Four-Channel Nanosecond Pulse Combination in the Non-Polarization-Maintaining Fiber System

Abstract

We report a novel coherent nanosecond pulse combination approach using four-channel non-polarization-maintaining large-mode-area (LMA) Ytterbium-doped (Yb-doped) fiber amplifiers. The stochastic parallel gradient descent (SPGD) and frequency dithering algorithm are introduced to stabilize the synchronization in polarizations and phases among all the channels. The system delivers an average power of ~250 W and a pulse duration of 4 ns with a combination efficiency of around 87% when the repetition rate of a single pulse is limited to 1 MHz, the polarization extinction ratio (PER) at 30 μm core diameter and 250 μm cladding diameter remains around 96%.

1. Introduction

The investigation of extreme physical states has been driven by escalating demands for ultrafast fiber laser pulses with enhanced energy and power capabilities [1,2]. However, fiber-based laser systems face fundamental performance limitations imposed by critical challenges including strong thermal loads [3], nonlinear effects, mode instability [4], and material damage threshold. Increasing the energy and average power level of a single pulse is still challenging. Active phase-locked coherent beam combination (CBC) of fiber laser amplifiers has emerged as a viable strategy to transcend these boundaries, enabling power scaling and preserving beam quality [5,6]. Today, the emergences of the spatial combination of multi amplifiers, the temporal combination of multi-pulse sequences, and multi-dimensional combination have enabled the enhancement of magnitude by more than one order, e.g., 10.4 kW average power level in the architecture of spatial combination [7], 32 mJ pulse energy via the multi-dimensional combination [8], and passive 61 spatial femtosecond fiber amplifiers combination [9]. A critical requirement for polarization-maintaining (PM) CBC systems lies in maintaining phase synchronizations across all channels. Stabilization strategies including Hänsch–Couillaud (HC) detection [10], heterodyne detection [11], sophisticated parallel gradient descent (SPGD) algorithm [12,13,14], mutlidither frequency tagging (LOCEST) [15,16,17], and deep learning method [18] are widely explored in calibrating the random shifting phases among all the channels.

In the fiber-based CBC system, the combined average power is related to the number of channels and the power level of a single channel. Increasing the combined scale promotes the combined pulse with a higher average power level. Most previously demonstrated pulsed CBC systems have exclusively employed PM large-mode-area (LMA) fiber architectures. The PM LMA amplifier fiber has advantages in suppressing unwanted nonlinear-optical effects but still has challenges in implementing the single-mode amplifier due to the existence of waveguide asymmetry and limited nonlinear threshold in the PM amplifier. As one alternative method, non-PM LMA fibers present distinct advantages through simplified fabrication processes and enhanced nonlinear thresholds. These advantages enable the combined system with a higher power level. A promising solution for the replacement of PM-compatible systems involves implementing active polarization control in non-PM LMA fiber amplifiers, which enables polarization state correction, and phase control, and facilitates single-mode, single-polarization emission [19,20]. Beyond the fundamental requirements of phase synchronization, mode matching, and group delay alignment, comprehensive polarization control becomes indispensable in non-PM CBC systems to ensure identical polarization states across all emitter channels.

In this paper, we demonstrate a filled-aperture coherent beam combining system utilizing four-channel non-PM LMA Yb-doped fiber amplifiers (30 μm core/250 μm cladding). The system implements stochastic parallel gradient descent (SPGD) and LOCEST algorithms to achieve synchronized polarization control and phase locking. The four-channel combined nanosecond pulse with a 1 MHz repetition rate and 4 ns pulse duration demonstrates ~87% combined efficiency and 96% PER when the average power of a single nanosecond pulse is around 250 W.

2. Experimental Setup and Control Algorithm

Figure 1 shows the experimental setup of the combined system at the nanosecond pulse level. The seed source is one single polarized nanosecond pulse at the central wavelength of 1064 nm with a 1 MHz repetition rate. The nanosecond pulse is set to 4 nanosecond FWHM duration. The initial pulse is amplified to 100 mW by the PM amplifier. The amplified seed signal passes through one PM beam splitter to form four-channel beam signals. In each channel, there is a phase modulator for phase control, a programmable optical delay line for group delay control, and a polarization controller (PC) for polarization adjustment. The phase modulator and delay line are the PM elements, and the PC is the non-PM element. The adjustable delay line has one free space range of 9 cm and 0.1 μm increments. The polarization controller is used by adjusting the rotation angles of wave plates and has about ~20 μs response time for the rising time. The employment of non-PM amplifiers requires the demand of active polarization control among all the channels. The phase modulator has about 150 MHz bandwidth and ~2 V half-wavelength voltage. The beam is coupled into the main non-PM amplifier with three stages. In the first stage, the beam is amplified to 100 mW in the single-mode single-clad Yb-fiber with a core of 6.8 um and a length of 1.4 m. In the second stage, about 3 W output is obtained in the dual-clad Yb-fiber with a length of 4 m, a core of 10 μm, and inner cladding of 130 μm. The last amplifier with 3.5 m is based on the dual-clad Yb-fiber with a core of 30 μm and an inner cladding of 250 μm. To reduce the effect of amplified spontaneous emission, the isolators among all the fiber amplifiers have a 6 nm bandwidth with a central wavelength of 1064 nm. Each LMA gain fiber is pumped by one 976 nm laser diode through one (2 + 1) × 1 signal/pump combiner. To suppress the high-order modes and mode instabilities, each LMA in the water-cooled system is bent to 8.8 cm diameter, and the beam quality is better than 1.35. The output beams are collimated by the 4-f system with a 7 mm diameter. The combined system is steered by high-reflectivity mirrors and beam splitters. The half-reflectivity mirror combines each two channels and three combined mirrors are required. This combined framework is similar to the cascaded Mach–Zehnder interferometer (MZI) networks to control the propagating path [21]. To complete this combined process, all the beams must be coaligened or overlapped by monitoring the beams of near-field and far-field, and the optical propagating path must be adjusted for the reference channel assisted by a picosecond pulse with 10 ps duration. The controlling system completes the automatic optimization of optical propagating differences based on the overlapping temporal waveform. The transmission signal from the high-reflectivity passes through one beam splitter. The signals from the beam splitter are focused by the lens and coupled into the pinhole detectors. The focused lens has a 1 m focal length. One part beam is monitored by the high-speed detector and the s-polarized light signal from the half-wave plate and polarization beam splitter is monitored by the low-speed detector. The two detector’s operational roles are phase stabilization and polarization adjustment, respectively. The detector for polarization control has a 20 kHz electrical low-pass filter to eliminate the influence of the temporal signal. The detector for phase control is used to capture the pulsed peak value rather than the averaged power.

The implemented active control is based on a multi-frequency dithering method and SPGD algorithm. For the multi-frequency dithering method, one small phase dither $\delta \mathrm{\varnothing }\left(t\right)$ with certain modulated frequency and modulated amplitude is applied to all the channels by the phase controller and creates one amplitude dither at the interferometer output. $\delta \mathrm{\varnothing }\left(t\right)$ is related to the multiplication of the modulated depth and the modulated waveform. The modulated field can be expressed as follows:

$$E\left(t\right)={\sum }_k{A}_k\left(t\right){exp}^{i{\mathrm{\varnothing }}_k+i\delta {\mathrm{\varnothing }}_k\left(t\right)}$$

(1)

where $A_k$ and ${\mathrm{\varnothing }}_k$ are the nanosecond field amplitude and phase, respectively. The voltage signal from the detector is written as follows:

$$V\left(t\right)=R_{PD}S{\left|E\left(t\right)\right|}^2=R_{PD}S{\sum }_{j,k}{A}_{jk}{A}_k\left(t\right){exp}^{i\left({\mathrm{\varnothing }}_j-{\mathrm{\varnothing }}_k\right)+i\left(\delta {\mathrm{\varnothing }}_j\left(t\right)-\delta {\mathrm{\varnothing }}_j\left(t\right)\right)}$$

(2)

$R_{PD}$ is the responsivity of the detector and $S$ is the detecting area of the detector. For a smaller phase dithering signal, ${exp}^{i\left({\mathrm{\varnothing }}_j-{\mathrm{\varnothing }}_k\right)+i\left(\delta {\mathrm{\varnothing }}_j\left(t\right)-\delta {\mathrm{\varnothing }}_j\left(t\right)\right)}=1+i\left(\delta {\mathrm{\varnothing }}_j\left(t\right)-\delta {\mathrm{\varnothing }}_j\left(t\right)\right)$, the detected voltage signal can be written as follows:

$$V\left(t\right)=R_{PD}S{\sum }_{j,k}{A}_j{A}_k\left|cos\left({\mathrm{\varnothing }}_j-{\mathrm{\varnothing }}_k\right)-sin\left({\mathrm{\varnothing }}_j-{\mathrm{\varnothing }}_k\right)\left(\delta {\mathrm{\varnothing }}_j\left(t\right)-\delta {\mathrm{\varnothing }}_k\left(t\right)\right)\right|$$

(3)

In the filled aperture combination system, the phase errors between the k-channel and other channels could be demodulated by integrating with a similar dithering signal:

$$S_k={\displaystyle \frac{1}{\tau }}{\int }_0^{\tau }V\left(t\right)\delta {\mathrm{\varnothing }}_k\left(t\right)dt\approx A_k{\sum }_j{A}_j\left(t\right)sin\left({\mathrm{\varnothing }}_k-{\mathrm{\varnothing }}_j\right)$$

(4)

The control system should drive the phase modulators to decrease the phase errors for proper integrated time $\left(\tau \right)$. For the pulsed combination, to enhance the capacity of demodulating the phase errors, the pulsed peak is read rather than the integrated average power, which could obtain the phase errors at one shorter integrated time for the multi-frequency dithering control method. Through proper optimization of the controlling parameters, the phase errors $S_k$ are close to 0. In the PM system, the peak value of $A_k\left(t\right)$ is the constant field and only the phase error exists. In the non-PM fiber systems, the amplitude of the electrical field $A_k$ varies along with the polarization adjustment. The polarization variation induces a strong crosstalk between the phase errors and the polarization errors according to Equation (4). An efficient demodulation strategy for avoiding crosstalk is essential. Experimental results show that the frequency of phase noises induced by amplifiers, mechanical noises, and turbulence are lower than several kHz and the frequency of polarization variation is limited to several Hz. The period of phase variation is faster than the polarization variation with at least two orders of magnitudes, as a result, the optical field signal $A_k$ is a slow-varying function with a second level owing to the polarization variation and output instability. In a shorter time range, the phase-locking process enables a locally optimized solution. SPGD solver is an algorithm that adds the perturbation voltage with identical periods to search for the maximum value. For the combined control strategies toward different controllers, the demodulated phase error should eliminate the amplitude fluctuations of polarization control. The crosstalk between two different algorithms and native slower power fluctuations induces larger power fluctuations, locally optimized solutions, and larger mean square error (MSE) for averaged power. The crosstalk signal from two different control circuits should be avoided. A critical value exists, where only the phase control reaches the quasi-stationary value and then the polarization controller executes the controlling strategy in Equation (4). But, due to the power variation, the control period for the polarization controller is larger than the critical value in Equation (4). Given all the conditions, Figure 2 shows the flowchart of the optimized procedure for different control algorithms.

The control periods should consider the power fluctuation at the locked state. The crucial parts of the algorithm lie in the phase control bandwidth, the controlling period on the polarizers, and the lower mean square error in average power.

3. Experimental Results and Discussion

To implement the active control process, optical propagating differences (OPDs) should be carefully controlled. The optimization of OPDs is based on one mode-locked picosecond pulse with 10 ps duration and 58.15 MHZ repetition rate. Figure 3 shows the sampling pulse sequences for the conditions of initial OPDs and compensating the OPDs. The compensation of OPDs is based on actively increasing/decreasing the length of the fiber and controlling the programmable optical delay line. The temporal waveform overlaps after completing the optimization process, as depicted in Figure 3b.

We first stabilized the polarized state in one amplifier. The implemented active SPGD algorithm was adopted in optimizing the PERs of single beam amplifiers at different power levels. The p-polarized light signal is the solving objected polarization. Figure 4 shows the PER of the single amplifier at different power levels. Increasing the output power to 80 W, all the emitters maintain approximately identical PERs. The PER is still ~94.5% at the 80 W output power. The slight polarization degradation induced by strong mode degradation is observed after increasing the output level, as shown in Figure 4.

To implement the combined process with high efficiency, essential control is required. Except for the spatial overlap of all the beams and temporal overlap among all the channels, the peak powers of nanosecond pulses are adjusted to emit approximate average power, as a result, the decreasing combination efficiency induced by the accumulated nonlinear phase shift could be ignored. The phase stabilization is implemented by the multi-frequency dithering methods. Sinusoidal waveforms with different modulated carrier frequencies are added to all the channels. The modulated frequencies are set to 40 kHz, 55 kHz, 75 kHz, and 90 kHz. The modulated depth for all the channels is set to ${\displaystyle \frac{1}{50}}\lambda$. The multi-dithering method obtains the phase errors by searching the peak values of pulse sequences. In the single-mode PM fiber systems, the control bandwidth of four-channel phase stabilization is better than 1 kHz. The period of the SPGD solver is more than 1 kHz. A period frequency of 1 kHz on the polarizer controllers is added to all the channels and the detected s-polarized light signal is averaged with 25 ms integrated time via the optimization flowchart in Figure 3. Figure 5 shows the combined result when all the emitters are amplified to ~72 W with a total 290 W output. The average power from all the channels is stabilized by adjusting the currents of the diodes by monitoring the backscatter light signals, as a result only 1% power fluctuation is demonstrated. Figure 5a shows the average power traces from the open loop to the closed loop. There are three stages in the power traces. In the first stage (I: gray region), all the control algorithms are in the open loop, and the detected light intensity experiences a larger fluctuation owing to the random phase shifting of the interference pattern. Figure 5b shows the unstable temporal waveforms. In the second stage (II: green region), when the phase controller is turned on and the polarization is turned off, a stable power trace is obtained, but the locking average power is still at the locally optimized solution. All the channels are not at the identical polarized states which induces the lower phase locking efficiency. Phase control induces the locally optimized solutions. In the last stage (III: white region), once the polarization control algorithm and phase control algorithm are turned on, the combined average power increases owing to the implementations of identical polarization states among all the channels. There are tolerable power variations compared with the condition of the pure phase locking process which proves that the locking process of polarization control would not induce the extra strong crosstalk between multi-frequencies depicted in Figure 5c. The p-polarized light reaches a stable state as shown in Figure 5d. At this stage, the combined average power reaches 250 W corresponding to one combined efficiency of 87%. The pulsed waveforms of a single beam and a combined beam are depicted in Figure 5e. The FWHM duration of the combined pulse is 4 ns which shows identical pulse duration with a single emitter.

Figure 6a shows the M2 measurement (4$\sigma$-method) results at the maximum combined average power. The beam quality of the combined beam is about 1.18 which is close to the diffraction limit. Figure 6b shows the combined efficiency and PERs at the different combined power levels. At lower output power, the combined efficiency of ~93.4% is observed. The PER of the combined beam is approximately 96%. Increasing the output power levels, the combined efficiency decreases to ~87%. The efficiency decrease can be induced by the increase in the higher-order mode content and accumulated nonlinear phases. The enhancement of PER for the combined beam contributes to the higher fundamental mode ratio of the combined beam as shown in Figure 6a.

We also investigated the decreased combined efficiency. Figure 6b also shows the combined efficiency influenced by OPDs, accumulated nonlinear phase, residual phase errors, and fundamental mode ratio. We used a narrow linewidth laser with 100 kHz linewidth to avoid the OPDs. At the lower output, the efficiency loss (green dot in Figure 6b) induced by the OPDs was ignored. To investigate the accumulated nonlinear phases, we introduced a nanosecond pulse with a 10 MHz repetition rate, 16 ns pulse duration, and lower peak power. The ignored nonlinear effect at 72 W output level was introduced. The combined efficiency had about 0.70% enhancement along with the power scaling process. The combined efficiency induced by residual phase errors of the phase controller can be estimated by Equation (5) [22].

$$∆={\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2}}{\displaystyle \frac{\sqrt{4P_1{P}_2{cos}^2\delta +{\left(P_1-P_2\right)}^2}+\sqrt{4P_3{P}_4{cos}^2\delta +{\left(P_3-P_4\right)}^2}}{\sum _j^4{P}_j}}$$

(5)

$P_j$ is the output power of the j-th beam and $\delta$ is the residual phase prror (root-mean-square value). At the stable process in Figure 5a, the residual phase error of the system is ~${\displaystyle \raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$18$}\right.}$. The decreased efficiency influenced by residual phase error is about 1.2%. The PERs also influence the combined fundamental mode ratio. As shown in Figure 4, the PER is degraded by about 1.5% which induces at least 1.5% combination efficiency loss. Other optimizations in beam sizes, beam pointing errors, fast SPGD solver, and fundamental mode ratio of LMA fiber induce the enhancement of combined efficiency.

The beam splitter arrays still bring about extra power loss owing to the lower fundamental mode ratio. Further increasing the output average power is of vital importance for pulsed combination. On the one hand, optimizing the LMA amplifier with a lower numerical aperture could enhance the portion of the fundamental mode, which could reduce the extra mode dissipation. On the other hand, the tiled-aperture configuration of pulsed combination also provides one feasible to avoid extra power dissipation, which has been demonstrated in many fiber-based combination systems [23].

4. Conclusions

In summary, a one nanosecond pulse combination system based on four fiber amplifiers is presented in the non-PM system. The SPGD algorithm and frequency dithering method are introduced to control the polarizations and phases for different control periods. The system delivers the 250 W average power corresponding to one combined efficiency of ~87% when the pulsed repetition rate and duration are 1 MHz and 4 ns. The beam quality of the combined beam is better than 1.2. The PERs remain ~96% in the entire combined process. This work demonstrates the feasibility of high-power pulse combinations in non-PM amplifiers.