Yb-doped fiber laser systems have been rapidly developed for various industrial and military laser applications, facilitating the production of high-quality laser beams with power-scaled output power [1–3]. There have been recent attempts to increase Yb-doped fiber laser (YDF-laser) power even further, which include the use of the master-oscillator power amplifier (MOPA) configuration [4, 5] and beam-combining technologies [6, 7]. Among these technologies, beam combining the outputs from the MOPA has shown high feasibility for YDF-laser power scaling [8, 9]. However, this scheme requires multistage amplification and faces various technological bottlenecks, such as thermal effects [10], stimulated Brillouin scattering (SBS) [11], stimulated Raman scattering (SRS) [12], photodarkening [13], and transverse mode instability (TMI) [14].

The issue of SBS has been a persistent problem in laser systems, particularly in MOPA architectures. SBS is a phenomenon in which the light wave interacting with an acoustic phonon in the optical waveguide creates a backward-propagating wave that can damage the laser system and limit the output power [11, 15–18]. To mitigate the effects of SBS, various techniques have been proposed. One of the most widely used techniques is spectral linewidth broadening [19]. This technique involves adding a phase modulation component to the seed laser components, which can increase the threshold power of SBS with radio-frequency (RF) signals, including the white-noise source (WNS) [20] and pseudorandom binary sequence (PRBS) [21]. This technique has been shown to be effective in increasing the SBS threshold in MOPA systems. Another technique is the use of short-length large-mode area fibers [22] and a structural design of optical fiber [23]. These can help to reduce the acoustic phonon density in the fiber, which can lower the SBS threshold power. In spectral-linewidth-broadening schemes, the use of PRBS modulation has been preferred over WNS, as it provides a higher SBS threshold. PRBS modulation has been successfully employed in YDF-MOPA to achieve kilowatt-class laser power [12, 24, 25].

In addition to the issue of SBS, the spectral linewidth of lasers is also a critical parameter in beam-combining technologies, which is another avenue of laser power scaling. In particular, spectral beam combining (SBC) requires multiple lasers to overlap in both the spatial and spectral domains, with each laser having a narrow spectral linewidth to avoid undesirable interference among them [26]. Broad spectral linewidth of a laser can result in significant chromatic dispersion at a diffraction grating, which can adversely affect beam quality in SBC [27–29]. Therefore, finding an optimal amount of spectral broadening that can satisfy both SBS suppression and SBC enhancement is essential. Beam-combining technologies have been adopted for the outputs from MOPA configurations to increase the net output power several times without noticeable beam-quality degradation, compared to single-channel power-scaling attempts [30, 31]. However, it is not yet clear how the spectral linewidth would affect both SBS and the beam quality of SBC in YDF-MOPA systems. Further research is needed to determine the optimal spectral linewidth for SBC in YDF-MOPA systems. This involves investigating the tradeoff between SBS suppression and SBC enhancement, and determining the effect of spectral linewidth on beam quality. By finding the optimal spectral linewidth, it is possible to achieve high net output powers while maintaining excellent beam quality, which is essential for many applications, including laser processing and medical treatments.

This paper presents an experimental analysis of the impacts of the spectral linewidth of a single-channel YDF-MOPA on SBS and beam quality. The YDF-MOPA system consists of a distributed feedback (DFB) laser diode modulated in PRBS formats, and two-stage YDF amplifiers that increase the continuous-wave (CW) output power to over one kilowatt. To investigate the effects of spectral linewidth, the back-reflected SBS power from the final-state YDF amplifier is measured, and the beam quality is measured for the output laser diffracted by a grating. The grating specifications used in the experiment are chosen to be similar to those used in SBC, enabling the experimental configuration to be readily adopted for multichannel SBC. The experimental findings provide valuable information for designing multiwavelength SBC systems using MOPA configurations. By understanding the effects of spectral linewidth on both SBS and beam quality, it is possible to optimize the system design and achieve high net output powers while maintaining excellent beam quality. These results can have significant implications for laser processing and medical treatments, where high-power laser systems with excellent beam quality are crucial.

Figure 1 depicts the experimental setups employed to assess the impact of linewidth on a YDF-laser system. The diagram exhibits a systematic outline of the different stages of the experiment, which commences with the generation of a PRBS signal utilized for the phase modulation of the seed beam.

Figure 1. Scheme for the radio-frequency (RF) spectrum measurement of (a) pseudo-random binary sequence (PRBS) signal, (b) the phase modulated laser, and (c) the Yb-doped laser system for the measurement of SBS power and beam quality M ². The first YDF has a core diameter of 10 μm and a cladding diameter of 125 μm. The second YDF has a core diameter of 15 μm and a cladding diameter of 130 μm. FPGA, field programmable gate array; ESA, electric spectrum analyzer; PM, phase modulator; VOA, variable optical attenuator; PD, photodetector; LD, laser diode; WDM, wavelength division multiplexing.

Figure 1(a) illustrates a detailed schematic of the experimental setup utilized to measure the electrical PRBS signal used for phase modulation of the seed beam. The PRBS signal is generated using a field-programmable gate array (FPGA) board (Altera, Intel FPGA; Intel Co., CA, USA), which generates an RF square-wave signal that is converted to a PRBS signal. To verify the signal generated by the FPGA board, the RF spectrum of the PRBS signal is measured using an electrical spectrum analyzer (ESA). Additionally, a compiled program called Quartus Prime 17.0 (Altera; Intel Co.) is used to change the modulation frequency and PRBS pattern. The modulation frequency is varied within the range of 1 to 12 GHz, and the modulation frequency f_m and PRBS pattern n determine the spacing f_m/(2ⁿ − 1) between frequency combs. This spacing is a critical factor in determining the impact of linewidth on the laser system’s performance. The FPGA board in this experimental setup can generate PRBS patterns 3, 4, 5, 7, 8, 9, 11, 13, 17, 23, and 27; PRBS 7 is used in this study, as it offers the best mitigation of SBS under a modulation frequency of 5 GHz.

Figure 1(b) shows a heterodyne setup utilized to measure the increased linewidth of the phase-modulated beam with PRBS signals in the frequency domain. This setup is critical for accurately analyzing dispersion in the grating, as it confirms the increase in linewidth of the phase-modulated beam according to the modulation frequency. The FPGA board used in Fig. 1(a) is also utilized in Figs. 1(b) and 1(c). To modulate the phase of a seed laser with a modulation depth of π, the phase modulator (PM) (NIR-MPX-LN-20; iXblue Inc., CA, USA) requires a voltage of 5.5 V. However, the electrical signal used in the experiment has a power of only 0.1 V. To increase the voltage to the required level, an RF amplifier (DR-DG-20-MO; iXblue Inc.) is used. A DFB laser with a narrow linewidth of 5 MHz and wavelength of 1,064 nm is used as the seed beam. To prevent damage from backward propagation, the beam passes through an isolator. Then, the beam is split into two at a 5:5 coupler, with one part entering the PM and the other serving as the reference beam.

The reference beam is directed through the 5:5 coupler to reduce its power by half due, to the insertion loss of the PM. The beat signal between the modulated and reference beams is measured by ESA. This beat frequency is used to calculate the linewidth of the phase-modulated beam.

Figure 1(c) provides a comprehensive schematic diagram of a YDF-laser system, along with a measurement setup for SBS power and beam quality M ². The setup includes the components used in Fig. 1(b), such as the DFB laser, FPGA board, RF amplifier, and PM. However, in Fig. 1(c), there are two stages of ytterbium-doped fiber amplifiers (YDFA), to increase the output power. The first stage has a core diameter of 10 μm and a cladding diameter of 125 μm, while the second stage has a larger core diameter of 15 μm and a cladding diameter of 130 μm. To prevent SBS from damaging optical components, optical isolators are placed between the seed laser and PM, and between the first and second stages of YDFA. The SBS power generated in the second stage of YDFA is measured with a power meter. The lens is contained in the endcap, and the laser emitted from the endcap has a diameter of 8 mm, which is maintained until the beam profiler. After adjusting the vertical angle and height of the beam incident upon the grating, the beam quality M ² is observed using beam-quality measuring equipment (M2-200s; Ophir-Spiricon, UT, USA). The grating has a groove density of 1,740 lines/mm and a diffraction −1^th-order efficiency of 99%, to accurately analyze dispersion in the grating [32].

In Fig. 2, the PRBS 7 signals generated by the FPGA board are measured with ESA for modulation frequencies ranging from 1 to 12 GHz. In the frequency domain, the envelope takes on a sinc² shape, which broadens as the modulation frequency increases. This result is consistent with what is known about PRBS signals [25]. However, the frequency comb of PRBS 7 has intervals of f_m/(2⁷ − 1) Hz, which are too small to be seen by the naked eye. Theoretically, the PRBS spectrum should be zero at the modulation frequency, but spikes related to crosstalk signals [33] are observed. Figure 3 also shows these spikes in the modulated laser linewidth.

Figure 2. Pseudo-random binary sequence (PRBS) 7 signal for modulation frequencies of 1–12 GHz, in the frequency domain.

Figure 3. Spectral linewidth of the modulated beam with pseudo-random binary sequence (PRBS) 7 signal, in the frequency domain.

In Fig. 3, the linewidth of phase-modulated light in the frequency domain is depicted. To determine whether the modulation frequency increases the linewidth of the phase-modulated light, it is necessary to compare the RF spectra of the PRBS signal and the phase-modulated light, as well as to observe the dispersion of the beam diffracted by the grating due to the linewidth. Upon comparing Figs. 2 and 3, it can be noted that the first envelope’s shape in both spectra is identical. Additionally, the power at the modulation frequency is zero in both spectra. These results show that the modulation frequency broadens the linewidth of the phase-modulated light.

The phase-modulated light is utilized to demonstrate SBS suppression; Figure 4 shows the SBS power as a function of output power for the modulation frequency. The SBS power, achieved using a 99:1 coupler as shown in Fig. 1(c), is of the order of several milliwatts. DFB denotes a narrow-linewidth laser without phase modulation, and the SBS threshold power is observed to be around 5 W. When the linewidth is 1 GHz, it is confirmed that the SBS power rapidly increases near 25 W. This indicates that, in the case of modulation with PRBS, the SBS threshold power is approximately 5 times as high as that without modulation. It is verified that since the enhancement factor is 10 at the modulation frequency of 1 GHz for PRBS 7, as reported in [34], the SBS threshold power may be lower than the predicted power. When the modulation frequency is 3 GHz or higher, there is only a slight difference in the SBS power. Since the SBS threshold power at a modulation frequency of 3 GHz for PRBS 7 is around 3 times that at 1 GHz in [34], it is expected that the SBS threshold power can be confirmed when the output power exceeds 75 W.

Figure 4. Back-reflected stimulated Brillouin scattering (SBS) power as function of output power at the 2^nd ytterbium-doped fiber amplifiers (YDFA), for modulation frequencies of 1–12 GHz. Distributed feedback (DFB) indicates the unmodulated beam.

Figure 5 presents the measured results for beam quality M ² as a function of the modulation frequency. The x direction is chosen as the direction in which dispersion occurs due to the grooves of the diffraction grating. The analytical solution for beam quality $M_X^2$ Eq. (1) is explained in [27], and is modified for cases where the input beam quality is not 1:

Figure 5. Beam quality M ² as a function of spectral linewidth.

where $M_i^2$ is the input beam quality, ω₀ is the input beam’s radius, ∆λ is the linewidth, g is the grating’s groove density of 1,740 lines/mm, λ is the wavelength, and α is the angle of incidence upon the grating. When the laser is incident with radius ω₀, divergence angle θ₀, and incident angle α, the laser is diffracted with radius ω₁, divergence angle θ₁, and diffraction angle β. For ∆λ = 0, to first order, a single-mode Gaussian beam is obtained by

The angular spread due to the dispersion is

The beam quality for the diffracted beam can be written by

Assuming the Gaussian linewidth of 1/e² and $M_i^2$ ≠ 0, the beam quality in the x-direction can be represented by Eq. (1), taking into account the dispersion effect on the linewidth within the grating.

The increase in linewidth results in an increase in beam quality along the diffraction axis (x-direction). Dispersion of the diffracted beam, the input beam quality, and variations in the optical axis due to the vertical angle of the grating, contribute to the difference in beam quality M ². The vertical angle of the grating is set for beam-path separation, due to the Littrow configuration of the grating [32]. Furthermore, the measured beam quality may be degraded compared to the analytically calculated beam quality with a Gaussian linewidth of 1/e², since the light is modulated with a discrete frequency comb using PRBS and the linewidth is the full width at half maximum. In this experiment, the beam quality M ² exceeds 1.5 for linewidths above 3 GHz. However, in practical applications it is imperative to maintain the beam quality M ² below 1.5 [35–37] and analyze the crucial factors leading to its degradation. Variations in the optical axis due to input beam quality and the vertical angle of the grating contribute to an increase in beam quality M ², in addition to dispersion [28]. Furthermore, the measured beam quality M ² may degrade compared to the analytically calculated beam quality with a Gaussian linewidth, since the light is modulated with a discrete frequency comb using PRBS. This study is the first to report the measurement of the diffracted-beam quality of a laser modulated with a PRBS signal, in relation to the linewidth.

To summarize, this study has investigated the impact of linewidth on SBS suppression and beam quality in a high-power fiber-laser system. The results indicate that a modulation frequency of 3 GHz is optimal when the output power is in the range of several tens of watts. This modulation frequency allows for SBS mitigation while maintaining beam quality M ² below 1.5, as demonstrated in Figs. 4 and 5. Previous studies have shown that kilowatt-class lasers can be achieved with SBS mitigation and near-diffraction-limited beam quality, as shown in Table 1. However, little attention has been given to the diffracted-beam quality, which can be degraded by dispersion [38]. The diffracted-beam quality must be considered in a beam-combining system for power scaling to tens of kilowatts. Therefore, it is crucial to optimize the beam quality of high-power fiber-laser systems comprehensively, considering factors such as beam quality before linewidth broadening, mode-field diameter of the YDF, lengths of fibers, and number of combined beams, in consideration of the dispersion effect.

TABLE 1. Yb-doped fiber (YDF)-laser modulated with various radio frequency (RF) signals.

RF Signal	Wavelength (nm)	Linewidth (GHz)	Power (kW)	Beam Quality M 2	Diffracted Beam Quality M 2
PRBS 5 [27]	1,064	3	1.17	1.2	-
PRBS 8 [39]	1,034	3.5	1	1.1–1.2	-
PRBS 7 [40]	1,036–1,071	7	~1	1.19–1.21	-
PRBS 7 [This Work]	1,064	1~12	0.03	1.14	1.36–2.75
N/A [38]	1,060	40	0.01	1.02	1.86
WNS [41]	1,064.7	6.5	1.09	1.1	-
WNS [42]	1,064	20	3.25	1.22	-
WNS [43]	1,064	32	2.62	<1.3	-
WNS [44]	1,064	164.3	3.96	1.31	-
Sine [45]	1,064	7.6	1.08	1.14	-
Sine [46]	1,064.4	45	1.89	1.3	-

This study has investigated the impact of linewidth broadening on a YDF-laser system consisting of a master-oscillator power amplifier (MOPA) and SBC, suppressing SBS by phase modulation using a PRBS signal. To achieve this, the spectrum of the PRBS 7 signal generated by an FPGA board and phase-modulated light was measured within a frequency range of 1 to 12 GHz. The results showed that the linewidth increased in proportion to the modulation frequency. Furthermore, through phase modulation using the PRBS signal, the SBS threshold power was increased by more than a factor of 5, compared to the case without modulation, suggesting that linewidth broadening can effectively suppress SBS. However, the study also found that the diffraction-beam quality deteriorated as the linewidth increased. Therefore, the diffraction-beam quality as a function of modulation frequency in the YDF-laser system with phase modulation based on PRBS was measured for the first time. The findings from this study can be applied to improve the power and beam quality of high-power optical-fiber-laser systems.

This work was supported by the Agency For Defense Development by the Korean Government (UD160018RD).

National Research Foundation of Korea (NRF) grant, funded by the Korea government (MSIT) (No. 2019 R1A2C2011293).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.