Spectral broadening scheme for suppressing SBS effects based on time-domain optimized chirp-like signals

Jie Li; Mengyue Shi; Yong Wu; Zhiwei Fang; Jiajin Wang; Huan Mu; Weisheng Hu; Lilin Yi

doi:10.1364/OE.483307

1. Introduction

The high-power narrow-linewidth fiber lasers have great applications in spectral beam combining (SBC) [1] and coherent beam combining (CBC) [2]. Based on the master oscillator power amplification (MOPA) configuration, kW-level high-power fiber amplifiers have been demonstrated in several research. The further power scaling is limited by the nonlinear effect including transverse mode instabilities (TMIs) [3], stimulated Brillouin scattering (SBS), and stimulated Raman scattering (SRS), which requires a comprehensive optimization [4]. Although lasers with wide enough linewidth, sometimes in the sub-nanometer range, can be used to suppress the SBS effect [4], the 3 dB linewidth of the laser is often limited to <30 GHz in most SBC and CBC scenarios [5]. With such an extremely narrow linewidth, better suppression of SBS effects remains a primary concern owing to its lowest threshold.

The seed source scheme is a crucial factor to suppress the SBS effect, the design of which attracts the great attention of researchers. Compared with other schemes, such as narrow-linewidth fiber-Bragg-grating-stabilized laser diode seed source [6,7], the phase-modulated seed source is a more prevailing scheme because of its time-domain stability and spectral purity in the amplification process [8]. In recent research, the filtered periodic binary sequence was proposed to control the frequency domain power distribution of the spectrum and mitigate the effects of dwell time, providing a new perspective for PRBS-based scheme optimization [9–12]. As for the white noise driving scheme [13], some research is trying to further enhance the efficacy of noise modulation for SBS suppression by the incorporation of sinusoidal modulation [14]. Meanwhile, many researchers realized the flat-top spectrum by flexibly controlling the frequency domain distribution of the drive signal and demonstrated better SBS suppression [15]. In addition, related studies pointed out theoretically that linearly chirped diode laser can show great advantages in SBS suppression [16]. However, the design of linearly chirped diode lasers with a high chirp rate is difficult in the actual system. In previous research, the chirp seed laser with the highest swept rate up to $5 \times {10^{17}}$Hz/s has been realized, and the 1.6 KW fiber laser amplifier using chirped seed was demonstrated [17]. But the system structure is complex, and the rate and linearity of the linear chirp are still not stable enough. Recently, a study proposed a stepwise optical frequency pulse train (SOFPT) to suppress the SBS effect in a 200-m fiber by decreasing the interaction distance [18]. Similarly, in the continuous laser system, some studies have verified through numerical simulations that the parabolic signal-driven spectral spreading scheme can achieve better SBS suppression than conventional noise and PRBS modulation schemes [19,20]. However, only a maximum spectral bandwidth of 200 MHz has been achieved due to the limitation of the device [21]. Besides, a two-stage phase-modulated chirp scheme has been designed to generate signals through a high-speed AWG of 96 Gbps, which can theoretically construct linear chirp modulation in any bandwidth range [22]. The practical performance of this scheme has not been verified in actual fiber laser amplification systems, which are limited by the extremely high signal rate requirement of this scheme.

This research designs a chirp-like driving signal scheme by segmenting the parabola phase and time domain processing. The broadened spectrum of up to 10GHz@3 dB is achieved using a low-rate Digital-to-Analog Converter (DAC) of 2.5Gpbs and an electrical amplifier with a gain of 33 dB in the experiment. The SBS threshold model is constructed based on the three-wave coupling equation in the simulation. The SBS suppression effect between the chirp-like modulated spectrum, flat-top envelope spectrum, and Gaussian envelope spectrum is compared by simulation, and the advantages of the chirp-like signal modulation scheme in the SBS threshold and bandwidth-distribution normalized threshold are demonstrated. The watt-class fiber laser amplification system is also built, and the performance verification is completed in the experiment as well. An improvement of >18% in the SBS threshold and the highest bandwidth-distribution normalized threshold are obtained compared with the flat-top and gaussian spectra. This paper further indicates that the chirp-like characteristics of the phase can better suppress the SBS effect, and also provides a more complete explanation of the SBS effect suppression in phase-modulated narrow linewidth fiber laser systems from two different perspectives in the time and frequency domains.

2. Principle

2.1 Principle and challenge of achieving linear chirp through external phase modulation

The linear-chirp modulated seed source can achieve a uniform broadening for the SBS gain spectrum during the amplification in a MOPA so that efficient SBS suppression can be obtained. Mathematically, the linear sweeping property corresponds to a parabolic phase change, which can be expressed by the following equation

(1)$$\textrm{s}(t) = \exp (j({\omega _c}t + \phi (t))),\phi (t) = \frac{1}{2}k{t^2},$$

where ${\omega _c}$ is the center frequency of the laser, $\phi (t)$ is the phase and k is the sweep rate.

In the actual amplification system, the length of the fiber is generally only about 10 m, and the suppression of SBS requires a sweeping range of about tens of GHz within the time that the seed source passes through the fiber. Under such conditions, if a parabolic signal is used to drive the phase modulator, the maximum drive phase up to hundreds of π needs to be generated [19], which imposes extremely high requirements on the electrical power amplifier and the modulator and is almost impossible to achieve.

The problem of high drive power requirements caused by high chirp rates can theoretically be solved by partitioning the parabolic phase. The large drive phase can be scaled into the range of 0∼2π based on the periodicity of the cosine function.

In the experiment, the generation of such piecewise parabolic signals by hardware still requires a large sampling rate of the signal generation device, such as DAC, due to the large driving phase. Assuming a signal period of 30 ns and a sweeping range of 10 GHz, the required maximum drive phase can be calculated as

(2)$${\phi _{\max }} = 2\pi \times 10GH\textrm{z} \times \frac{1}{2} \times 30ns = 300\pi .$$

The corresponding minimal segment period is about 0.1 ns. To ensure signal integrity, the sampling rate of the output device needs to be greater than 10GSps. So a feasible way is to design an arbitrary parabolic signal, then do a Modulo operation with an arbitrary number $\alpha $, and then amplify it through a power amplifier until it meets the required sweep range. The signal ${\phi _{partition}}(t)$ generated in this way can be expressed as

(3)$${\phi _{partition}}(t) = m(\phi (t) - n\alpha ),n = 0,1,2 \cdots ,$$

where $\alpha $ is the number which the Modulo operation is made with and $m$ is the linear amplification factor.$n$ represents the different segments of the signal, and $n\alpha $ denotes the phase difference that needs to be subtracted due to the Modulo operation. As for this scheme, the instantaneous frequency within the same signal segment can be amplified by a factor of m compared to the original. So the range of scanning frequency can be adjusted by changing the value of m. However, at the location of the splitting point, there exists distortion due to the different values of n corresponding to the front and rear fragments, which can be written as

(4)$${\phi _{partition}}({t_2}) - {\phi _{partition}}({t_1}) = m(\phi ({t_2}) - \phi ({t_1})) + m\alpha ,$$

where ${t_1}$ and ${t_2}$ denote the locations of the splitting points. In Eq. (4), when $m\alpha $ is not equal to an integer multiple of 2π, it distorts the instantaneous frequency at the splitting point. As result, the linear chirp characteristics will be destroyed, and thus the uniform spreading of the SBS gain spectrum cannot be achieved. Therefore, although this approach can reduce the power and sampling rate requirements, it demands strict control of the signal power, which is still difficult to implement in practical systems.

2.2 Principle of chirp-like signal design

Based on the piecewise parabolic signal, we further propose a chirp-like signal scheme to drive the phase modulator for spectral broadening. For the segmented parabolic signal, a phase difference distortion of $m\alpha $ is generated at the jump point, and we notice that the difference between the maximum and minimum phase of each segment after amplification is also exactly $m\alpha .$Therefore, the segmented signal is processed in the time domain to eliminate this phase difference distortion term. The specific design scheme is shown in Fig. 1.

Fig. 1. Principle of the chirp-like signal generation.

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The segments in the time domain are selectively flipped so that the maximum and minimum phases of the different segments are connected, thus eliminating the distortion term caused by the splitting. Compared with the parabolic signal, to realize the same spectral spreading bandwidth, the chirp-like signal not only effectively reduces the signal sample rate and drive power requirements, but also further solves the phase distortion problem of the piecewise parabolic signal at the jump point. It does not require strict power control, and therefore can be better used in spectral broadening scenarios.

3. Numerical Simulation

3.1 Spectral simulation based on chirp-like phase modulation

To further illustrate the advantages brought by the chirp-like signal over the piecewise parabolic signal scheme in spectral broadening, spectra modulated by chirp-like signals are simulated in this section. The modulated spectrum can be described by the following equation

(5)$$s(t) = \exp (j(\frac{\pi }{{{V_\pi }}}M{\phi _{chirp - like}}(t))),$$

where ${\phi _{chirp - like}}(t)$ is the chirp-like signal mentioned in the second part, ${V_\pi }$ is the half-wave voltage, and M is the linear amplification factor.

From the simulation results in Fig. 2, for the piecewise parabolic signal, the 3 dB bandwidth of the modulated spectrum is 1.75 GHz, 1.9 GHz, and 2.25 GHz when the signal power is 1.5 W, 2 W, and 2.5 W. The carrier wave (corresponding to the center of the simulated spectrum) is not effectively suppressed. However, for the chirp-like signal, the bandwidths of the spectra can reach 4.25 GHz, 5.25 GHz, and 5.75 GHz respectively with the same driving power, and the spectra achieve an approximately uniform spreading within 3 dB bandwidth. Obviously, the chirp-like signal is more effective in spreading the spectrum at different modulation depths, while the piecewise parabolic signal suffers from the problem of spikes in the spectral carrier position when the maximum phase in the signal is not an integer multiple of 2π.

Fig. 2. Spectral broadening result of chirp-like signal and piecewise parabolic signal with different modulation depths. (a) spectra modulated by piecewise parabolic signal, (b) spectra modulated by the chirp-like signal.

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Further, the spectral time-frequency relationship of the two schemes can be analyzed using the Hilbert-yellow transform as shown in Fig. 3. Set the carrier frequency to 5 GHz, and the sweep range to 1 GHz in the simulation.

Fig. 3. Time-frequency characteristics of the chirp-like signal and piecewise parabolic signal based on the Hilbert-Yellow transform.

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For the piecewise parabolic signals generated by Eq. (3), the time-frequency relationship of the modulated spectrum shows a steep change at each segmentation point, which does not fall within the originally defined sweep range. For the chirp-like signal after processing by time-domain selective flipping, the instantaneous frequency transitions from one linear segment to another at the segmentation point. From the overall point of view, the swept frequency range of the signal is not changed, only the order of the swept frequency is changed.

3.2 SBS threshold simulation based on the three-wave coupling equation

The transmission of phase-modulated signals in optical fibers and the Stimulated Brillouin scattering effect can be modeled by solving the three-wave coupling equations [11]. Under simplification, all fields can be considered as slow-varying fields with liner polarizations, so that the distribution of the signal in space can be characterized by the signal envelope. Further neglecting the group velocity dispersion as well as the background loss, the time-space variation relationship between the laser seed light, the acoustic field, and the Stokes light can be described by the following three-wave coupling equation [11,23]

(6)$$\begin{array}{l} \frac{n}{c}\frac{{\partial {A_L}}}{{\partial t}} + \frac{{\partial {A_L}}}{{\partial z}} = i\gamma ({|{{A_L}} |^2} + 2{|{{A_S}} |^2}){A_L} + i{\kappa _1}{A_S}\rho ,\\ \frac{n}{c}\frac{{\partial {A_S}}}{{\partial t}} - \frac{{\partial {A_L}}}{{\partial z}} = i\gamma ({|{{A_S}} |^2} + 2{|{{A_L}} |^2}){A_S} + i{\kappa _1}{A_L}{\rho ^ \ast },\\ \frac{{\partial \rho }}{{\partial t}} ={-} \frac{1}{2}{\Gamma _B}\rho + i{\kappa _2}{A_L}{A_S}^ \ast{+} f, \end{array}$$

where ${A_L}$, ${A_S}$ and $\rho $ denote the amplitude distribution of signal light, Stokes light, and acoustic field, respectively. n denotes the refractive index of the fiber core, $\gamma = {{{n_2}} / {c{A_{eff}}}}$ is the nonlinear parameter, where ${n_2}$ is the nonlinear refractive index, ${A_{eff}}$ is the effective mode field area of the fiber, c is the speed of light, and γ is mainly used to describe the intensity of self-phase modulation as well as cross-phase modulation. ${\kappa _1} = {{\omega {\gamma _e}} / {2nc{\rho _0}}},{\kappa _2} = {{\omega {\gamma _e}} / {2{c^2}{v_A}{A_{eff}}}}$ characterize the coupling coefficients between the acoustic and optical fields [24], where $\omega = 2\pi {c / {n\lambda }}$ is the signal light angular frequency, corresponds to the signal light wavelength $\lambda $. ${\gamma _e}$ is the electrostriction constant, ${\rho _0}$ is the density of the fiber, and ${v_A}$ is the speed of acoustic wave propagation. ${\Gamma _B}$ is the acoustic wave damping rate, whose inverse description responds to the magnitude of the phonon lifetime $\tau $. f describes the thermal noise source excited by the acoustic field and is the initial noise of the SBS process. Statistically, the stochastic process f satisfies

(7)$$\begin{array}{l} \left\langle f \right\rangle = 0,\\ \left\langle {f(t){f^ \ast }(t + \Delta t)} \right\rangle = Y\delta (\Delta t), \end{array}$$

here $Y = {{2kT{\rho _0}{\Gamma _B}} / {{v_A}^2{A_{eff}}}}$ denotes the intensity of the noise [24], where k is Boltzmann's constant and T is the temperature. The fiber length in the simulation is 9 m, and the simulation step is 0.01 m. The SBS threshold is defined as the power when the backward power reaches one-thousandth of the forward power. To ensure the stability of the simulation values, the backward power is calculated over a range of 10 transit times and run several times simultaneously to take the average value. Setting the appropriate simulation parameters, as shown in Table 1, the unmodulated signal is supplied to the three-wave coupled model, which corresponds to an SBS threshold of about 22.5W.

Table 1. Parameters and the values used for simulation

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To comprehensively evaluate the threshold enhancement brought by the chirp-like scheme, the spectra modulated by the chirp-like signal are compared with flat-top spectra and Gaussian-type spectra for SBS thresholds in simulations.

We considered the SBS threshold under the same 3 dB bandwidth of about 10 GHz as a criterion to evaluate the performance. Binarized multi-frequency signals [25] proposed by our previous work were used for the flat-top and Gaussian spectra. By adjusting the composition of the frequency components and the amplitude of each frequency component, the modulated spectra with different spectral power distributions can be obtained. In short, the driving signal of the flat-top spectrum should have more power at high frequency than at low frequency, while for the gaussian spectrum, it reversed. Based on the phase modulation model of Eq. (5), the desired target spectra were obtained by applying different driving signals under the condition that the ${V_\pi }$ was 4 V. The drive signal and the corresponding spectrum are shown in Fig. 4.

Fig. 4. Three drive schemes and the corresponding broadened spectra after phase modulation. (a) Chirp-like signal in the time domain. (b) Driving signal for flat-top spectrum in the frequency domain. (c) Driving signal for Gaussian spectrum in the frequency domain. (d) Broadened spectrum modulated by the chirp-like signal. (e) Flat-top spectrum. (f) Gaussian spectrum.

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The above three sets of drive signals are sampled at 20 Gb/s for the SBS simulation and the maximum effective frequency is only 1.25 GHz. By controlling the drive power, the 3 dB bandwidth of all three spectra is 9.75 GHz. The three spectra are input to the amplification model to measure their threshold. By scanning the backward Stokes light intensity at different powers, we can obtain the amplification characteristic curves of different spectra in Fig. 5.

Fig. 5. Power variation during amplification of spectrum using chirp-like signal, flat-top spectrum and gaussian spectrum.

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The forward power and return power can be approximately fitted by the exponential function. From the simulation result, the SBS threshold measured by the amplification model is 2180W for the flat-top spectrum. The gaussian spectrum has an improvement in the SBS threshold compared to the flat-top spectrum, reaching 2400W. The chirp-like scheme has the highest SBS threshold of up to 2700W among the three schemes, which achieves a 24% improvement over flat-top spectra and a 12.5% improvement over Gaussian spectra.

The SBS threshold under the same 3 dB bandwidth is an effective and widely used criterion to evaluate the performance of the different schemes, but sometimes the result may be not enough because the power distribution of different schemes might be distinct. In the simulation above, the power distribution of three spectra can be described as the relationship between the fraction of total power and the corresponding bandwidth as Fig. 6 shows. At the point of 0.85 of total power, the gaussian spectrum has the maximal bandwidth of ∼11.5 GHz, while the corresponding bandwidth of the chirp-like scheme is ∼9.5 GHz. The flat-top spectrum has the minimal bandwidth. However, the result differs a lot at the point of 0.6 of total power. Based on these, although an improvement of the SBS threshold on certain 3 dB bandwidth has been verified, it is necessary to further consider the effect of the shape difference of the above three schemes. In the related research, both the 2^nd moment about the mean and the combination of 3 dB bandwidth and 20 dB bandwidth are criteria to define the shape of the spectrum more exactly. However, the 3 dB bandwidth and 20 dB bandwidth are hard to control the same simultaneously with different schemes. While the 2^nd moment about the mean is more useful for the beam-combining system and is still not reliable enough for the MOPA with only one laser.

Fig. 6. Relationship between the fraction of the total power and spectral bandwidth of the three spreading spectra.

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To further evaluate the threshold enhancement by the chirp-like signal on the basis of the threshold of certain 3 dB bandwidth, we define the bandwidth-distribution normalized threshold $\sigma $ as

(8)$$\sigma = {P_{th}}{{F{R_{3dB}}} / {{B_{3dB}}}},$$

where ${P_{th}}$ is the SBS threshold, $F{R_{3dB}}$ denotes the fraction of total power within 3 dB bandwidth, and ${B_{3dB}}$ denotes the 3 dB bandwidth. This criterion can be used as a better indicator to describe the performance of different spectra combined with the 3 dB bandwidth and can also reflect the efficiency of threshold improvement under unit power.

From the result in Fig. 6, the $F{R_{3dB}}$ of chirp-like scheme, flat-top spectrum and gaussian spectrum in the simulation is 0.88, 0.91 and 0.78 respectively. The corresponding bandwidth-distribution normalized threshold is calculated. The Gaussian spectrum has the minimal normalized threshold ${\sigma _{\min }}$, which is about 192. The flat-top spectrum and the chirp-like scheme have an improvement of 25% and 5% respectively compared with the ${\sigma _{\min }}$. This indicates the fact that the chirp-like scheme not only can enhance the SBS threshold but also has the best threshold improvement efficiency under unit power among these three spectra.

4. Experiments

4.1 Experimental setup

The experimental setup is shown in Fig. 7, which mainly includes the spectral broadening module and the threshold measuring module. In the seed source broadening part, a polarization-maintaining seed source centered at 1061.2 nm is used. The seed source laser is connected to a phase modulator (PM) for spectral broadening. The half-wave voltage of the PM is 2 V, and the bandwidth is 2 GHz. In the drive signal generation part, we use a Field Programmable Gate Array (FPGA) to control a 2.5Gbps DAC chip to generate the analog signal. After passing through an electrical amplifier (EA) with a saturation output power of 33dBm, the electrical signal is connected to the PM. A low-pass filter (LPF) is connected between the EA and the PM to eliminate high harmonics generated during the amplification process. The seed source is amplified by a ytterbium-doped fiber amplifier module (YDFA). An optical isolator (ISO) is involved between different stages to avoid the reflected light. The YDFA is a customized commercial module with a GSF-10/125 Ytterbium-doped fiber, which is backward pumped by diodes (LDs) operating at 976 nm through the polarization-maintaining combiner (PMC). The output power can be adjusted in the range of 0-10W by using a two-stage amplification structure. a 1 km Hi1060 fiber is used as the energy transfer fiber to measure the SBS threshold. A mode-field adapter (MFA) is used to couple the YDFA output power into the subsequent HI1060 fiber. Before the 1 km Hi1060 fiber, an optical circulator (CIR) with high power tolerance is used to detect the backward power with a power meter. In addition, the output power of port 2 of the CIR and the backward power of port 3 can be read from the panel of the YDFA and the power meter respectively. At the output port of the Hi1060 fiber, the endcap is utilized to deliver the output laser into free space.

Fig. 7. The experimental setup of the spectral broadening module and the threshold measuring module. FPGA, Field Programmable Gate Array, LD, laser diode, EA, electrical amplifier, LPF, low-pass filter, PM, phase modulator, ISO, optical isolator, PMC, polarization-maintaining combiner, MFA, mode-field adapter.

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4.2 Experimental results

In the experiments, broadened spectra with a 3-dB bandwidth of around 10 GHz were achieved by chirp-like scheme. The chirp-like signal for the modulation is generated according to Eq. (3). The $\alpha $ for modulo operation is set as 0.18. Then after the operation of the time domain selectively flipping, the signal is output with a DAC of 2.5Gbps. The m in the Eq. (3) is about 30 dB based on the EA in the experiment. Similarly, we obtained flat-top spectra and Gaussian spectra using the binarized multi-frequency signals based on the same experimental setup as a comparison. Different from the simulation, the period of the driving signals is prolonged to $2\mu s$ due to the fiber length being much longer in the experiment. The spectra we obtained in the experiment are shown in Fig. 8.

Fig. 8. The corresponding spectra of different spectral spreading schemes in the experiment. (a) Broadened spectra modulated by the chirp-like signals. (b) The flat-top spectra and gaussian spectrum.

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Based on the high-precision spectral measurement device with a resolution of 50 MHz, enough details of spectral power distribution can be displayed for precise comparison. The spectra modulated by chirp-like signals in Fig. 8 (a) correspond to two measurement records with the same driving signal. Both of them have a 3 dB bandwidth of 9.5 GHz and $F{R_{3dB}}$ are 0.65. The flat-top and Gaussian spectra are shown in Fig. 8 (b). The 3 dB bandwidth of the flat-top spectra above is 10.74 GHz and 9.6 GHz, which corresponds to different driving power respectively. The gaussian spectrum has a 3 dB bandwidth of 10.33 GHz. The $F{R_{3dB}}$ for spectra in Fig. 8(b) are 0.94, 0.9, and 0.737, respectively.

The relationship between backward optical power and forward power for the above five spectra is depicted by the threshold measuring device, as Fig. 9 shows. Considering only the SBS threshold, the spectra obtained by the chirp-like signal have the highest performance in the experiment at a similar 3 dB bandwidth. The chirp-like scheme with 9.5GHz@3 dB has a threshold improvement of about 46% compared with the flat-top spectrum with 9.6GHz@3 dB, 35% compared with the flat-top spectrum with 10.74GHz@3 dB and 18% compared with the gaussian spectrum with 10.33GHz@3 dB in the watt-class amplification. Although the bandwidth of the five spectra is not exactly equal, the chirp-like scheme shows obvious advantages with the lowest bandwidth and highest SBS threshold.

Fig. 9. Power variation during amplification of spectrum using chirp-like signal, flat-top spectrum, and gaussian spectrum in the experiment.

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Further, in terms of the bandwidth-distribution normalized threshold $\sigma $, the chirp-like scheme also shows improvement to a certain extent, as Table 2 shows. The Gaussian spectrum has the minimal normalized threshold ${\sigma _{\min }}$. The spectrum modulated by a chirp-like signal achieves up to 14% enhancement compared to the Gaussian spectrum. And the performance outperforms the flat-top spectrum comprehensively as well in the experimental results.

Table 2. Threshold results of different schemes in the experiment

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For the chirp-like signal scheme, the spectra with a bandwidth of ∼10 GHz can be achieved with the 2.5Gbps DAC. Under the criterion of the threshold with certain 3 dB bandwidth, the chirp-like scheme realizes an improvement of > 18% compared with the other schemes. Meanwhile, consistent with simulation results, a higher $\sigma $ is obtained, showing an advantage in the threshold improvement efficiency under unit power. This can be attributed to the special time-domain design of our proposed chirp-like scheme. In addition, it can be inferred that the SBS suppression effect is not only related to the power distribution of the spectrum but also can be improved by the time domain design. The time and frequency domain can be two independent dimensions in a way that can be optimized in the actual system.

5. Conclusion

We analyze the limitations of piecewise parabolic signals in spectral broadening scenarios and propose a novel driving signal named chirp-like signal, which has the characteristic of linear frequency chirp and can realize spectral broadening efficiently. The SBS threshold theoretical model is constructed based on the three-wave coupling equation, and the modulation scheme using the chirp-like signal shows advantages in the SBS threshold at a 3 dB spectral bandwidth of ∼10 GHz. In the experiment, we achieved a broadening spectrum with a 3 dB bandwidth of up to 10 GHz based on the chirp-like signal modulation with a 2.5Gbps DAC. Meanwhile, the chirp-like scheme achieves a 35% improvement in the SBS threshold over flat-top spectra and an 18% improvement over Gaussian spectra under the same conditions in W-class fiber amplification experiments. The bandwidth-distribution normalized threshold $\sigma $ is defined to eliminate the effect of the difference in bandwidth and power distributions. The normalized threshold improvement of the chirp-like modulation scheme is demonstrated numerically and experimentally.

Meanwhile, the experiment setup with 2.5Gbps DAC can be applied to the KW-class MOPA system after adjusting the period of the chirp-like signal to match the short fiber. As for the complicated scenario of coherent beam combining, our chirp-like scheme may provide a potential way for comprehensive optimization.

Funding

China Postdoctoral Science Foundation (2021M702096); National Natural Science Foundation of China (62025503, 62205198).

Acknowledgments

The authors thank Shanghai Feibo Laser Technology Co. Ltd. for supplying the laser power measurement system and AIOPTICS Technology Co. Ltd. for supplying the precise spectrum measurement system.

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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$λ$	1064nm	$ρ_{0}$	$2201 k g / m^{3}$
$A_{e f f}$	$3.53 \times 10^{- 10} m^{2}$	$T$	293.15K
$n$	1.45	$v_{A}$	$5.897 \times 10^{3} m / s$
$n_{2}$	$2.6 \times 10^{- 20}$	$τ$	20ns
$k$	$1.3806 \times 10^{- 23} m^{2} k g s^{- 2} K^{- 1}$	$γ_{e}$	$0.092$
$L$	9m	$Δ L$	0.01m

	Chirp-like-1	Chirp-like-2	Flat spectrum-1	Flat spectrum-2	Gaussian spectrum
$P_{t h}$	3.06 W	3.06 W	2.26 W	2.09 W	2.58 W
$σ / σ_{min}$	1.14	1.13	1.08	1.07	1

$λ$	1064nm	$ρ_{0}$	$2201 k g / m^{3}$
$A_{e f f}$	$3.53 \times 10^{- 10} m^{2}$	$T$	293.15K
$n$	1.45	$v_{A}$	$5.897 \times 10^{3} m / s$
$n_{2}$	$2.6 \times 10^{- 20}$	$τ$	20ns
$k$	$1.3806 \times 10^{- 23} m^{2} k g s^{- 2} K^{- 1}$	$γ_{e}$	$0.092$
$L$	9m	$Δ L$	0.01m

	Chirp-like-1	Chirp-like-2	Flat spectrum-1	Flat spectrum-2	Gaussian spectrum
$P_{t h}$	3.06 W	3.06 W	2.26 W	2.09 W	2.58 W
$σ / σ_{min}$	1.14	1.13	1.08	1.07	1

Spectral broadening scheme for suppressing SBS effects based on time-domain optimized chirp-like signals

Abstract

1. Introduction

2. Principle

2.1 Principle and challenge of achieving linear chirp through external phase modulation

2.2 Principle of chirp-like signal design

3. Numerical Simulation

3.1 Spectral simulation based on chirp-like phase modulation

3.2 SBS threshold simulation based on the three-wave coupling equation

4. Experiments

4.1 Experimental setup

4.2 Experimental results

5. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (2)

Equations (8)

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