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Abstract
A coaxial multibeam passive coherent combination of lasers with improved beam quality is proposed and verified using cascaded Michelson-type cavities, in which 4f optical systems are used to compensate for the beam waist separation between the combined adjacent lasers. A proof-of-concept experiment shows that three 65 W Nd:YAG lasers with an M2 factor of about 5.5 were coherently combined into a 124.4 W single-lobed output improving the M2 factor to 1.36. The central lobe accounted for 76% of the total power, corresponding to a total combined efficiency of 66.7%.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-power lasers (HPLs) with good beam quality have attracted great attention due to their widespread applicability in various areas such as material processing, scientific research, and military services [1–3]. However, single-aperture HPLs are typically achieved with a trade-off on the beam quality. A coherent beam combination (CBC) of multiple lasers is a promising solution to increase the output power while improving the beam quality of laser sources [4]. In the past two decades, significant attention has been paid to CBCs or phase-locking technology of multiple lasers using one of the following techniques: the Talbot cavity [5–8], Fourier cavity [9, 10], Michelson cavity [11, 12], grating cavity [13, 14], master oscillator power-amplifier (MOPA) technique with active phase control [15–18], and multichannel laser cavity [19, 20]. However, side-by-side elements may cause a near-field intensity fill factor to be less than one and result in multiple lobes in the far field if the phase difference between adjacent elements is not zero. For example, single-lobe output techniques using the Talbot cavity involve in-phase mode selection and multimode suppression, and thus their implementation requires careful design [5, 21]. In these phase-locking techniques, precise and complex control of the phase of laser arrays is required. MOPA techniques based on the active phase correction are typical representatives of controlling the phase of each channel. The center wavelength of each individual amplifier channel is locked by optical injection from a master oscillator [22]. In 2011, MOPA design made significant progress. Massachusetts Institute of Technology has demonstrated a coherent combined 4-kW output when it is operated at full power with a beam quality of 1.25 times of diffraction limit [23]. To date, such an active phase-locking CBC technology is very promising, except that its feedback control technique is slightly complicated. The Michelson cavity-based techniques are also the representatives of the passive phase-locked method because they are characterized by self-organized phase locking. In general, a Michelson-type cavity is applied to the combination of two lasers; nevertheless, the beam-combination features are different from those of laser arrays because the output is common modes of two equivalent cavities [11, 24], which do not produce interference fringes in the best state of adjustment.
In this paper, we present a coaxial multibeam passive coherent combination technique using cascaded Michelson-type compound cavities (CMTCCs) that can combine multiple lasers into a single beam rather than intersecting in the far field. In this new structure, the laser beam emitted from each laser element is forced to coaxially overlap with the same waist position, waist size, and divergence angle. The beam waist separation caused by the optical path difference (OPD) between adjacent laser elements is compensated for by a 4f optical system which commonly used for image relay in Fourier Optics [25]. A CBC occurs when the laser elements are mutually injection locked, and the beam quality can be improved in the case of in-phase output when the phase differences among the laser beams are adjusted to zero at the coaxis. In this way, the total output power can be increased by summing the outputs of all the laser elements used with an improved beam quality.
2. Experimental design
To achieve a beam combination of multiple lasers, three key conditions should be satisfied: (i) the output beam emitted from each laser must propagate along the same optical axis. (ii) All of beams to be combined must have the same waist position, size, and diverging angle. (iii) All laser elements must be injection-locked into each other. The following three steps were taken when designing the experiment in accordance with the requirements above. First, to make the output beam after the combination perpendicular to the direction of the laser beam from the oscillator, an equivalent Michelson-type cavity with an output coupler, which has a partial reflection at 45°, can be used. This forms the basis of coaxial beam combination. Second, to achieve complete overlapping of the propagation paths of the laser beams, it is necessary to eliminate the beam waist separation caused by the OPD of different beams by inserting a 4f optical system between adjacent laser elements. Finally, according to the first two steps, we can choose the reflectivity of the OC to realize the mutual injection of laser components. Thus, multiple combined lasers can be added on a coaxis with the same waist position, size, and divergence angle. As a result, the total output power will be increased, and the beam quality will be improved in the case of in-phase output.
Figure 1 shows the schematic view of an equivalent Michelson-type cavity with the same output characteristics as a symmetrical parallel planar cavity (SPPC) (see Fig. 2). G1 is a gain medium. Mirrors M1, M2, and M3 are cavity mirrors with high reflectivity at the laser wavelength and are designed to have the maximum reflectivity of R1 = R2 = R3 = 1. Lens has a focal length of f1. Figure 1 illustrates the location of Lens as well as its compensation for the beam waist separation caused by the OPD between Beam1 and Beam2. Since the mirror position is also where the waist is located, distance L1 plus distance L2 must equal f1: L1 + L2 = f1. OC1 is an output coupler with reflectivity r at an angle of incidence of 45°, which acts as a beam splitter. If losses in the two cavities (shown in Fig. 1 and Fig. 2) are equal, the required reflectance r of OC1 can be calculated. Beam1 refers to the beam that is amplified by the gain medium G1, which also acts like a focal lens due to the thermal lensing effect, reflected via OC1, and eventually focused at the position of the co-waist plane as shown by the dashed line in Fig. 1. Beam2 is the transmitted portion through OC1, and it is completely reflected by mirror M2 and returned at OC1. It is partially reflected by OC1 and focused for the first time through Lens, whose focal plane is on mirror M3. It is then fully reflected by M3 and focused through Lens for the second time. After passing through OC1, the beam waist overlaps with the beam waist position of Beam1. This eliminates the beam waist separation of Beam1 and Beam2 caused by the OPD and establishes the co-waist plane of the two beams. To eliminate the beam waist separation and achieve a co-waist plane, both beams must be carefully adjusted, so that they propagate coaxially.
Fig. 1 Schematic of an equivalent Michelson-type cavity that has the same output characteristics as a symmetrical plane-parallel cavity (SPPC in Fig. 2) when the output losses in the two cavities are the same. M1, M2, and M3: Cavity mirrors; OC1: output coupler; G1: gain medium.
Fig. 2 Schematic of the symmetrical plane-parallel cavity (SPPC) with a reflectance of R for OC. OC: output coupler.
Figure 2 is the equivalent SPPC structure of Fig. 1. OC is an output coupler with a reflectivity of R. As mentioned earlier, OC1 in Fig. 1 acts as an output coupler for the equivalent cavity, and its reflectivity r is determined by the reflectivity R of the output coupler of the SPPC. It is assumed that intracavity losses of the two cavities shown in Fig. 1 and Fig. 2 are the same, and the power Pleft, which is the power of laser light propagating from the left to the right after passing through G1, is the same. Then the power output by the SPPC passing through the OC can be written as: P1 = Pleft × (1−R). The power output by the equivalent resonator through OC1 is composed of two parts: the output produced by Beam1 is Pout1 = Pleft × r and the output produced by Beam2 is Pout2 = Pleft × (1−r) r (1−r). The total output of the equivalent cavity is P2 = Pout1 + Pout2. If the output powers of the two cavities are the same, then P1 = P2, and the relationship between the OC reflectivity R and the OC1 reflectivity r can be found to be: R = 1−r (1−r) 2. The calculated relationship between R and r are shown in Fig. 3. For a given value of R in Fig. 2, one can find the corresponding value of r for OC1 in Fig. 1 from the curve in Fig. 3.
Fig. 3 The calculated reflectivity r of OC1 in the equivalent Michelson-type cavity as a function of the reflectivity R of OC in the SPPC.
Figure 4 illustrates the optical architecture of the combination of two laser elements. Mirrors M4 and M5 perform similar functions as M1 and M2. The 4f optical system is the most important component to achieve the perfect combination of lasers. It has the same beam waist position, size and divergence angle as these individual lasers. As is known, the 4f optical system consists of two identical lenses, which are placed at the same optical axis with a common focus. When we input a light spot with a specific spatial structure into the object plane of the optical system, the image will be reconstructed on the image plane with one-to-one correspondence. Therefore, the 4f optical system can be used to compensate for the beam waist separation caused by the OPD between two parallel laser elements. As shown in Fig. 4, a 4f optical system consisting of two identical lenses with a focal length f2 is located between the two laser elements. Its optical axis is coaxial with the laser beam. The path distance between the two laser elements is four times f2. The 4f optical system acts like f1 in Fig. 1. It is apparent that the beam waist separation caused by the parallel displacement of the two laser elements is eliminated by the 4f optical system. Therefore, two beams emitted from each laser element are combined into a single beam. In theory, it is also possible to continue and add a third laser element after the combination and continue one by one if needed. Based on the two architectures above, the output beams emitted from N similar laser elements can be combined into a single beam. As shown in Fig. 5, a beam combination of N laser elements using CMTCCs with 4f optical systems can be achieved. The distance between two adjacent laser elements is the same as the length of the 4f optical system.
Fig. 4 Schematic of the beam combination of two laser elements using CMTCCs, where the 4f optical system is used to compensate for the beam waist separations caused by the parallel separation of the two laser elements.
Fig. 5 Schematic of the beam combination of multiple laser elements. The output beams originating from N similar elements using CMTCCs can be combined into a single beam using 4f optical systems to compensate for the beam waist separation between adjacent laser elements.
The architecture of the combination of N laser elements is also an interferometer, in which the individual gain mediums Gi are laser amplifiers. If mutual seeding is established between the laser elements, there is a possibility of producing a coherent output. In this case, the output of the first laser can be partially reflected into the second laser by controlling the reflectance of the coating of OCi and interfere with the operation of the second laser, resulting in a coherent combination. Therefore, a small amount of injection from the previous combiner can interfere with the oscillation of the next laser participating in the combination and result in some degree of coherence in the combination. By adjusting the alignment carefully, so that all the beams are coaxial and the mutual injection meets the threshold of the injection locking, the coherent addition is then built up among laser elements. In the case of overlapping concentric laser beams with a fixed phase difference, a coherent output with some ripples like Newton’s rings may be generated with improved beam quality.
3. Experimental results and discussion
To test the feasibility of the proposed method, an experimental device as shown in Fig. 5 was constructed. For proof-of-concept experiments, three Nd:YAG lasers were combined based on the proposed technique. G1, G2, and G3 were diode side-pumped continuous wave laser modules in which the rod-shaped gain medium was pumped by 9 of 40-W laser diode cm bars. The medium rod was 3 cm in diameter and 6.5 cm in length and its length of the pump area is 3.5 cm. The bars were equally separated into three one-dimensional linear arrays and arranged around the medium rod in circular symmetry. The each module delivered an output power of 65 W with an M2 factor of ~5.5 in the SPPC, where the physical length of the resonator was 900 mm and the reflectivity of the output coupler was R = 70% which is an optimal value experimentally. The physical length of the resonator was the same as that of the SPPC in all CMTCCs, and they are 900 mm. Since the reflectivity of the OC in the SPPC is R = 70%, one of the surface of OC1 is coated by a layer with reflectivity r = 18% (In the CMTCCs, r was calculated when the losses of both the equivalent Michelson-type cavity and the SPPC were equivalent, as shown in Fig. 3) and another surface of OC1 is coated with an anti-reflection layer. For the sake of convenience, a plano-convex lens with a focal length of 300 mm was used as the compensating lens for Laser element 1, and four identical plano-convex lenses with a focal length of 60 mm were used to construct two 4f optical systems inserted into the space between the parallel laser elements. A CBC could be achieved when M1, M3, M5, and M7 were carefully adjusted, so that the three Nd:YAG lasers were injection-locked and established phase-correlated relationship.
Experimental results show that three output beams radiating from each element overlapped completely into a concentric beam both in the near field and far field. Figure 6 shows some typical beam patterns for a single Nd:YAG laser and the three Nd:YAG lasers to be combined using the CMTCCs in the same observed plane. Figure 6(a) shows the beam pattern of a single laser that can serve as a reference for us to measure changes in the intensity distribution of the combined beam. Figures 6(b) and 6(c) show some interference patterns when the three Nd:YAG lasers are injection-locked and establish phase-correlated relationship. Figure 6(b) shows the beam pattern of three lasers with a random phase relationship among them and presents a chaotic intensity distribution. Although this intensity distribution was distinctly different from that shown in Fig. 6(a), its corresponding beam quality was about the same as that of a single laser (M2 ~5.5). Figure 6(c) displays the case where the phase relationship is fixed and the phase difference of the three lasers is zero near the propagation axis, so that one can see a single lobe at the center of the beam with a ring-shaped background. It is clear that the size of the spot shown in Fig. 6(c) was basically the same as that of the single laser, with a spot diameter of 2.88 mm, while the size of the single lobe was reduced significantly to a diameter of 0.89 mm at the center of the beam. The residual beam outside the single lobe is unavoidable since it is a byproduct of coherent addition. However, it can be removed by using a spatial filter, whose aperture matches the size of the single lobe, after the combination is done. This finding is interesting especially because when we focused on the central lobe, the M2 factor was improved to 1.36, which was close to the diffraction limit. This great improvement in the beam quality results from the interference of multiple concentric beams with a gradually increasing phase difference along the radial direction in the spot. In other words, the energy coming from each laser arrives at the locations around the axis with approximately the same phase relationship resulting in constructive interference, and at the locations away from the axis with nearly the opposite phase relationship, which may result in destructive interference. Thus, the result of the interference distribution is advantageous for the energy concentration near the beam center. The radial phase difference between the beams in the observed plane may be attributed to non-ideal characteristics of 4f lenses that compensates for the beam waist separation, but homogenize the beam intensity distribution and change the phase along the radial direction from the spot [26].
Fig. 6 Pattern of a single beam and combined beams using CMTCCs in the same observed plane in the near field. (a) Beam pattern of a single laser. (b) Beam pattern of the three combined lasers with a random phase relation. (c) Beam pattern of the three combined lasers with in-phase output presenting a single lobe in the beam center.
Figure 7 shows the output power as a function of the pump current for each laser module in the cases of the single beam, two combined beams, and three combined beams with random phase-correlated relationship. The maximum output powers for single laser, combined two and three lasers are 62.1, 114.2, and 163.7 W, respectively. It is important to note that the corresponding optical pump power of a single module at the maximum current of 32A is about 210W. Accordingly, the total maximum pump power of three modules is about 630W. As the number of laser elements increases, the combined efficiency drops noticeably from 0.92 to 0.86. The lower efficiency can be presumably attributed to the use of OCs with the same reflection. In fact, this reflection should be optimized separately for each stage with a gradually reduced reflectivity as the number of elements is increased. At the maximum output power level, the power in the central lobe was 124.4 W and accounted for 76% of the total power, which corresponds to a total combined efficiency of 66.7%. However, in our experiment, when the pump power started from the oscillation threshold and increased to the maximum output, the single lobe distribution shown in Fig. 6(c) could not always be maintained. As the pumping power was increased, it would gradually evolve into Fig. 6(b) owing to the thermal lensing effect and thermally induced phase fluctuation, and one needed to carefully re-adjust the optics to maintain the phase locking as the pump increased. The phase locking was eventually unsustainable after the pumping power exceeded a certain limit. The pattern evolution may mainly be attributed to the asymmetrical thermal lensing effect for each laser rod. The increased pumping power would result in the distortion of the gain distribution and lead to degradation of the passive phase locking. However, it is possible to reduce the impact of these problems by using a moderate pump for individual lasers, at which the thermal effect is minimized and the beam quality is excellent and stable. In addition, one can also use such a technique to combine the lasers, which produces less heat, such as optical fiber lasers or semiconductor lasers or using active control of phase-locking. Further investigation may provide useful results.
Fig. 7 Output power as a function of the pump current for each laser module in the cases of the single beam, two combined beams, and three combined beams with random phase-correlated relationship.
4. Summary
In summary, a passive CBC, using CMTCCs with 4f optical systems to compensate for the beam waist separation caused by the OPD between adjacent lasers, was demonstrated and characterized. A single lobe with ripples similar to Newton’s rings was obtained, and the M2 factor was improved from 5.5 to 1.36. If one only focuses on the central lobe, which accounts for 76% of the total power and corresponds to an output power of 124.4 W, a total beam combining efficiency of 66.7% can be obtained. It was confirmed that this technique is useful for improving the beam quality of laser sources and can also be implemented for power scaling within certain power levels. In further experiments, OCs should be optimized for each stage with gradually reduced reflectivity, and there is a possibility that the total power can be scaled to a higher level by combining more laser elements with improved beam quality if one carefully controls the thermal effect in the individual laser elements.
Funding
National Key Research and Development Program of China (2016YFB0402102); Key Deployment Program of Chinese Academy of Sciences (KGZD-SW-T01-2).
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