1. INTRODUCTION

Recently, Nelson et al. analyzed coherent beam combination (CBC) of high-power lasers in the context of propagation of a tiled phased array through turbulent atmosphere [1]. Among their conclusions was that CBC of high-power lasers requires phase control systems with loop bandwidths substantially beyond existing technology, and that “target-in-the-loop” architectures cannot function when the transit time exceeds the laser coherence time. Similar points have been made by one of the same authors (Sprangle et al.) in an earlier publication [2]. These conclusions are incorrect and prima facie belied by work from multiple groups over the past decade that has demonstrated successful implementation of high-power CBC [3]. In this Comment, we clarify that the conclusions of [1] do not apply to CBC of lasers using a shared master oscillator power amplifier (MOPA) architecture, which comprises all high-power CBC work of which we are aware.

2. CBC WITH HIGH-POWER BROADBAND LASERS

As noted in [1], operation of continuous wave (cw) fiber lasers above the single-frequency threshold for stimulated Brillouin scattering requires broadening of the laser linewidth. Typical kilowatt-class, step-index fiber amplifiers require operating linewidths of the order of $\sim 10\mathrm{GHz}$ [4–7].

The analysis in [1] simulates each broad linewidth laser as an ensemble of independent radiators whose number and frequencies are determined by the laser linewidth. Figure 1(a) shows the CBC system architecture for an array of such laser master oscillators (MOs). Depending on the MO power, the channels may optionally contain laser amplifiers. Since the MOs of each CBC channel are optically independent, their outputs are mutually incoherent. In the absence of locking electronics, the phase and amplitude (power) fluctuations between channels are statistically uncorrelated. The analysis in [1] suggests that CBC of such sources would require phase-locked loops (PLLs) with servo bandwidths of the same order as the laser linewidth (while also, erroneously, failing to recognize a need for equivalent-bandwidth amplitude-locking controls [8]). Since $\sim 10\mathrm{GHz}$ class PLLs are well beyond the existing technological state of the art, the authors conclude the laser source linewidth represents a fundamental limit on the ability to coherently combine beams [1].

 

Fig. 1. (a) CBC architecture of $N$ optically independent lasers with (optional) laser amplifiers. (b) Typical actively phase-locked CBC MOPA architecture with a single MO split to seed $N$ laser amplifier channels.

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We agree with the authors of [1] that CBC of mutually incoherent sources as shown in Fig. 1(a) is impractical. For this reason, all published work (to our knowledge) on actively phase-locked CBC uses the architecture shown in Fig. 1(b) [3]. This is a MOPA architecture in which a single MO is split to seed a plurality of laser amplifier channels. The source linewidth is defined by the common seed laser, not by the individual laser amplifiers. Hence, the intrinsic MO phase and amplitude fluctuations of the laser fields are common among all amplifier channels. The PLL servo need only correct for phase noise imposed by the non-common amplifier channels and propagation paths.

For typical fiber laser amplifiers, the bandwidth of this phase noise has been shown to be confined to kilohertz-class frequencies and is typically dominated by thermal transients and acoustic coupling [11]. Numerous groups over the past decade have successfully demonstrated CBC of broadband high-power lasers in the architecture of Fig. 1(b) via straightforward application of PLL servos operating at acoustic frequencies [3,5,12–15].

It is true, even for MOPA architectures, that CBC of broad-bandwidth sources is more challenging than for single-frequency sources. The amplified spectral phases and spectral amplitudes must be matched between channels. This issue has been explored in detail, both for cw (phase-modulated) systems as well as for ultrafast laser systems [16–18]. Typical engineering solutions involve precision matching of group delays (path lengths), group delay dispersion, nonlinear phase shifts, and amplifier gain profiles. In no case do these solutions lead to higher bandwidth requirements on the piston phase controller, even with terahertz-class optical linewidths.

Nonlinear self-phase modulation (SPM) can, if not properly managed, lead to uncontrolled multi-gigahertz linewidth broadening in kilowatt-class fiber amplifiers [13]. As such nonlinear linewidth broadening is not necessarily equal among all fiber amplifiers, CBC of SPM-broadened MOPAs would require PLLs with multi-gigahertz control bandwidth. However, SPM can arise in a fiber amplifier only when the propagating laser exhibits time-varying intensity (amplitude modulation, or AM). For this reason, the seed source for CBC MOPAs is typically purely phase modulated so that any residual AM is small, and SPM leads to only marginal decoherence loss for a CBC system [5].

3. ATMOSPHERIC PROPAGATION OF CBC SOURCES

The misleading premise of CBC with optically independent lasers impacts other aspects of the turbulence analysis in [1]. For instance the authors base their analysis of CBC efficacy on postulated gigahertz-class phase-locking (and, implicitly, amplitude-locking [8]) electronics with RMS errors of $\sim 1\mathrm{rad}$. However, RMS residual errors for the kilohertz-class PLLs that are actually used for CBC MOPAs are of the order of 0.1 rad [12–14]. The use of realistic 0.1 rad phase residuals in Figs. 6–8 of Ref. [1] would increase “Coherent combining” to be within 1% of the “Monochromatic phase matched” performance.

The authors of [1] also note that it is “inconceivable” to coherently combine lasers by using backscattered light from a distant target to acquire an error signal for phase correction, if the transit time of light to and from the target exceeds the laser coherence time. Again, this is relevant only to architectures that use mutually incoherent broadband sources similar to Fig. 1(a). For the CBC MOPA architecture of Fig. 1(b), phase locking with large transit times can be performed regardless of the coherence time of the source. For example, typical $\sim 10\mathrm{GHz}$ linewidth, kilowatt-class fiber amplifier chains contain tens of meters of fiber [4–7]. This leads to transit times of the order of 100 ns, or 3 orders of magnitude longer than the optical coherence time. Yet such lasers are routinely phase locked with high precision [12–15].

Transit time imposes two constraints on atmospheric “target-in-the-loop” phase locking. The first is that the difference in transit times between channels must be less than the laser coherence time; i.e., the group delays must be matched [10]. This is true for any CBC MOPA architecture and imposes no direct constraint on propagation distance, only on differences in propagation distance between channels. Such differences are typically small and can be easily compensated to within a small fraction of a coherence length [18].

The second constraint is that, with large transit times, the PLL control bandwidth will be reduced due to data latency. Ultimately this will constrain the propagation distance owing to phase lag in the feedback circuitry. For example, to compensate 1-kHz-class atmospheric turbulence dynamics, the transit time must be significantly less than 1 ms, limiting propagation distances to $<150\mathrm{km}$. This consideration is independent of laser linewidth.

In their simulations of atmospheric propagation, the authors of [1] identified specific cases of aperture size, turbulence, and propagation parameters for which the complexity and expense of CBC is not justified. However, they also noted there was potential for adaptive optics (AO) to improve performance under these same simulation parameters. If indeed AO can improve performance, then in principle a similar improvement could be realized for the same size beam director without AO using a higher channel count CBC MOPA array, with individual tiles appropriately sized relative to the transverse Fried coherence length. This case was not simulated in [1]. A complementary Comment by Vorontsov and Weyrauch [19] discusses parameter selection to ensure fair comparisons of coherent and incoherent beam combining performance under turbulent conditions.

4. CONCLUSION

In summary, the analysis of actively phase-locked (and power-locked) CBC of high-power lasers presented in [1] is specific to the case of mutually incoherent oscillators. The resulting broad conclusion that high-power CBC is fundamentally limited by laser linewidth is incorrect, since it does not apply to the shared MOPA architecture that is effectively an industry standard for high-power laser CBC [3]. Contrary to the conclusions of [1], high-power CBC has proven successful in achieving high efficiency peak and average brightness well beyond the capability of single laser sources [3]. CBC is undergoing further rapid development for diverse applications such as high field laser accelerators [20] and military uses in directed energy [21].