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Abstract
Continuous fiber laser with ultra-high power and narrow linewidth is one of the key devices in the field of high-precision industrial processing, beam combining, and nonlinear frequency conversion. Under the premise of ensuring the signal quality, continuously increasing the output power is the focus of high-power narrow-linewidth fiber lasers. Driven by the white noise or pseudo-random binary sequence (PRBS), using cascaded phase modulations to broaden the spectrum of the seed source to suppress the stimulated Brillouin scattering (SBS) effect in the master oscillator power amplifier (MOPA) structure is an effective solution to increase the output power. However, this type of optical spectrum needs to be optimized, and the randomness of the driving signal causes a self-pulsing effect, which limits the further increase of the output power. In this paper, the influence of the frequency interval and randomness of the driving signal on the SBS effect in the laser system is analyzed. The modulated spectral type can be simply adjusted through changing the bit rate and inversion probability. Combining with high-order phase modulation, an approximate rectangular spectral broadening of the seed source with a tunable bandwidth up to 30 GHz is achieved. Compared with the cascaded white noise case, the output power of this scheme is increased by 600 W under the extended bandwidth of 27 GHz. It is fully verified that the seed source spectrum with high in-band flatness and low randomness can effectively suppress the SBS effect in the fiber laser and increase the output power.
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1. Introduction
The development of high-power narrow-linewidth continuous fiber lasers has greatly expanded the applications in advanced industrial processing, beam combining, and nonlinear frequency conversion. It has the irreplaceable advantages of high beam quality, high monochromaticity, stable energy, high electro-optical conversion efficiency, and convenient thermal management. All of those characteristics make laser manufacturing become one of the most advanced industrial processing methods in applications such as laser marking, micromachining, and drilling. These applications and developments put forward higher requirements on the performance of high-power narrow-linewidth fiber lasers, that is, under the premise of ensuring the beam quality, continuously increasing the emission power.
For a long time, the master oscillator power amplifier (MOPA) structure has been considered as a preferred structure for high-power narrow-linewidth all-fiber lasers. In this method, the output of a laser with a certain wavelength is used as the seed source whose power is amplified in the subsequent multi-stage amplifiers to form a much higher power output. However, the maximum output power is affected by various nonlinear effects in the fiber, such as cross-phase modulation, stimulated Raman scattering, stimulated Brillouin scattering (SBS), and four-wave mixing. Among them, the SBS effect having the lowest threshold becomes a bottleneck problem that limits the maximum power. There are four conventional methods for suppressing the SBS effect, including using fibers with a thicker core and larger effective mode area [1,2], controlling the temperature or stress gradient to change the Brillouin gain spectrum [3,4], reducing the effective length of the optical fiber [5,6], or increasing the seed linewidth [7,8]. The scheme of using phase modulation to broaden the seed source bandwidth has the characteristics of simple operation and controllability, high power improvement efficiency, which has become the research focus of suppressing the SBS effect in high-power fiber lasers.
Based on the MOPA structure, conventional phase modulation methods to broaden the seed source mainly include sinusoidal signal modulation, white noise source (WNS) modulation and pseudo-random binary sequence (PRBS) modulation. Dual-tone signals have been used as the driving signal of a phase modulator (PM) to achieve a 1 kW output power [9]. Ma et al. have used a three-level phase modulation to broaden the spectrum, and finally achieved a power output of 1890 W with a maximum linewidth of 45 GHz [10]. Although using sinusoidal microwave signals for spectrum broadening is relatively easy to achieve, the output power is limited by the modulation depth of the PM and the tolerable power. The WNS having a continuous and constant power spectral density in the entire frequency domain is preferable as the driving signal of the PM [11], and a laser system with an output power of 1.43 kW and a linewidth of 25 GHz has been achieved using a cascaded-WNS phase modulation method [12]. Using PRBS which has similar spectral characteristics to WNS to drive cascaded PMs, Clint Zeringue et al. have verified the SBS effect suppression performance in high-power fiber lasers with a maximum output power of 1 kW and a linewidth of 6 GHz [13–15]. For a given fiber length and linewidth, PRBS provides better control capabilities and the SBS effect threshold enhancement factor than WNS [16].
WNS and PRBS phase modulation technology has suppressed the SBS effect and increased the output power in high-power narrow-linewidth fiber lasers to some extent. But the Gaussian-shaped optical spectrum achieved by the WNS and PRBS may not be the optimal spectrum to suppress the SBS effect. Besides, recent studies have found that when the laser power is further increased, the self-pulsing effect appears in the time domain at the output [17]. The signal randomness of WNS and PRBS causes occasional spikes in the forward direction, which stimulates the backward first-order SBS effect. When the power is high, it then triggers the generation of forward second-order Stokes light. As the laser power increases, random pulses increase sharply. Self-pulse has the characteristics of high peak power, short pulse width, and strong randomness, which has become an important factor restricting the use of random signals modulation. Besides, the ultra-high instantaneous energy of the self-pulsed signal will seriously threaten the safety of high-power laser systems [18,19].
The purpose of this paper is to study new driving signals with tunable spectrum to optimize the phase-modulated spectrum, suppress random spikes, and further increase the output power of MOPA-based high-power narrow-linewidth fiber lasers. On the strength of the high-order phase modulation, a broadened seed source spectrum with a bandwidth up to 30 GHz is achieved using a single-stage PM while the bandwidth of the driving signal is lower than 1.5 GHz. The optical bandwidth can be changed simply by tuning the power and bandwidth of the PM driving signals. The effects of signal frequency interval and randomness on laser output powers are demonstrated using PRBS with different lengths to drive PM. The results show that PRBS with longer lengths has stronger randomness and is easier to simulate the self-pulsing effect. Besides, the spectrum envelope can be tailored by tuning the inversion probability of “1” and “0” bits in a quasi-PRBS. The larger the inversion probability is, the higher the power of the high-frequency components of the driving signals is. An approximate rectangular spectral shape is realized with a word length of 27-1 and an inversion probability of 7/8. Compared to the WNS modulation case with the same bandwidth, the laser output power has been increased up to 150%, which fully verified the necessity and effectiveness of optimizing the modulation signal spectrum.
2. Principle
In this part, the principle of the proposed high-power narrow-linewidth fiber lasers based on seed source spectrum broadening and the MOPA structure is introduced. The theoretical analysis and mathematical simulation of the electrical signal used to drive the PM are described in detail.
2.1 Comparison of SBS effect suppression schemes
The threshold calculation formula of the SBS effect in the fiber laser can be expressed as [20]
Table 1. Comparison of SBS effect suppression schemes for fiber lasers.
2.2 Principle of optical spectrum broadening using high-order phase modulation
The key to suppressing nonlinear effects of the seed source during the multi-stage power amplification process is to ensure that the total power is high enough while reducing the average power. The spectrum broadening strategy using phase modulation has shown a significant effect on the improvement of the SBS effect threshold in the fiber laser system. The modulated output spectrum is expanded according to the envelope form of the Bessel function. By increasing the modulation depth, more high-order sidebands can be excited. Different from using two cascaded PMs to extend the bandwidth of the seed source signal, this structure proposes to use the high-order modulation sidebands of a single PM to obtain a broadened signal having the same bandwidth. When a PM is driven by a high-power single-frequency electrical signal, a series of high-order modulation sidebands will be produced, as shown in Fig. 1(a). In this case, the obtained signal spectrum is completely discrete. When an electrical signal with a Gaussian-like envelope and high power is used to drive the PM, the seed source linewidth is broadened and has a Gauss-like envelope, as shown in Fig. 1(b). Theoretically, using the phase modulation method, only the phase information of the optical signal is changed, and the amplitude information remains unchanged. It can be guaranteed that the signal within the bandwidth range has a relatively low power while the total power of the seed source remains basically the same as before the modulation. The power of the expanded seed source can be greatly improved after multi-stage amplification based on the MOPA structure. As the non-linear effect with the lowest threshold, SBS is most easily excited and limits the maximal output power. As long as the signal power of a single frequency point in the bandwidth is higher than the other signals, it may give priority to the SBS effect during the amplification process. Therefore, broadened seed source having a flat in-band spectrum and steep out-of-band roll-off curve can fully ensure that the in-band signal obtains high gains while reducing the waste of the out-of-band power.
Fig. 1. The principle of the high-order phase modulation to broaden the seed source bandwidth using various electrical driving signals. (a) A single-frequency signal. (b) White noise. (c) A broadband signal with a rectangular-like envelope. (d) A broadband signal with a steep triangle-like envelope.
2.3 Principle of programmable electrical driving signal generation
Using cascaded WNS or PRBS phase modulation methods, the in-band spectrum of the broadened seed source is not flat enough, and the out-of-band power is high, thereby limiting the maximum laser output power. Therefore, it is necessary to design the frequency spectrum of the electrical driving signal to optimize the phase broadening spectrum. Ideally, if the electrical driving signal has an approximate rectangular spectrum, the spectrum of the seed source after a high-order phase modulation is also near rectangular. However, due to the nonlinear response of signal generators, electrical amplifiers (EA), and PM at different frequencies, the power of electrical signals is reduced to a certain extent at high frequencies, which in turn affects the flatness of the spectrum after PM, as shown in Fig. 1(c). This research intends to design a driving signal with a near-triangle envelope to compensate for the low responsivity at high frequencies, and to achieve a near-rectangular broadening spectrum, as described in Fig. 1(d). Using the high-precision controllability of the arbitrary waveform generator (AWG) to design programmable electrical driving signals of the PM, flexible control of the spectrum shape and in-band power distribution of the broadened waveform can be performed. The effect of spectral shape control on the spectral broadening of the seed source is theoretically analyzed to provide a theoretical basis for guiding the subsequent experimental verification.
PRBS is a classic sequence in which “0” and “1” bits appear with equal and random probability, and the spectrum distribution is a frequency comb with a Gauss-like distribution envelope in the frequency domain. By changing the sequences distributions of “0” and “1” in the time domain, a variety of signals composed of “0” and “1” in a specific distribution in the time and frequency domain can be formed. The inversion probability (from “0” to “1” or from “1” to “0”) between adjacent bits in the sequence is defined as P. This sequence type is defined as probability-tuning quasi-PRBS. For a completely randomly distributed sequence, the inversion probability is 0.5. For a sequence with a fixed distribution of “010101…”, the inversion probability is 1. In a binary sequence, the frequency domain distribution of the signal is determined by the distribution of “0” and “1” in the time domain. For a sequence with a specific inversion probability, the time-domain autocorrelation function can be described as [21]
where, B is the bit rate of the signal, and n is an integer determined by the bit rate and time $\tau$. The autocorrelation function of the random signal is Fourier transformed to obtain the corresponding power spectrum. The relationship between the power spectrum distribution of the signal and the inversion probability P can be expressed as [21]Fig. 2. The simulated signal spectra of power distribution in the frequency domain with different inversion probability P.
Take P = 6/8 as a simulation example, when the sequence length within a period is 500 bits, the generated signal spectrum and the theoretical spectral envelope are shown in Fig. 3. It can be seen that the simulation envelope distribution in the frequency domain is basically consistent with the theoretical analysis using Eq. (3). Therefore, the overall frequency domain distribution can be controlled by simply adjusting the value of P.
Fig. 3. The simulated signal spectrum and the theoretical spectral envelope with the sequence length of 500 and inversion probability P = 6/8.
3. Experiment and analysis
In this part, the experimental setup of the proposed structure is described. The relationships between signal frequency intervals and randomness on laser powers are analyzed. The power improvement using the proposed inversion probability-tuning sequence is also exhibited.
3.1 Experimental setup
The experimental setup of the proposed high-power narrow-linewidth fiber lasers based on seed source spectrum broadening using high-order phase modulation of inversion probability-tuning sequence is shown in Fig. 4, which mainly includes the optical spectral broadening of the seed source, multi-level optical power amplification, and the laser output power measurement. A polarization-maintaining seed source outputs a continuous optical signal with a center wavelength of 1050.5 nm and a power of 100 mW, then is sent into a polarization-maintaining PM with a 3-dB bandwidth of 2 GHz and half-wave voltage of 2 V. The output of an AWG (Tektronix, AWG7122C) is amplified by a high-power electrical amplifier (EA) as the driving signal of the PM. The EA has a gain of 35 dB and maximum output power of 33 dBm. The frequency spectrums of the driving signals can be easily controlled through corresponding algorithms which are designed by a personal computer (PC). The spectrum of the seed source is expanded after the PM, then is divided into two paths by a polarization-maintaining optical coupler 1 (OC1) with a coupling coefficient of 95:5. The first path with the lower power is input to an optical spectrum analyzer (OSA, Yokogawa AQ6373) for the spectrum measurement. The other path with the higher power is sent to the multi-level optical power amplification links. The expanded seed passes through two cascaded optical isolators (ISO) and optical pre-amplifiers (OA) to pre-amplify the signal power, then is input into port 1 of an optical circulator (CIR) for main power amplification processing. The output of port 2 from the CIR transmits a 10 m-long ytterbium-doped fiber and the corresponding optical power is amplified to be higher than 1 kW at the same time. Two mode field adaptors (MFA) are added at each side of the ytterbium-doped fiber to improve the power coupling efficiency with the single-mode fiber. A bidirectional pumping method is adopted and the pumping efficiency can reach more than 80%. The output of port 3 from the CIR is sent into a power meter to record the backward-light power, which mainly origins from the SBS effect. The amplified laser output is divided into two paths by a 95:5 OC2. The path with higher optical power is measured by a power meter. And the output of the other path with the lower power is sent to an oscilloscope (OSC) for real-time waveform observation after passing through a photodetector (PD). The self-pulsing phenomenon can be measured in this way.
Fig. 4. The experimental setup of the proposed high-power narrow-linewidth fiber laser based on seed source spectrum broadening. AWG, arbitrary waveform generator, EA, electrical amplifier, PM, phase modulator, PC, personal computer, OSA, optical spectrum analyzer, OC, optical coupler, ISO, isolator, OA, optical amplifier, CIR, circulator, LD, diode, MFA, mode field adapter, PD, photodetector, OSC, oscilloscope.
3.2 Analysis of signal frequency intervals and randomness on laser powers
In this part, the influences of frequency intervals and the randomness are analyzed through experiments. The seed source spectrum envelope obtained by the WNS modulation is a Gaussian type, which has many internal power peaks due to the signal randomness, and these peaks can easily reach the SBS threshold, resulting in the self-pulsing effect. Since the time domain waveform of WNS is completely free, the spectrum and the maximum power corresponding to different measurements will be different. For the PRBS or inversion probability-tuning quasi-PRBS, the frequency interval and randomness are related to the sequence length which can be represented as ${L_{PRBS}} = {2^m} - 1$ bits, where m is an integer. The longer the sequence length is, the smaller the signal frequency interval is. In principle, the driving signal with better continuity is conducive to reducing the average power of the optical spectrum to avoid non-linear effects. But the problem that followed is the signal randomness is also stronger and the frequency spikes are much easier generated, which will lead to nonlinear effects during the power amplification process. Using quasi-PRBS with 2.5 Gbps bit rate and P = 6/8 as an example, when m is set to 5, 7, 11, 15, 21, 23, the corresponding seed source spectra after high-order phase modulation and the laser output powers are shown in Fig. 5 and 6, respectively.
Fig. 5. Optical spectra of broadened seed source using quasi-PRBS with P = 6/8 and different lengths as the driving signal of PM.
Fig. 6. The relations between laser output powers and backward powers using quasi-PRBS with P = 6/8 and different lengths as the driving signal of PM.
As can be seen, the bandwidths of the broadened optical spectra under different signal lengths remained basically the same, which are about 26.5 GHz. In the experiment, when the self-pulsing effect is observed in the system, that is, the secondary SBS effect affects the forward output of the laser, the corresponding laser power is defined as the maximum output. When $m = 5$, the frequency interval of PRBS is about 80.6 MHz, and the frequency interval of the seed source spectrum after broadening is relatively large, which leads to high and uneven in-band average power and easy to stimulate the self-pulsing effect. When $m = 7$, the frequency interval of PRBS is about 19.7 MHz, and a maximum laser power of 1643 W is obtained. The frequency interval of PRBS is smaller than 77 kHz while $m \ge 15$ . The driving signal has strong randomness, which leads to in-band frequency spikes and limits the increase of output powers. When m = 21 and 23, the maximal output power is only around 700 W. The relation among frequency intervals, randomness, and output powers can be seen in Fig. 7. Therefore, there is a trade-off between the frequency interval and randomness of an electrical driving signal. For a PRBS with a given bandwidth, when the signal frequency interval is less than 80 MHz, the influence of randomness on the laser power is stronger than the frequency interval.
3.3 Waveform optimization of electrical driving signals
As described in the principle part, in order to compensate for the lower response of optical and electronic devices at high frequencies compared to low frequencies, the waveform optimization of electrical driving signals is necessary. Through tuning the inversion probability P of the quasi-PRBS, the amplitude of the high-frequency components in the frequency domain can be compensated to different degrees. In the experiment, the bit rate of the electrical driving signal is set to 2.5 Gbps, and the corresponding signal bandwidth is 1.25 GHz. When P is set to 5/8, 11/16, 6/8, 13/16, 7/8, the generated electrical signals by AWG are used as driving signals to obtain the broadened spectrum of the seed source as described in Fig. 8. The broadened bandwidths are about 27 GHz with different driving signals. The optical spectrum using cascaded WNS as a driving signal is also shown in Fig. 8. Compared with the Gaussian spectrum using cascaded WNS modulation, the in-band flatness of this scheme has a certain improvement. Limited by the measurement accuracy of the one-micron OSA, the measured bandwidth differs by nearly 0.5 GHz, but it is basically guaranteed to be at the same bandwidth level.
Fig. 8. The Broadened optical spectra of the seed source using cascaded WNS and quasi-PRBS with various inversion probability as the driving signal, respectively.
The relationships between the output power and backward power under different driving signals are shown in Fig. 9, and the corresponding power statistics are summarized in Table 2. When P = 5/8, the laser output power is 1243 W, and the backward power is 81.6 mW. As the value of P increases, the laser output power gradually increases. The maximum power of 1748 W is obtained with P = 7/8, and the backward power is 182 mW when the self-pulsing effect is observed. However, using cascaded WNS modulation, the self-pulsing phenomenon is observed when the backward power is only 57.6 mW while the output power is 1150 W. This result proves that inversion probability-tuning quasi-PRBS has a better random pulse suppression performance than WNS. With the same broadened bandwidth, as the P value increases, signal components at high frequencies have higher power. The in-band spectrum flatness is improved, and the laser output power increases correspondingly, which fully verifies the necessity and effectiveness of compensating the driving signal power at high frequencies. In addition to nonlinear effects, the maximum laser power is limited by the current experimental system. The output power is supposed to further increase by using a better MOPA structure.
Fig. 9. The laser output powers and backward powers using cascaded WNS and quasi-PRBS with various inversion probability as the driving signal, respectively.
Table 2. The output power of high-power fiber laser using cascaded WNS and the proposed scheme.
WNS is an analog signal having irregular and unpredictable randomness. When the cascaded WNS modulation is used to broaden a seed source, random pulses are also induced. This feature causes the maximum output power of the laser to be unstable under different measurements. To verify the power stability of this scheme, the output powers of the proposed fiber laser using quasi-PRBS modulation with m = 7 and P = 6/8 under different measurements are recorded in Table 3. When the broadened bandwidth is 26 GHz, the laser output power is 1638 W, and the backward power is about 188 mW. The laser output power varies by 2% under different tests, which verifies the laser power stability of this scheme.
Table 3. The output power of the proposed fiber laser using quasi-PRBS modulation with m = 7 and P = 6/8 under different measurements.
3.4 Comparison and analysis
Performance comparison of using various electrical signals to drive the PM is described in Table 4. The single-frequency signal is the easiest to generate in the driving signals below. However, the completely separated spectrum leads to a high average power of the seed source spectrum. Therefore, it has the worst suppression performance on the SBS effect. WNS has a continuous spectrum, but the power spectral distribution is limited to Gaussian shape. Generally, a cascaded phase modulation scheme is required to achieve a seed source spectrum with a super-Gaussian shape but brings to much higher costs. In addition, the randomness of the analog sequence in the time domain results in random spikes which limit the maximal output power. PRBS is a digital signal with separated spectral lines, whose envelop distribution is similar to the WNS case. By controlling the frequency intervals, the RRBS-driven optical spectrum can achieve equivalent output power with the WNS case but provide an alternative digital solution.
Table 4. The performance comparison of different electrical driving signals.
In contrast, the driving signal designed in this scheme has more adjustment dimensions. In addition to adjusting the amplitude, frequency, and bandwidth of the driving signal, the shape design of the broadened spectrum can also be achieved by adjusting the spectrum type of the driving signal. The advantages of the proposed quasi-PRBS seed source are double: first, the modulated spectral type can be simply modified through changing the inversion probability of adjacent bits, which shows better nonlinear suppression performance. With the increase of the inversion probability P, the energy of the high-frequency components is also increased. Quasi-PRBS are easy to implement and adjust, which results in the spectral bandwidth can be adjusted simply by changing the bit rate and amplitude. Second, the single-stage high-order phase modulation with low bandwidth is adopted to achieve wide spectral bandwidth, which can effectively reduce the structural complexity and size. Thus, an approximate rectangular spectral broadening with a tunable bandwidth up to 30 GHz is realized, while the driving single bandwidth is lower than 1.5 GHz. This flexibility of spectrum control is difficult to achieve with the first three schemes and shows obvious advantages. Besides, the time sequence is pre-designed and fixed rather than random as in the cascaded WNS case therefore there are much fewer random spikes in the broadened optical spectrum, resulting in high stability of the output power. By further designing the driving signal with more adjustment dimensions, the bandwidth, waveform, roll-off, and other properties of the seed source spectrum are expected to be improved, thereby optimizing the MOPA structure-based high-power narrow-bandwidth fiber laser systems.
4. Conclusion
As one of the key equipment for advanced industrial processing, beam combining, and nonlinear frequency conversion, the power increase of high-power narrow-linewidth fiber lasers has received extensive attention from researchers in various fields. Using a single-stage high-order phase modulation and variable inversion probability quasi-PRBS as a driving signal, an effective method for optimizing the spectral profile of the seed source is proposed. The boosting effects of the output power and the suppression of the SBS effect are verified by experiments based on a fiber laser system with a MOPA structure. When the broadened bandwidth is 27 GHz, this solution obtains a near-rectangular seed source spectrum, and the laser output power is 1748 W. Compared with the cascaded WNS modulation scheme under the same bandwidth, the output power is increased by 600 W. Further, the experiment proves that the spectrum continuity, in-band flatness, and the randomness of the broadened seed source play a key role in the suppression of the SBS effect. In particular, the randomness of the driving signal is most likely to excite the SBS effect, which in turn leads to the forward self-pulsing effect and limits the increase of laser powers. This result has an important guiding value for the design of the driving signal of PM in the future.
Funding
The Key-Area Research and Development Program of Guangdong Province (2018B010114002); Project funded by China Postdoctoral Science Foundation (2021M702096).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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