We present the coherent beam combination of four 2100 nm holmium amplifiers with their phase controlled through acousto-optic modulators driven by the RF output of direct digital synthesizer chips. Phase alignment was achieved through the use of a field programmable gate array based stochastic parallel gradient descent algorithm.
Holmium-doped fibre lasers have many materials processing, medical and defence applications. The holmium-doped silica emission lies in the 2.1 μm atmospheric transmission window allowing for increased range in atmospheric propagation. In addition, its operation in the eye-safe wavelength range lends its use to applications where exposure from scattered and reflected light is of concern.
Single-mode holmium lasers and amplifiers have now demonstrated output powers of 407 W and 265 W, respectively, showing their potential for use in some higher power directed energy applications . The holmium-doped fibre amplifiers employed in this paper were resonantly core-pumped by thulium oscillators operating at 1950 nm .
Laser beam combination for power scaling has been demonstrated using a number of laser technologies and more recently extensively investigated in ytterbium-doped fibre laser systems . The three most widely demonstrated techniques for beam combination are; geometrical (incoherent beam) combination, which requires the pointing of multiple incoherent lasers on a target; spectral beam combination, involving the overlapping of multiple lasers of set wavelengths using a dispersive or wavelength selective optical element or elements; and coherent beam combination (CBC). In the 2 μm spectral region, spectral  and coherent beam combination  techniques have been demonstrated. Examples, however, have been limited to thulium based systems and at wavelengths shorter than 2040 nm. The power scaling potential of thulium doped fibre lasers and their use in CBC systems has been described by Goodno el al . (Section 126.96.36.199). Here the relaxed tolerances for efficient coherent beam combination, associated with the longer wavelength of operation, are presented. The increased SBS threshold of laser systems operating at 2µm is also presented by Goodno et al. . The higher SBS threshold enables the further power scaling of these systems without the need for frequency broadening and the associated path length matching that would be required in a CBC system.
Here we present our results for a coherently combined holmium-doped fibre amplifier system operating at 2100 nm. This system consisted of four channels whose phase alignment was optimized using a field programmable gate array (FPGA)-based stochastic parallel gradient descent (SPGD) algorithm.
There have been a number of different coherent beam combination approaches previously demonstrated. These include, heterodyne approaches , multiple and single frequency dithering techniques (frequency tagging) [8, 9] and the SPGD technique [10, 11]. A more comprehensive comparison between these different approaches is presented in reference . Previous demonstrations where the phase control is applied through an acousto-optic modulator (AOM) have been limited to the heterodyne approach  and some frequency tagging demonstrations , both of which use a temporal frequency shift to impart a phase change. The novelty of the approach presented in this report is in the use of a direct digital synthesizer (DDS) chip to simultaneously provide the driving 80 MHz RF signal as well as apply the desired phase shift, through control of the RF signal phase, to the AOM of each channel. In contrast to the heterodyne phase control approach, implementing the SPGD algorithm allowed for the use of a single photodetector and removed the requirement for the reference beam. When compared to the frequency tagging techniques, the SPGD algorithm didn’t require the demodulation of each channel’s phase error from the detector signal. We also note here that AOM control via a DDS chip is not limited to SPGD phase control and can be adapted to other active beam combination techniques. The DDS chip provides agile and independent control of frequency, phase and amplitude of the RF signal driving the AOMs. As previously reported by Augst et al. , using the AOM as the phase modulator provides continuous phase control without needing to reset the voltage driving the electronic phase controller, piezo stretcher or electro-optic modulator (EOM) once the voltage limit of the device is reached. This is particularly important during the turn-on stage of the high power holmium amplifiers when the relative optical path length changes between the different channels can be in the order of hundreds or thousands of waves [8, 12].
2. Experimental setup
To alleviate the requirement to path length match each of the channels, the linewidth of the seed laser needed to be sub-MHz. A commercial 2100 nm single longitudinal mode seed laser (AdValue) satisfied this requirement. The linewidth was calculated from the phase noise to be 500kHz. Its output was amplified and subsequently split into the four channels using in-house fabricated 50:50 polarization maintaining (PM) couplers. An isolator (Shinkosha) was used to prevent the amplification of backward propagating light by the pre-amplifier and protected the narrow linewidth master laser. The lasers used to pump the holmium-doped fibre amplifiers consisted of thulium-doped fibres (Nufern) spliced between in-house written fibre Bragg gratings  at 1950 nm, and were pumped by 790 nm laser diodes (LIMO). The 1950 nm pump light was coupled into the holmium-doped fibre amplifiers through in-house fabricated wavelength division multiplexers (WDMs), while the 2100 nm seed signal was coupled through the PM inputs and outputs of the WDMs. A second WDM was used to remove all the unabsorbed 1950 nm pump light from the output of the amplifier. After the holmium pre-amplifier, the light was split into the four channels and propagated through the AOMs (Gooch and Housego), where the phase control occurred. The AOMs used were specified for QCW operation with 6 W of RF power and their insertion loss was optimized for use at 2000 nm. In this setup we ran the AOMs CW with 3 W of RF power and at a longer wavelength of 2100 nm. The outputs of the AOMs were amplified by each of the channel’s first stage amplifiers. These first stage amplifiers increased and balanced the power in each channel from ≈50 mW to 2.5 W (17 dB gain).
The first approach used to recombine the amplified channels was the filled aperture approach. This consisted of a coupler based beam splitter tree architecture and a wedge usedto sample the output chosen to emit the combined beam onto a photodetector. The photodetector provided a relative measurement of the output power and was used to measure the effect of the SPGD phase dithers. The setup is illustrated in Fig. 1.
The beam recombination setup was later converted to demonstrate the tiled aperture recombination approach. In this demonstration, the four output beams were collimated and aligned into a 2 × 2 array. A representation of this setup is illustrated in Fig. 2. The 6 mm focal length lens and positioning of the Pyrocam III 250 mm from the lens produced a 40 × magnified image of the focal plane intensity profile on the camera. The iris in front of the detector was positioned the same distance from the magnifying lens as the Pyrocam III camera. As such the image observed from the camera was representative of the intensity distribution in the aperture plane.
The SPGD algorithm provides each channel with a unique random amplitude phase shift. The magnitude of these phase shifts was constrained to a set maximum value. By repeated measurement and comparison of the resultant photodetector output and that for an oppositely signed phase shift, the system can be made to move toward a maximum or minimum. In this instantiation, an FPGA program generated the random number used for each channel’s phase dither amplitude, updated the phase of each channel based on the result of the previous iteration, calculated the new phase shifts required for this iteration’s dither and made the comparison between the responses of this dither ready for updating in the next iteration. The amplitude of the FPGA random number generator determines the phase dither amplitude.
The DDS parameters (frequency, amplitude and phase) are set using a resulting digital word from the FPGA.
The signal from the feedback detectors present on both recombination techniques, illustrated in Figs. 1 and 2, was used as the metric for optimization by the FPGA-based SPGD algorithm.
A Pyrocam III was used to observe the coherently combined output and to calculate the efficiency of the two recombination techniques.
3. Results and discussion
After propagating through the AOMs, each channel was amplified up to 2.5 W. Measurements of the outputs from each of the amplifiers are provided in Fig. 3. The differing performances of each of the amplifiers was predominantly due to the different seed powers. This seed power variability was caused by the different insertion losses of the AOMs which ranged from 3.0 dB to 4.5 dB. The output power of each channel was adjusted to be equal by using individual diode driver current control. This is also illustrated in Fig. 3. Balancing of the output powers of each of the channels maximized the recombination efficiency of the filled aperture beam combination as well as maximized the power in the central lobe of the far field profile for the tiled aperture approach.
To test the performance of the phase control setup described in Section 2, a maximum phase dither amplitude was set for the SPGD algorithm, and the phase control was initiated. A representative output, using the Pyrocam III camera, of the filled aperture recombination is presented in Figs. 4(a) and 4(b) for the unlocked and locked cases respectively. Similarly Figs. 5(a)-(d) illustrate the output of the tiled aperture recombination.
In the unlocked filled aperture case, the power in the four output beams was temporally varying with power moving between the outputs. In the phase controlled (locked) case, the combined output beam intensity was maximized and the power in the three low power outputs was reduced to just above the background noise of the Pyrocam III camera.
For the tiled aperture recombination, the near field profile consisted of four collimated beams with a beam radius of 3.1 mm and an array pitch of 10 mm. This corresponded to a fill factor of 30%. The near field profile is provided in Fig. 5(a). Some diffractive effects are observable in each of the beams due to a slight amount of clipping of the beams by the other channel’s beam steering mirrors. In the unlocked case, represented in Fig. 5(b), the coherence between the channels was removed. In Fig. 5(c) each of the AOMs were driven at a common frequency and hence each channel underwent the same frequency shift. In this case, there was no control over the phases. The fringe pattern is scrolling in both the horizontal and vertical directions depending on the temporally varying phase relationship between each of the channels. In Fig. 5(d) the phase control electronics was activated and a stable intensity profile was generated.
The steady-state noise and the bandwidth of the system were studied as a function of the maximum phase dither amplitude. The system response time was measured by alternating the SPGD functionality between minimizing and maximizing the detector signal and measuring the time and hence number of iterations required to reach 90% convergence. These results arepresented in Fig. 6(a). Using the left hand axis, the convergence time is plotted as a function of the maximum permitted dither amplitude. The right hand axis shows the number of iterations required for convergence for the iteration time of 5.8 μs. As expected, the convergence time was dependent on the amplitude of the phase dithers. Once the detector signal converged on a maximum, the phase dithers associated with the SPGD optimization were then responsible for the residual phase misalignment between the channels in the combined output beam and hence intensity noise. Determining the optimum dither amplitude was a compromise between the bandwidth, and response time of the system, and the amplitude noise in the combined beam output. Figure 6(b) depicts an oscilloscope trace showing the convergence to a maximised output when using stochastic phase dithers on each channel up to a maximum of π/2. Due to the large phase changes that were occurring in each iteration, a maximised output was able to be achieved in less than four iterations. For an iteration time of 5.8μs, this corresponds to a convergence time of approximately 20 µs. The increased intensity noise that was consequential to allowing these large phase dithers to be applied is evident in Fig. 6(b) where the red arrow is pointing to a drop in the detector signal, which is proportional to the output beam intensity, of almost 50%. This drop in intensity occurred for half an iteration cycle and would have been caused by multiple channels undergoing large phase changes within the same iteration cycle.
To determine the noise that was present in the combined output, photodetector and Pyrocam III outputs were characterised after convergence. The relative intensity noise was measured to be approximately 10% for the maximum phase dither amplitude set to 0.2 rad (λ/32). The temporal stability of the output beam following activation of the phase control is illustrated in the BeamGauge intensity plot in Fig. 7(a) and 7(b). Figure 7(a) corresponds to the filled aperture recombination output with the plot illustrating the percentage of output power from the combined beam aperture before and after phase locking. Figure 7(b) is a plot of the peak intensity of the tiled aperture output before and after phase control.
The recombination efficiency was calculated from the Pyrocam III image of the output. For the filled aperture, recombination efficiencies of ≈80% were typical. This combination efficiency is attributed to a combination of the polarization miss alignment, the unbalanced channel powers and the residual phase offsets caused by the SPGD algorithm. Whenconsidering the polarization, the polarization extinction of the narrow linewidth seed temporally varied between 10 and 15 dB and the polarization extinction of the couplers were approximately 13 dB, the polarization offset is accountable for a drop in efficiency of ≈8%. The coupling ratios of the fibre couplers were accurate to within 3%, however this also resulted in a coupling loss of ≈6%. The residual phase offset between the channels associated with the SPGD algorithm’s phase dither also contributed to a drop in efficiency. For a maximum phase dither of 0.2 rad, which corresponds to an RMS residual phase error of λ/23, calculated from the relative phase change that could be imparted between the channels in one iteration, a drop in efficiency of 4% would be observed. The measured combination efficiency of 80% is comparable to this maximum theoretical value of 82%. Recombination efficiencies of the tiled aperture demonstration were ≈35%, which was in close agreement with the fill factor of the near field array profile (≈30%). The slightly high measured value would have been due to the capturing of some side lobe power in the aperture set in the BeamGauge software as pictured in Fig. 5(d).
In summary, we have reported on, to our knowledge, the first demonstration of the coherent combination of a number of holmium-doped fibre MOPAs operating at a wavelength of 2100 nm. We believe this is the first demonstration where the phase control is applied through an AOM, with its RF driving frequency and phase information being controlled by the output of a DDS chip. The system used a SPGD-based phase alignment optimization technique and was demonstrated using filled aperture and tiled aperture recombination architectures. For the combination of four 2.5 W amplifiers, a filled aperture combination efficiency of ≈80% (~8 W) was observed. Convergence times were studied to optimize the maximum phase dither amplitudes that are applied to each channel. For a set maximum dither of 0.3 rad, which corresponds to a RMS relative phase offset between the combined channels of λ/10, convergence was able to be achieved in less than 100 µs and maintained through any perturbations at frequencies <10 kHz.
We anticipate that the modularity of the electronics and optical channels will provide system scalability through addition of extra channels and the further amplification of each channel. Investigation into the scalability of the system, both in the power per channel and the number of channels is ongoing.
Portions of this work were presented at the OSA Laser Congress (ASSL, LAC) in 2017, “Coherent beam combination of four holmium amplifiers using direct phase control from a DDS chip and a SPGD algorithm”, ATu3A.3.
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