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Abstract
Stimulated Brillouin scattering (SBS) is a critical problem for fibers and fiber amplifiers as it severely limits single-frequency output powers; thus, we propose a seed source to mitigate it. The proposed seed source generates a high-duty-cycle N-pulse train in which the optical frequency of each subsequent pulse is shifted by a specific fixed amount with respect to the previous pulse, a stepwise optical frequency pulse train (SOFPT). In a watt-class power experiment, for a SOFPT with a 200-MHz optical frequency step, the SBS threshold for a 200-m single-mode fiber was enhanced by a factor of N compared with that for the CW seed source.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Output powers of conventional cladding-pumped fiber lasers have reached several kilowatts in simple cavity configurations with ytterbium-doped fibers (YDF). The large gain bandwidth of YDFs leads to broad laser linewidths on the order of nanometers. The resultant linewidths are too broad for many interesting applications, including coherent beam combination. Rather, master-oscillator power-amplifier (MOPA) configurations are employed to achieve narrow-linewidth, high-power output.
In a MOPA, a low-power narrow-linewidth seed is amplified through several amplifiers. A key breakthrough has been the suppression of stimulated Brillouin scattering (SBS), which otherwise limits the single-frequency output power of typical fiber amplifiers to, theoretically, 100 W or less. A five-fold enhancement of the SBS threshold, to 500 W, has been demonstrated in a single-frequency MOPA with YDFs [1]. The reduced SBS intensity is understood to result from thermal Brillouin gain broadening induced by a thermal gradient unintentionally generated along the YDF. A 170-W linearly polarized single-frequency single-mode ytterbium amplifier with a core diameter of 10 µm has been reported [2]. In this case, to suppress the SBS, a longitudinal variation in strain was applied to the gain fiber. Thus, a seven-fold enhancement in the SBS threshold was achieved. A large mode area (LMA) fiber design to increase the SBS threshold that used aluminum and germanium co-doped LMA fiber cores has been reported [3]. A five-fold enhancement of the SBS threshold, as well as 500 W of output power, has been demonstrated for a single-mode beam by using the designed fiber [4].
A phase-modulation technique with a single-frequency laser has been used to mitigate SBS in a long (13 km) optical fiber [5]. Beam combinability has also been demonstrated for a 1.4-kW YDF amplifier in which the 25-GHz linewidth of a phase-modulated seed source was used to suppress SBS [6]. Beam combining in a lower-power (500 W) YDF amplifier was demonstrated by using a seed source with a narrower linewidth (10 GHz), easing path-length-matching requirements [7]. Despite the reduced linewidth, the path lengths of the amplifiers were matched, with a difference of less than 0.1 cm. Similar issues are expected in systems using pseudo-random binary sequence (PRBS) phase modulation [8–10] because coherent lengths are inversely proportional to the clock rate of PRBS signal. A 3-GHz PRBS modulated 1.17-kW fiber amplifier was demonstrated with 8-m non-polarization maintaining 25/400 µm YDF [8]. In a previous report [9], a filtered PRBS approach was proposed to allow for a higher SBS threshold. A low-pass filter with a 6.5-GHz PRBS modulated, 1.27-kW fiber amplifier was demonstrated with 7-m non-polarization maintaining 20/400 µm YDF [10]. The 6.5-GHz clock rate PRBS signal was filtered with a 2.2-GHz low-pass RF filter. SBS becomes more difficult for long fibers, and it is a severe problem for lengths that work best for power scaling of broadband light. To mitigate SBS in longer fiber lengths, the phase-modulation techniques require a wider linewidth of phase modulated sources or a larger clock rate of PRBS signals, which reduces coherent length.
Mitigation of SBS in optical fibers and fiber amplifiers has also been demonstrated using linearly chirped diode lasers (distributed feedback lasers, DFBs, and vertical-cavity surface-emitting lasers, VCSELs) [11,12]. The frequency chirp rates are limited by the current tuning range of diode lasers, up to ∼1015 Hz/s. For example, if we assume a frequency chirp rate of 1015 Hz/s and a 100-MHz SBS band, the Stokes wave will experience an interaction time of 100 MHz/1015 Hz/s = 10−7 s. Thus, the interaction length would be ∼10 m; any length above this would be too long for fiber amplifiers. Such a constraint is brought about because the method depends on only one parameter, the frequency chirp rate. With subsequent efforts, a chirp rate of ∼1017 Hz/s has been achieved by moving the external MEMS mirror of a laser diode [13]. However, because the mirror moves back and forth, the sign of the frequency chirp of the source changes periodically.
The present work describes the use of a stepwise optical frequency pulse train (SOFPT) seed to mitigate SBS in an optical fiber. Each pulse in the SOFPT is frequency-shifted by Δν compared with the preceding pulse. As will be discussed in the next section, an average chirp rate above 1018 Hz/s can be achieved by using the SOFPT. Furthermore, either positive or negative frequency shift can be obtained. Because there is no limit to the number of pulses in SOFPT, it can be applied to longer fibers. We demonstrate an increase in the SBS threshold using the SOFPT seed and compare the result with that produced using a single-frequency CW seed. For the comparison, the pulse width was set to be sufficiently longer than the phonon lifetime, and the linewidth of the pulse was set to be sufficiently narrower than the Brillouin gain bandwidth.
2. Stepwise optical frequency pulse train (SOFPT)
The SBS threshold power Pth in a single-mode fiber is related to the Brillouin gain gB, the interaction length Leff, and the effective mode area Aeff by the following equation [14]:
Neglecting the intrinsic fiber losses, the interaction length for a continuous pump wave is equal to the fiber length L. Expressions for the interaction length for a pulsed pump wave have been discussed in other papers [15,16]. The interaction length generally depends on the pulse durationτ, the pulse repetition rate f, and the fiber length.
When the pulse width is relatively short and the pulse period T (=1/f) is relatively long, a single pulse (N = 1) can be isolated in the fiber, as shown in Fig. 1(a) (low-duty-cycle). The pulsed pump wave and Stokes wave travel in opposite directions at a speed V; therefore, the effective interaction length is equal to Vτ/2. Starting from the situation in Fig. 1(a), if we reduce the pulse period until T < 2L/V, a Stokes wave can interact with multiple (N) pulsed pump waves in the fiber, as shown in Fig. 1(b) (high-duty-cycle). Under this condition, the value of Leff corresponds to NVτ/2. When T = τ (i.e. duty cycle, 100%), the situation is the same as that for a CW laser.
Fig. 1. Schematic of optical pulse propagation in a fiber: (a) low-duty-cycle and (b) high-duty-cycle with the same optical frequency, and (c) stepwise optical frequency pulse train (SOFPT).
Here, we propose a method to mitigate SBS utilizing a SOFPT containing N pulses. Each pulse in the train is frequency-shifted by Δν with respect to the previous pulse, as shown in Fig. 1(c). To mitigate SBS, Δν should be larger than the Brillouin gain bandwidth ΔνB, so that the Brillouin amplification of the Stokes wave occurs only within each pulse (i.e., Leff = Vτ/2). If a number N is chosen such that N ≥ 2L/VT, the average SBS threshold is 2L/VT times as high as that of low-duty-cycle in Fig. 1(a). This condition (N ≥ 2L/VT) corresponds to the case when all pulses that exist in the entire length of the fiber have different frequencies for a duration corresponding to one roundtrip. The average SBS threshold power is maximized when T = τ . The situation T = τ is equivalent to a CW seed having stepwise optical-frequency increases or decreases. This condition is closer to that of a linearly chirped diode laser. An average chirp rate above 1018 Hz/s can be achieved by choosing a gigahertz frequency shift and nanosecond pulse width as the parameters of SOFPT. The frequency shift Δν must be chosen according to the Brillouin gain bandwidth, which varies depending on the fiber type. The pulse duration τ (and N, at the same time) should be selected according to the desired enhancement in the SBS threshold. The SOFPT seeder, as described above, provides a flexible and reliable architecture for SBS suppression.
With the often-used phase-modulation techniques (including PRBS modulation), the increased SBS threshold can be approximately written as
where ΔνL is the linewidth of a phase-modulated seed source and is much broader than ΔνB. The coherent length LPM of the phase-modulated source with a Lorentzian line-shape is c/πΔνL. If the SBS thresholds with phase-modulation and with SOFPT are the same, the ratio of LPM to the characteristic length LSOFPT (= cτ) of the SOFPT is given by3. Experiments
The experimental setup is illustrated schematically in Fig. 2. The SOFPT is amplified by two-stage Yb amplification and directed toward a 200-m passive fiber. All the fibers shown in Fig. 2 are polarization maintaining and have the same mode-field diameter (6.6 µm).
Fig. 2. Experimental setup for observing SBS suppression. The backward-reflected power from a 200-m fiber is measured by a power meter (PM) through a fiber tap (TAP2). WDM: Wavelength division multiplexer, LD: Laser diode.
In the SOFPT seeder depicted in Fig. 2(a), seed pulse of 85-ns duration was generated via the intensity modulation of a 1030-nm DFB (EYP-DFB-1030-00500-1500-BFY12-0010 from Eagleyard) laser by an acoustic-optic modulator (AOM1: T-M200-0.1C2G-3-F2P from Gooch & Housego) operated with an open gate time of approximately 100 ns and a repetition rate of 500 kHz. The pulse duration is considerably longer than the phonon lifetime of 4 ns [13]. The seed pulse is coupled into a 24-m fiber loop through a coupler. A 200-MHz shift in optical frequency of the seed pulse is induced by another AOM (AOM2: T-M200-0.1C2G-3-F2P from Gooch & Housego) in the loop. The open gate time for AOM2 is approximately 1.86 µs, which determines the number of pulses over which the frequency is shifted. The amplifier in the loop compensates the total loss of the loop and makes the peak power of each pulse equal. The seed pulse then passes through a band-pass filter (BPF) and back into the coupler, where a part of the pulse is coupled out of the loop and the other part passes back into the loop again. Upon each repeated circulation through the loop, a new pulse is coupled out with an optical frequency shifted by 200 MHz compared with the previous pulse.
Figure 3 shows a typical SOFPT trace measured at the exit of the coupler before splicing with an isolator. Each pulse of the SOFPT has the same pulse energy except the first pulse, due to the imperfect coupling ratio (30/70) of the coupler. The use of a 50/50 coupler would solve this problem. The average power of the SOFPT was 0.3 mW. The waveform of each pulse is super-Gaussian like.
The two-stage Yb amplification boosts the average power of the SOFPT by up to 3.5 W. Figure 4 shows the amplified SOFPT trace measured at PD2 with a 20-GHz bandwidth. The pulse shapes are maintained after the 40-dB amplification. The amplified SOFPT contains 17 pulses. The value N = 17 satisfies the condition N≥2L/VT for L = 200 m, V = 0.207 m/ns (V = c/n; c is the speed of light and n is the refractive index of the fiber), and T = 116 ns. The SOFPT is cycled at the repetition rate of 500 kHz. Because the first pulse in a SOFPT has one-fifth the power of the others, the actual value of N is ∼16 under the current experimental condition. The output power was varied by changing the current to the LD pumping the final amplifier. In the practical stage, it would better to use AOM1 to generate only one pulse in the single-shot mode, and AOM2 to keep the diffraction mode (N → ∞). In such a stage, the synchronization of AOM1 and AOM2 would not be needed.
To observe the spectrum of the amplified SOFPT, we applied a heterodyne technique. Another CW DFB laser (the same model as Fig. 2) was used as a local oscillator. The amplified SOFPT was superimposed with the light from the local oscillator through TAP2, and the resulting beat notes were measured with PD2 and Fourier transformation in the oscilloscope. As shown in Fig. 5, each beat note is separated by 200 MHz with respect to the adjacent beat note. The inset in Fig. 5 corresponds to the spectrum of a pulse in the SOFPT. Each pulse in the SOFPT has a linewidth of 5.3 MHz, which is much narrower than the Brillouin linewidth of 58 MHz [14].
The backward-reflected power from the 200-m passive fiber is plotted versus the incident power in Fig. 6. Data acquired with the CW DFB seed is shown for comparison. In CW operation, the DFB laser is directly connected to the pre-amplifier through an isolator. The DFB laser has a linewidth of 3 MHz. Data acquired in low-duty-cycle operation (85 ns at 500 kHz: N=1) is also shown in Fig. 6. In low-duty-cycle operation, AOM1 is directly connected to the pre-amplifier via an isolator. We define the SBS threshold as the point where the backward power is a factor of 10−3 of the incident power. For both the CW and low-duty-cycle modes, this threshold is approximately 95 mW. However, when the SOFPT is used, the threshold increases to 1.5 W, i.e., 16 times greater than the CW threshold. Regarding the self-phase modulation, the power of 1.5 W in the 200-m passive fiber can be scaled by approximately 400 W in an 8-m 25/400 µm fiber as described in Introduction. Nevertheless, each pulse in the SOFPT transmitted through the passive fiber has a linewidth of 5.65 MHz, which corresponds to the linewidth broadening factor of 1.07.
4. Conclusion and discussion
In conclusion, with a 200-MHz optical frequency step for the 16-pulse SOFPT, the SBS threshold in a 200-m single-mode fiber was enhanced by a factor of 16 compared with the low-duty-cycle threshold (N=1), which clearly establishes a scaling law. When adjacent pulses overlapped in the SOFPT, a beat signal of 200 MHz was generated in the overlapped portion, and this beat signal was emphasized in the ring and multi-stage amplification processes. Beat signals are a serious problem in high-power laser systems as they cause system damage. The maximum duty cycle of SOFPT without overlaps is determined by the rise time of AOM1 (10 ns). Under the conditions described schematically in Fig. 2, the duty cycle of the SOFPT is 73% for a pulse duration of 85 ns.
The use of a 40-GHz lithium niobate electro-optic modulator instead of AOM1 can reduce the rise time to 10 ps, achieving a duty cycle of 99% for a pulse duration of 2 ns. If a fiber amplifier has a length of 20 m, N = 96 satisfies the condition N ≥ 2L/VT for L = 20 m, V = 0.207 m/ns (V = c/n), and T = 2.02 ns. Under this condition, the SOFPT should achieve an SBS threshold 96 times greater than that for the low-duty-cycle threshold. If the 2-ns pulse is transform-limited, its linewidth is 220 MHz for a Gaussian pulse shape, or 430 MHz for a square pulse shape. An x-cut lithium niobate electro-optic modulator can produce chirp-free square pulses [17]. Because the energy content occupied by the edges of square (higher-order super-Gaussian) pulses are nearly zero, it is effective in suppressing self-phase modulation [14,18–20]. Another concern would be the collapse of the pulse shape due to dynamic gain saturation [21]. However, even if the duty cycle is in the order of 10−4, when the pulse width τ is very short such that τ < 10 ns, no remarkable pulse shape collapse occurs [20,22]. Moreover, the high duty cycle of SOFPT should help suppress a pulse shape collapse.
It is unlikely that the Brillouin gain bandwidth for any type of fiber exceeds 100 MHz for low-power lasers. However, one report [15] gives a theoretical prediction that the Brillouin gain bandwidth will increase dramatically for high-power lasers, from tens of MHz to 1 GHz or more. Acousto-optic modulators (AOMs) realize high-contrast frequency shifts because their operation is based on Bragg diffraction. Fortunately, gigahertz frequency shifts (>1 GHz) can be achieved by AOMs using their first-order diffraction output. The seeder we presented in this paper, shown in Fig. 2, is just one example, and the SOFPT could be achieved in other ways, e.g., by the optical coupling of multiple delayed pulsed sources.
Acknowledgments
We would like to thank Editage (www.editage.com) for English language editing.
Disclosures
The authors declare no conflicts of interest.
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