the multi-pass amplification channels. However, with the laser pulse energy increasing, the ranges of dynamic aberrations become bigger and bigger. So this way of arranging for the wavefront to traverse the deformable mirror once, cannot efficiently ensure the good beam quality. Then, the deformable mirrors replace the end mirrors in the amplifiers [5, 6]. In this way, the beam bounces more times by the deformable mirror, the distortions are corrected more times, so the distortion compensation is evenly distributed in multi-passing amplification procedure. Certainly, when two deformable mirrors are employed in the same channel, the aberrations are better corrected [9, 10].
In the conventional methods mentioned above, the AO systems aim at minimizing the overall aberrations in the multi-pass amplifiers, to optimize the wavefront quality of output beam [5–10]. This is called as the target-oriented AO control method. However, with the passing numbers increasing, even if the pulse energy is not very big, the accumulated aberrations can greatly worsen the beam quality, because of increased plasma generation and closure effects within the pinholes in the spatial filters of the amplifiers  and the remove of relay-imaged planes. These problems make that the near-fields of output beam incomplete and the wavefront measurement results inaccurate, which seriously disturb the AO closed-loop correction processes. So in order to solve the problems of optical aberration accumulation in multi-pass amplifiers, a novel wavefront control approach is proposed for the first time. The process-oriented wavefront compensation method divides the aberration correction process into several steps, along with the amplification passing numbers increasing. The experiments demonstrate that this new approach can gradually optimize the wavefront quality and effectively solve the problem of optical aberration accumulation, to ensure the successful reality of multi-pass amplification.
2. The multi-pass amplifier and the problem of aberration accumulation
A schematic diagram of relay-imaged multi-pass coaxial laser amplifier prototype is given in Fig. 1, which is designed to realize a total gain of 104 to attain 1053 nm, 1J/1Hz, ns laser pulses output. This kind of amplifier can be predominately used in several fields, such as the pre-amplifier modules for inertia confinement fusion (ICF) or the pump lasers for chirped pulse amplification (CPA) and optical parametric amplifiers (OPA). It should be noted that in this article we mainly pay attention to the AO system and its control method, the laser system will be detailed in another article.
We briefly introduce the relay-imaged multi-pass amplifier as below. Pulses as short as 1-3 ns are generated in the fiber front-ends running at 1053 nm, then are regenerative amplified to about 0.1mJ and reshaped to top-hat beam profile as the seed light for the multi-pass amplifier. As can be seen from Fig. 1, the seed light, of 16 × 16 mm square area, passes through one polarizer (P1), one half-wave plate (HWP),and one 45-degree Faraday rotator (PR1) in turn. After that, the beam enters the multi-pass amplifier, which consists of one polarizer (P2), one quarter-wave plate (QWP), one Pockels cell (PC), one Nd:glass amplification rod (AMP), two 45-degree Faraday rotators (FR2 and FR3), one 45-degree reflecting mirrors (M2), and two end mirrors (M3 and DM). One of the two end mirrors is deformable mirror (DM). To suppress the effect of self-focusing and amplified spontaneous emission (ASE), mitigate the effect of wavefront profile transforming into intensity variations via propagation effects, and to match the beam areas on gain media and end mirrors, low-pass spatial filters and 4f relay-imaging systems are applied [12, 13]. Here, two 4f relay-imaged telescope pairs are used in spatial filters, each is comprised of two convex lenses (L1 and L2, L3 and L4), one pair with focal lengths of 1200/600 mm (L1 and L2) and one pair with focal lengths of 400/1600 mm (L3 and L4). Two vacuum tubes (VT1 and VT2) ended by optical windows are placed separately between two lens pairs, in order to avoid the air breaking down around the far-field focal points. The two pinholes of the spatial filters both are 20 times diffraction limit. The two pairs of lenses separately resize the beam diameter to 8 mm onto the AMP and 32 mm onto the DM. After multi-pass amplified, the beam returns through the P2, the PR1 and the HWP in turn, then is rejected by the P1. Finally, a beam splitter (BS) intercepts a little part of the output beam and direct it onto the wavefront measurement module. The wavefront measurement module is composed of one pair of lenses (L5 and L6), attenuating filters (AF), and one Shack–Hartmann wavefront sensor (SH-WFS). The pupil aperture on the lenslets of the SH-WFS is matched to be 3.2 mm by the 5:1 relay-imaging telescope (L5 and L6), and the lenslets are in the plane conjugate to the plane of the DM. The beams during the process of multi-pass amplification are all coaxial, nearly using same optics for different passings, so the beams can better utilize the gain medium.
Here, the passing numbers in the amplifier can be adjusted by controlling the beam polarizations, and the transformation of polarizations can well restrain the amplified spontaneous emission (ASE). Simply speaking, the seed beam is p polarization firstly, then after going through the P1, the HWP and the FR1 in turn, it is also p polarization. After entering the amplifier, if the PC is not working, the beam is adjusted to be circular polarization by the QWP, and then passes through the FR2 and the FR3 twice separately, it is also circular polarization. Here, the FR3 is used to compensate for the thermally induced birefringence of the AMP, because after the laser passes the 45-degree Faraday rotators (FR3) for two times the polarization will change 90 degree . After going through the QWP again, it turns to be s polarization, then bounced by the P2, the M2 and the M3 in turn. In this way, one double-pass amplification is finished. If the PC is working as one quarter-wave plate, there is one added half-wave change. In fact, by controlling the power on and off of the PC, the passing numbers of the multi-pass amplifier can be adjusted. For example, before the beam enters the amplifier, if the PC has been powered on by quarter-wave voltage, the laser pulses are only double-pass amplified; if the PC is not powered on at all times, it is four-pass amplified; if the PC is powered off at the beginning, then is switched into power on just after the pulses pass the PC for the second time, and the PC returns to power off just after the pulses pass the PC for the fourth time, the amplifier works under the six-pass amplification. For the same reason, the eight-pass and the ten-pass amplifications are realized, and so on. With the passing numbers increasing and until the needed energy is achieved, the laser beam leaves the amplifying channel in p polarization. Then after passing the FR1 and the HWP, it is changed to s polarization, and rejected by the P1 to leave the whole channel in s polarization finally. Here, via controlling the polarizations and changing the passing numbers of amplification arbitrarily, this kind of amplifiers has the potential to be scaled to more high-energy and high-power laser systems, though the layout is complicated with a lot of polarization multiplexing control devices.
The reasons for aberrations in an amplification chain are manifold. For example, the aberrations result from unachievable perfections of optical components like mirrors, lenses, beam splitters, polarizers or compromises in the optical set-up. However, the largest portion of aberrations results from thermo-optical aberrations. In order to minimize the thermal effect, the 12 × 12 × 150 mm Nd-doped phosphate glass gain media, is quasi-continuously side-pumped by laser diode bars, and is cooled by water circulation running without interruption, through bonding the sides of amplifying media onto a water-cooled heat sink. Heating of the glass rod by the pump diodes, combined with surface cooling, leads to the nonuniform temperature and thermal distortion distributions inside the rod. With the pump powers and the passing numbers increasing, the aberrations accumulate bigger and bigger. The square gain media rod can better be utilized by the square beam, but the pump-induced aberrations are high-ordered , compared with the conventional round rod . After the thermal equilibrium is established under the pumping frequency of 1Hz, the thermal aberrations are roughly stable. The simulation results of the thermal aberrations, when the 8 × 8 mm laser beam passes the gain material once, are shown in Fig. 2. It can be clearly seen that the overall aberrations [Fig. 2(a)] of the square rod medium are consisted of not only defocus [Fig. 2(b)] but also some skirt components [Fig. 2(c)] induced by side-pumping. Whereafter, we have to carefully consider the influence of distortions on the amplifier, especially a large number of roundtrips can significantly change the output beam quality of the amplifier.
Firstly, the low-pass spatial filters in the 4f-configurations are applied to filter the aberrations of high spatial frequency . However, with the aberrations of low spatial frequency accumulating in the process of multi-passing amplification, the sizes of the focusing spots become bigger and bigger. This induces the increased plasma generation and closure effects within the pinholes of 20 times diffraction limit in the spatial filters. The pinhole-passing efficiencies in the spatial filters are shown in Fig. 3, when the laser pulses traverse two, four, six, eight, and ten roundtrips in the amplifier separately. It can be clearly seen that with the passing numbers increasing, the pinhole-passing efficiencies become smaller and smaller. Here, the pinhole-passing efficiencies are decided by the spatial filters just after the pulses are amplified by two, four, six, eight and ten times. It should be noted that after the pulses are amplified for several times, the pulse energies are increased and the pinhole-passing efficiencies are reduced gradually. It is very dangerous because the problems of plasma generation and closure effects within the pinholes become more and more severe. So the transport and amplification processes are seriously influenced by the accumulated aberrations in multi-pass amplifiers.
Secondly, the multi-pass amplifier is set up in such a way that each pass is reimaged via the 4f-configurations [9, 10], to preserve the flat intensity profile in the middle of the gain medium rod and on the end mirrors. Shown in Fig. 4, there are seven planes (the Planes 1-7) which are relay-imaged each other via the three 4f-configurations (L1 and L2, L3 and L4, L5 and L6). At the entrance of the amplifier an aperture defines an object plane (the Plane 1), then it is relay-imaged on to the rod middle plane (the Plane 2) and on to the planes of the end mirrors (the Plane 3 and Plane 4), after outputted by the amplifier the object plane is sequentially relay-imaged on to the output planes (the Plane 5 and Plane 6) and the wavefront measurement plane (the Plane 7).
However, the thermal aberrations will change the positions of the relay-imaged planes, because the thermal lensing effect [7, 14] along the length of gain medium can destroy the relay-imaged relations, even if the middle plane of the gain medium rod is rightly in the position of relay-imaged. The remove of relay-imaged positions can be calculated by the ABCD matrix method. Shown in Fig. 2(b), the gain media rod produces a thermal lens with a P-V aberration of 0.52 μm. Here, the thermal lens of the medium rod can be simply equivalent with a number of lenses. Obviously, shown in Fig. 5, after ten-pass amplification, when there is only one equivalent lens, no movements of relay-imaging positions are brought, and this is commonly adopted [9, 10]; however, when there are two equivalent lenses, the remove of relay-imaged position (of the Plane 5) is 3.7 mm; similarly, the results with three, four, and more equivalent lenses are also shown in Fig. 5, finally the infinitely approaching values (for example, 4.7 mm for the Plane 5) are adopted in the next simulations.
For example, shown in Fig. 6, with the ten-passing amplification process going, the positions of the relay-imaged Plane 2 are removing at all times, from rightly in the middle of gain medium rod at the beginning. The removes of relay-imaged planes induce that the wavefront profiles transform into intensity variations via the diffraction propagation effects.
To sum up, the accumulated aberrations in multi-pass amplification will not only influence the pinhole-passing efficiencies in the spatial filters, but also destroy the relay-imaged relationships in 4f-configuration. These problems make that the near-fields of output beam become strongly deformed and incomplete. For example, the simulated near-field intensity of output beam in the wavefront measurement plane (with a diameter of 3.2 mm) is shown in Fig. 7, after the pulse is ten-pass amplified. So in order to realize the good output beam quality, these problems should be solved.
3. The process-oriented wavefront control method and experiments
Nowadays, many laser systems include adaptive optics for controlling the beam wavefront [5–10], and this technique is used mainly to compensate for the pump-induced thermal aberrations in amplifiers. Shown in Fig. 1, similar with the conventional layout [5, 6], here the wavefront correction is provided by an AO system that includes one deformable mirror (DM), one Shack-Hartmann wavefront sensor (SH-WFS) and one controller. As mentioned above, the DM is positioned as one end mirror in the multi-pass amplifier, it is coupled to the SH-WFS to lock the wavefront toward a reference. Obviously, the best wavefront correction results can be obtained when measuring the final aberrations at the output end of the channel, where the SH-WFS is placed . The wavefront measurement plane (the Plane 7) and the correction plane (the Plane 3) have to be optically conjugated to each other in order to have a linear response between them. To have an optimum correction capability, here we use a unimorph DM with 25 actuators distributed on 5 × 5 grid, with a pitch of 10 mm. The dimension of the DM is 50 × 50 mm and only the central 32 × 32 mm area is used for actual wavefront correction, leaving a ring of actuators outside the optical pupil . The applied voltages on the actuators range from −500V to + 500V, corresponding to a dynamics for wavefront correction of more than 10 μm. The SH-WFS uses a array of 20 × 20 square lenslets, with a pitch of 300 μm and 8 mm focal length. It is well known that this kind of deformable mirrors with discrete actuators can well compensate for low-order aberrations in conjunction with the use of SH-WFS.
In fact, in conventional target-oriented wavefront control method, after calibrating the reference wavefront between the amplifier output position (the Plane 5) and the wavefront sensor position (the Plane 7), the controller will correct the aberration in the amplifier by a one-time adjustment of the deformable mirror based on the aberration target [5, 6]. However, as we analyzed above, after the laser pulses pass through the amplifier several times, the quality of the beam may become substantially degraded because of the accumulated aberrations. For example, in our experiments, the output near-field images in the wavefront measurement plane are shown in Fig. 8, when the amplifier works on double-pass [Fig. 8(a)], four-pass [Fig. 8(b)] and six-pass [Fig. 8(c)] amplification respectively. In fact, for the AO systems, this kind of incomplete and unclear near-field images induces that the wavefront cannot be precisely measured. So the conventional target-oriented AO control method is difficult to implement here. Besides, the beam of degraded quality is intrinsically dangerous, especially when the laser power is high, so it must be avoided during the process of multi-passing amplification. Therefore, for the sake of safety, the experiments are only implemented on the conditions of double-pass, four-pass and six-pass amplifications.
In order to ensure the successful realization of high-quality output beam, the novel process-oriented wavefront control approach is proposed and experimented, through compensating for the aberrations step by step during the multi-passing amplification course. Simply speaking, this is achieved by first performing a loop under double-pass amplification, then after the aberrations are corrected by closed-loop, we switch to four-pass amplification and continue to lock the loop, and so on. So with the passing numbers are raising, the AO wavefront corrections are going on until the final multi-pass amplification is realized. The new approach is detailedly implemented as below.
Shown in Fig. 1, through inserting one plane reflecting mirror (M1) between the P2 and the P3, to turn the laser backwards and exclude the amplifying channel, the reference 1 of the SH-WFS is calibrated; and the reference 2 of the SH-WFS is calibrated with a planar wavefront, which comes from a collimater (the reference light in Fig. 1) in front of the wavefront measurement module. The wavefront compensation is achieved by first performing a convergence with the reference 1 of the SH-WFS, and then with the reference 2, in the stepwise wavefront compensation manner. Besides, the global tip and tilt aberrations are corrected by alignment system, so in the experiments, these two parts are ignored.
By controlling the PC, the amplifier works on double-pass amplification. Before the wavefront correction, to calibrate the deformable mirror, we measure the wavefront deformations induced by each actuator. Twenty-five phase-map influence functions are obtained by applying a voltage of 100V to each of the actuators one after another. Considering the nonlinear behavior of actuators, the wavefront compensation is executed under the closed-loop iteration .
Firstly, the exact relation in the double-pass amplification can be expressed as Eq. (1):
Here, M is the influence function matrix which is measured in double-pass amplification, P2 is the aberration of double-pass amplification, f(V) describes the nonlinear relation of the unimorph actuators, the controlling voltage V2 can be obtained by solving the linear equation based on a least squares fit, shown in Eq. (2):
Here, M+ is pseudo-inverse matrix of M.
Secondly, with the voltage V2 unchanged, the amplifier is switched into four-pass amplification. In fact, the controlling problem in four-pass amplification can be stated as Eq. (3):
Thirdly, after switching into six-pass amplification, the according voltage V6 is solved based on the voltage V4, shown in Eq. (6):
Here, the Pa is the overall aberration in the ten-pass amplifier, so the correction of the Pa ensures the good output beam quality. In fact, the corrections of the P2, P4, P6, P8 and P10 ensure that the processes of the ten-pass amplifications are successfully realized, without being influenced by the problems of aberration accumulation.
The process-oriented wavefront controlling experiments are conducted as below. In our experiments, firstly under the double-pass amplification, after the influence functions are measured, the wavefront peak and valley (P-V) value is improved from 2.1 μm to 0.71 μm, and the wavefront root mean square (RMS) value is improved from 0.27 μm to 0.067 μm, shown in Fig. 9.
In fact, the aberration in the Fig. 9(a) contain two parts, the static part and the dynamic part, which are separately shown in Fig. 10. The static aberration [Fig. 10(a)] is mainly consisted of defocus and astigmatism, and the dynamic part [Fig. 10(b)] is one concave spherical aberration with four convex fringes.
Secondly, the beam is switched to four-pass amplified, with the actuators are powered on with the voltages of double-pass amplification above. Using the influence functions measured above, the AO closed-loop is continued based on double-pass AO compensation. As can be seen from Fig. 11, the wavefront is reduced to P-V 0.87 μm and RMS 0.075 μm [Fig. 11(b)], compared with when the correction is performed only in double-pass amplification, with P-V 1.5 μm and RMS 0.18 μm [Fig. 11(a)].
Similarly, the beam is switched to six-pass, eight-pass, ten-pass amplification in turn. The results are shown in Fig. 12, for example, with six-pass amplification, the aberrations reduce to P-V 1.1 μm [Fig. 12(b)] from P-V 1.7 μm [Fig. 12(a)]; then the aberrations continue becoming P-V 0.99 μm [Fig. 12(d)] from P-V 1.7 μm [Fig. 12(c)] after switching to eight-pass amplification; after that, when the beam is ten-pass amplified, the aberrations are optimized to P-V 1.3 μm [Fig. 12(f)] from P-V 1.4 μm [Fig. 12(e)]. Here, it should be noted that there is always one high-order aberration component in one corner, which cannot be corrected by the DM. It is believed that if one DM with more actuators is implemented here, the correction results will be better.
Finally, when the aberrations as seen in the final output end are corrected, the wavefront of the whole channel output laser will be more satisfying. So we switch to lock the AO loop with reference 2 of the SH-WFS. In fact, the similar method was introduced, where two wavefront sensors are used . As can be seen from Fig. 12(g) and Fig. 12(h), the wavefront RMS value evolves around 0.27 μm and can reach 0.18 μm, which exceeds the optical requirement of device module. Besides, in our experiences, every AO closed-loop process converges in a few iterations in several seconds with a very stable convergence, and the wavefront of ten-pass amplification output beam is kept watching in real time. In the experiments, the pulse-to-pulse wavefronts of the amplified output pulses are insensitive to noise perturbation and thermal relaxation, of a dithering within 0.2 μm over several tens of minutes of continuous operation.
As mentioned above, performing wavefront correction step by step allows us to obtain excellent wavefront quality. With the help of the process-oriented AO controlling method, the pinhole-passing efficiencies in the spatial filters are always above 99% and the remove distances of relay-imaged plane positions are negligible, during the whole process of ten-pass amplification and transport. Although the laser chain is under the influence of multi-pass cumulative thermal effects, after using the stepwise AO control approach, the satisfying laser output can be reached totally. In our current setup, the total gain of the amplifier is 1 × 104, and the desired output energy of 1J/1Hz is achieved.
In practice we are able to achieve more passing numbers, there are no obvious saturation behaviors in multi-pass amplification, but the needed pulse energy has been achieved with ten-pass amplification. Besides, the experiments using the conventional target-oriented AO compensation method cannot be sufficiently actualized and revealed here, because there are big risks in destroying the optical elements and materials during the process of propagating and amplifying. As mentioned above, shown in Fig. 8(c), the near-field image has already been obviously incomplete and degraded when the amplifier works under six-pass amplification. Comparatively, in the stepwise process-oriented AO compensation manner, the near-field images are obviously improved. For example, compared with the near-fields in Fig. 8, with the help of the novel approach, the near-field images after double-pass [Fig. 13(a)], four-pass [Fig. 13(b)], six-pass [Fig. 13(c)], eight-pass [Fig. 13(d)] and ten-pass [Fig. 13(e)] amplification, are easily distinguished. The far-field image after ten-pass amplification is shown in Fig. 13(f), here 95% of the beam energy is encompassed within the 4.1 times diffraction limit. It should be noted that the degraded corners in Fig. 13(a)-(e) are caused by the high-order aberrations which still exist after the compensations of the low-order DM.
So the novel control approach can avoid the problem of aberration accumulation and gradually minimize residual aberrations by taking advantage of the stepwise process-oriented wavefront compensation strategy. The proposed procedure provides an attractive alternative for correcting the wavefront aberrations of multi-pass amplifiers. Here without loss of generality, the approach is generic and applicable to a large range of multi-pass amplifiers, including off-axis multi-pass amplifiers, and so on.
4. The conclusion
In summary, in order to overcome the problem of optical aberration accumulation in multi-pass amplification, an adaptive optics system is designed and a novel process-oriented wavefront control approach is proposed for the first time. The key feature of the approach is that the wavefront closed-loop processes are smoothly implemented with the courses of multi-passing propagation and amplification. The experimental results demonstrate that the wavefront quality is gradually improved, which ensures the effective employment of multi-pass amplifier. Besides, the concept described here paves the way toward the AO wavefront correction in multi-pass amplifiers.
National Natural Science Foundation of China (NSFC) (61605187).
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