293 W, GHz narrow-linewidth, polarization maintaining nanosecond fiber amplifier with SBS suppression employing simultaneous phase and intensity modulation

Yang Ran; Rongtao Su; Pengfei Ma; Xiaolin Wang; Haibin Lv; Pu Zhou; Lei Si

doi:10.1364/OE.23.025896

1. Introduction

High power narrow-linewidth fiber lasers have been receiving intense interests due to their diverse applications in gravitational wave detection, material processing, coherent beam combination and nonlinear frequency conversion [1–5]. This latter application benefits from pulsed lasers, which are able to provide high peak power [6]. Often, Q-switched fiber lasers are reported to provide nearly Gaussian shaped pulses in the nanosecond regime [7, 8], but this makes the pulse parameters (duration, repetition rate, pulse shape) are often not freely adjusted. To overcome this limitation, a directly modulated fiber seed laser using an electro-optic intensity modulator or acoustic-optic modulator (EOIM or AOM) is introduced [9]. However, in the power scaling process, nonlinear effects, such as stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS) and optical Kerr effect can always limit the performance of these lasers. Especially for those narrow-linewidth lasers, SBS is the most challenging obstacle for power scaling and thus different methods have been reported to mitigate SBS effect in pulsed laser systems. Wei Shi et al. reported a 15 ns pulsed laser with transform-limited linewidth at ~2 μm based on highly Tm-doped germinate fibers, corresponding to peak power of 63 kW [9]. Qiang Fang et al. reported a 15 ns pulsed laser with peak power of 33 kW based on an EOIM at ~1918.4 nm [10]. By using a large-core, single-mode photonic crystal fiber, C. D. Brook et al. reported a 1 ns diffraction-limited pulses of peak power >1 MW, average power >10 W at 1062 nm [11]. However, the average power of the pulsed laser is relative low in these works, triggering some new methods to improve it.

For a continuous wave (CW) single-frequency laser, phase modulation techniques are often used to suppress SBS through spectral linewidth broadening. Narrow-linewidth, kW class Yb-doped fiber amplifiers have been recently demonstrated through external phase modulation [12]. Along this line, we add the phase modulation techniques to that intensity modulation technique (directly modulating seed by using an EOIM) to further suppress SBS in narrow-linewidth pulsed laser systems. In time domain, this way can adjust the pulse width to be shorter than the photon lifetime due to intensity modulation, which contributes to inadequate buildup time for acoustic phonons and insufficient spatial overlap between SBS pulses and the amplified signals [13]. In frequency domain, the linewidth of modulated spectrum is broadened due to phase modulation, thus the energy of the optical signal is distributed to a great amount of optical side frequency waves to reduce the energy density of optical power spectra [14]. In this way, SBS threshold of pulsed laser can be largely increased.

In this paper, we report a nanosecond all-fiber narrow-linewidth polarization-maintaining (PM) Yb-doped amplifier based on simultaneous phase and intensity modulation. ~3.5 ns pulsed laser with 293W/3.9 kW average/peak power is obtained. The beam quality (M²) is ~1.1 and the output linewidth can be calculated to be ~4.5 GHz.

2. Experimental setup

The experimental configuration of the narrow-linewidth PM Yb-doped all-fiber amplifier is illustrated in Fig. 1. A single-frequency CW laser is first modulated by an EOIM, which is driven by a commercial arbitrary function generator (AFG). The single-frequency CW laser with maximal output power of ~30 mW and a linewidth of 20 kHz is a distributed feedback PM Yb-doped fiber (YDF) laser. The pulse width and the intensity repetition rate of the modulated pulsed laser can be adjusted by setting the electrical signal of the AFG. Then the modulated pulsed laser is amplified by a preamplifier (A1) and coupled into an electro-optic phase modulator (EOPM). The EOPM is driven by the same AFG with that of the EOIM, thus the two modulation signals can be synchronized to effectively control the modulated spectral lines. Another stage of preamplifier (A2) is set to boost the output power to be ~500 mW before entering into a PM-YDF amplifier (1st stage AMP). Between A2 and 1st stage AMP, a tapper with 99% and 1% coupling ratios is used to monitor the signal of the pulsed seed, and a Fabry-Perot interferometer (FPI) is used to detect the modulated spectra of the seed.

Fig. 1 Experimental configuration of the 1064 nm narrow-linewidth YDF pulsed amplifier.

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Then the pulsed seed laser is launched into the 1st stage AMP with 1.5 m double-clad active fiber. The cladding absorption coefficient of this active fiber is 8.7 dB/m at 976 nm, and the output power can be boosted to be ~7 W. A tapper with 99.9% and 0.1% coupling ratios is placed after the 1st stage AMP, contributing to detect the backward power of the main amplifier. When SBS occurs, the backward power will show nonlinear increase. Besides, isolators (ISO) are used between each stage of the amplifiers in order to protect the whole system.

In the main amplifier, a 9 m long PM large mode area (LMA) double clad YDF is used as active fiber. The cladding absorption coefficient of this active fiber is 1.45 dB/m at 976 nm, and six high power laser diodes (LDs) with 976 nm central wavelength are coupled into the LMA YDF by using a (6 + 1) × 1 PM signal/pump combiner. Then, a 3 m long double-clad PM passive fiber is spliced to the active fiber followed by a collimator. A pump dump section is made in the passive fiber for stripping out the residual pump laser. Finally, a beam splitter is used to split the output pulsed laser, with more than 99% of the output sent to a power meter and less than 1% of it sent to a photo diode (PD) to detect the pulse shape or an optical spectrum analyzer (OSA) to detect the output spectrum.

3. SBS theoretical simulation framework

According to the SBS suppression method afore-mentioned, we first theoretically simulate the dynamic interaction process of the main amplifier based on the SBS three coupled amplitude equations [15] and the rate equations to predict the SBS threshold in this simultaneous phase- and intensity-modulated pulsed amplifier system. These equations illustrate the temporal and spatial evolutions of the pump, laser, Stokes, acoustic phonon fields and the upper level population, which can be expressed as follow:

\frac{d P_{p}}{d z} + \frac{1}{v_{g p}} \frac{d P_{p}}{d t} = - α_{p} P_{p} - Γ_{p} [σ_{a}^{p} N - (σ_{a}^{p} + σ_{e}^{p}) N_{2}] P_{p}

\frac{\partial A_{s}}{\partial z} + \frac{1}{v_{g s}} \frac{\partial A_{s}}{\partial t} = - \frac{α_{s}}{2} A_{s} + \frac{1}{2} [(σ_{a}^{s} + σ_{e}^{s}) N_{2} - σ_{a}^{s} N] A_{s} + i γ_{s} ({| A_{s} |}^{2} + 2 {| A_{B} |}^{2}) A_{s} + i κ_{1 s} A_{B} Q

- \frac{\partial A_{B}}{\partial z} + \frac{1}{v_{g s}} \frac{\partial A_{B}}{\partial t} = - \frac{α_{s}}{2} A_{B} + \frac{1}{2} [(σ_{a}^{s} + σ_{e}^{s}) N_{2} - σ_{a}^{s} N] A_{B} + i γ_{s} ({| A_{B} |}^{2} + 2 {| A_{s} |}^{2}) A_{B} + i κ_{1 B} A_{s} Q^{*}

\frac{\partial Q}{\partial t} + ν_{A} \frac{\partial Q}{\partial z} = - [\frac{1}{2} Γ_{B} + i (Ω_{B} - Ω)] Q + \frac{i κ_{2}}{A_{e f f_a o}} A_{p} A_{s}^{*} + f

\frac{\partial N_{2}}{\partial t} = - \frac{N_{2}}{τ} + \frac{Γ_{s} λ_{s}}{h c A_{c}} [σ_{a}^{s} N - (σ_{a}^{s} + σ_{e}^{s}) N_{2}] (P_{s} + P_{B}) + \frac{Γ_{p} λ_{p}}{h c A_{c}} [σ_{a}^{p} N - (σ_{a}^{p} + σ_{e}^{p}) N_{2}] P_{p}

where the index p, s, and B represent the pump, signal, and Stokes light, respectively. Here P_p, A_s, A_B and Q are normalized amplitudes of pump wave, signal wave, Stokes wave and acoustic wave respectively, while v_gp and v_gs represent the group velocity of pump and signal. α is the fiber loss coefficient and Г is the overlap factor. σ_a and σ_e represent absorption cross-section and emission cross-section. N is the doping concentration of Yb³⁺ and N₂ is the upper level population. γ_s is the nonlinear coefficient of signal and κ_1s, κ_1B and κ₂ are coupling coefficients. ν_A is the acoustic speed and Г_B is the acoustic damping rate, while Ω_B represents the acoustic angular frequency and Ω indicates the varied angular frequency. A_{eff_ao} and A_c are acoustic-optic effective area and fiber core cross-section area, respectively. τ represents the average lifetime of the upper level Yb³⁺ and h indicates the Planck constant. λ represents wavelength and c is the speed of light.

f

represents a langevin noise source describing the thermal excitation of acoustic waves. It can be expressed as [16]:

〈 f (z, t) 〉 = 0

〈 f (z, t) f^{*} (z^{'}, t^{'}) 〉 = N_{Q} δ (z - z^{'}) δ (t - t^{'})

where

N_{Q} = 2 k T_{0} ρ_{0} Γ_{B} / (ν_{A}^{2} A_{e f f})

is the fluctuation strength parameter, k is the Boltzmann constant and T₀ is the temperature. ρ₀ and A_eff represent the fiber density and the effective mode area, respectively.

After intensity modulation, the input signal A_s can be expressed in this Gaussian-like form as:

A_{s} = \sum_{- m}^{m} \sqrt{P_{s}} \exp [- \frac{1}{2} {(\frac{t - m T}{Δ T})}^{2}]

where m decides the number of the modulated pulses. T and ΔT are pulse period and pulse width of the modulation signal.

Further, when the input laser is then modulated by a phase modulator, the modulated seed can then be given by:

A_{s} = \sum_{- m}^{m} \sqrt{P_{s}} \exp [- \frac{1}{2} {(\frac{t - m T}{Δ T})}^{2}] \exp [i δ \sin (Δ ω (t - t_{0}))]

where

δ = π E_{M} / V_{π}

is the modulation amplitude, E_M is the modulation voltage and V_π is the half-wave voltage of the phase modulator. Δω is the modulation angular frequency and t₀ is the delay between the two modulation signals.

Table 1 gives other simulation parameters, chosen all based on the experimental condition and the typical values of silica fibers. F_ao represents the acousto-optic effective overlap factor, and $A_{e f f_a o} = 1 / F_{a o}^{2}$ .

Table 1. SBS threshold simulation parameters

View Table

Here n_p is the refractive index of pump and β is the cladding absorption coefficient of gain fiber. n₂ is the nonlinear-index coefficient and $γ_{e}$ represents electrostrictive constant. n_{co_s} and n_{co_B} are core refractive index of signal and Stokes wave respectively.

4. Experimental results and analysis

Before employing phase and intensity modulation simultaneously to the all-fiber amplifier system, we need first to choose the modulation parameters. As for intensity modulation, short pulse width contributes to less buildup time for acoustic phonons and less spatial overlap between SBS pulses and the amplified signal [13]. So we choose to set the pulse width to be 4 ns, which is the shortest pulse width we can achieve (limited to the experimental condition). When it comes to phase modulation, larger modulation amplitude will suppress SBS in a better degree. So in experiment, we set the modulation voltage to be 5 V. Then we choose two groups of intensity modulation parameter (10 MHz 4 ns and 20 MHz 4 ns) and two groups of phase modulation parameter (100 MHz 5 V and 200 MHz 5 V) respectively and combine them in different ways to test the SBS suppression effect.

Figures 2(a)-2(d) shows the Fabry-Perot scanning spectra of the phase- and intensity-modulated seed under different modulated conditions. By regulating the delay between the phase and intensity modulation signal, we get the modulated spectra with best homogeneity and symmetry. The free spectral range of the FPI is 4 GHz and we define the linewidth of the spectra to be the full width at 30% maximum. So the linewidth of the modulated seed is estimated to be 1.112GHz, 1.841GHz, 1.110 GHz and 1.839 GHz respectively for the spectrum of Figs. 2(a)-2(d).

Fig. 2 Fabry-Perot scanning spectra when intensity- and phase-modulated parameter are set to be (a) 10 MHz 4ns and 100 MHz 5 V (b) 10 MHz 4 ns and 200 MHz 5 V (c) 20 MHz 4ns and 100MHz 5 V (d) 20 MHz 4 ns and 200 MHz 5 V.

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Figure 3(a) shows the backward power of the main amplifier as a function of the output power under four different modulation conditions, which all show nonlinear increase trend indicating the emergence of SBS. Here we define the SBS threshold as the output power at which the Stokes wave power increases rapidly and comparable with μ (μ = 0.2‰) of the output power. Blue dotted line in Fig. 3(a) depicts 0.2‰ of the output power. Before SBS occurs, the maximum average power of 293 W is achieved at intensity modulation parameter of 20 MHz 4ns and phase modulation parameter of 100 MHz 5 V. Figure 3(b) shows the average output power of the main amplifier with a linear fitting to 85.8% slope efficiency against absorbed pump power.

Fig. 3 (a) Backward power as a function of output power under different modulation condition. (b) Average power of the pulse under different pump level at 20 MHz intensity repetition rate and 100 MHz phase repetition rate.

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As for the intensity and phase modulation at 20 MHz 4 ns and 100 MHz 5 V, we use the theory and simulation parameters described in section 3 to further calculate the SBS threshold, as shown in Fig. 4. When the output power increases to ~300 W, the backward power shows a sharp nonlinear increase, which is in good agreement with that of experimental result.

Fig. 4 Simulated and measured backward power as a function of output power.

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Tracing back to what has been depicted in Figs. 2(a)-2(d), we find that modulated linewidth of the pulsed seed at intensity and phase modulation of 20 MHz 4 ns and 100 MHz 5 V to be 1.110GHz, which is the smallest one compare with other three scanning spectra. To the best of our knowledge, a great amount of equivalent ideal spectral power density (SPD) contributes to higher SBS threshold [17]. In our cases, other three modulated spectra have a large number of optical side frequency waves, but show obvious inhomogeneity between different spectral lines. By contrast, the modulated spectrum at intensity and phase modulation of 20 MHz 4 ns and 100MHz 5 V respectively shows the best homogeneity and symmetry, contributing to suppress SBS in a better degree. Further, because of the self-phase modulation (SPM) effect in fiber amplifier, the spectrum will be broaden after amplified by the main amplifier. This SPM-induced spectral broadening can be estimated by the numerical value of the maximum nonlinear phase shift $φ_{N L}$ , which is given by Eq. (10) [15, 18]:

φ_{N L} = (2 π / λ) n_{2} L_{e f f} I

where λ is the laser wavelength, n₂ is the nonlinear index coefficient and L_eff is the effective fiber length. I = P/πr² is the laser intensity, P is the input laser peak power and r is the mode field radius.

L_{e f f} = L_{e f f_Y D F} + L_{e f f_p a s s i v e}

here

L_{e f f_Y D F} = (G - 1) L / \ln G

[19], L is the actual length of YDF. G is the fiber amplifier power gain factor.

Further, because the input average power of the main amplifier is 7 W, the intensity repetition rate and pulse width of the pulsed laser is 20 MHz and 4 ns. P can be calculated to be 82.2 W based on the formula of Guassian-like pulses given by Eq. (12) [7]:

P_{p e a k} = 2 \sqrt{\ln 2 / π} P_{a v e} / t_{F W H M} f_{R R}

where P_peak is the peak power, P_ave is the average power, t_FWHM is the full width at half maximum (FWHM) of the modulated pulse, and f_RR is the modulation frequency.

According to the experimental conditions afore-mentioned, we know G = P_out/P_in = 293/7, P_out and P_in are the average output and input power of the main amplifier. For silica glass fiber, n₂ = 2.6 × 10⁻²⁰m²/W [15]. Given λ = 1064 nm, L = 9 m, L_{eff_passive} = 3 m, P = 82.2 W, r = 10 μm, the nonlinear phase shift $φ_{N L}$ can be calculated to be about 4.08. This indicates that the spectrum is broaden by a factor of ~4.08 [18], thus the output linewidth can be calculated to be ~4.5 GHz.

Based on the experimental and simulation results afore-mentioned, we remain the frequency for both phase and intensity modulation unchanged, and go further to optimize the modulation parameters by changing the voltage of phase modulation and the pulse width of the intensity modulation respectively. From Figs. 5(a) and 5(b), we can see that the SBS threshold can continue to increase by employing higher phase modulation voltage as well as shorter intensity modulation pulse width. In our experiment, the response frequency of the phase modulator (Photline NIR-MPX-LN-0.1) is 150 MHz and because of the limitation of the experimental instruments, the highest modulation voltage and the shortest pulse width we can achieve are 5 V and 4 ns. On the other hand, both high modulation voltage and short pulse width will influence the linewidth of the fiber pulsed amplifier system. When phase modulation voltage increases, the modulated linewidth increases accordingly. It is calculated to be ~2.24 GHz at phase modulation of 100 MHz 10 V and intensity modulation of 20 MHz 4 ns. When intensity modulation pulse width is set to be too narrow, the peak power of the output laser will increase greatly, which may lead to easy access to nonlinear effects, such as stimulated Raman scattering (SRS). This will also increase the linewidth of output laser. Through simulation, we find the output linewidth is broaden to ~10.66 GHz at intensity modulation of 20 MHz 2 ns and phase modulation of 100 MHz 5 V. Compared with what we have measured experimentally at phase modulation of 100 MHz 5 V and intensity modulation of 20 MHz 4 ns, the linewidth is largely broaden in both cases afore-mentioned, this may limit the applications of the output laser. Thus the experimental result we get with 100MHz 5 V phase modulation and 20 MHz 4ns intensity modulation is relatively optimized.

Fig. 5 Simulated SBS threshold power as a function of the (a) phase modulation voltage and (b) intensity modulation pulse width.

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Figure 6 illustrated the pulse shape of the main amplifier at the maximal output of 293 W, which is recorded by a fast detector and an oscilloscope. The pulse keeps a good shape and the pulse width is slightly reduced from 4 ns to ~3.5 ns. Based on Eq. (12), the peak power can be calculated to be 3.9 kW.

Fig. 6 Pulse shape of the amplified pulses with 20 MHz 4 ns intensity modulation and 100 MHz 5V phase modulation.

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For the amplified pulses at 293 W under modulation of intensity and phase, the spectrum is measured using an OSA with wavelength resolution of 0.02 nm and time response resolution of 0.2 second/100 nm, as shown in Fig. 7(a). Confined to the experimental condition, the time response resolution of the OSA is not adequate to detect ns pulse directly, but the spectrum measured in this way gives an average effect of the output laser spectrum, which can also provide some useful information about the characteristics of the output laser. It is clear that no SRS, amplified spontaneous emission (ASE) as well as residual pump light are observed in the amplified output laser. The M² factor of the whole pulsed amplifier architecture at maximal output power is measured using M2-200, as shown in Fig. 7(b). One can see that the beam quality of the pulsed laser at 293 W is M_x² = 1.128 and M_y² = 1.117.

Fig. 7 (a) Output spectrum of the amplified pulses and (b) The M² factor of the amplifier chain at 293 W output power.

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5. Conclusion

We demonstrate a new method to suppress SBS in pulsed amplifier system based on simultaneous phase and intensity modulation, then a high power GHz narrow-linewidth PM near-diffraction-limited (M²~1.1) Yb-doped all-fiber nanosecond amplifier is reported. A SBS numerical simulation framework is developed to calculate the SBS threshold in phase- and intensity-modulated YDF amplifier system. In experiment, ~3.5 ns pulsed laser with average/peak power of 293 W/3.9 kW is obtained at intensity repetition rate of 20 MHz and phase modulation of 100 MHz 5 V, which shows good agreement with the simulation result. Considering SPM effect, the linewidth of the output laser is estimated to be ~4.5 GHz. This new method provides references to design and optimize the narrow linewidth pulsed amplifier systems to achieve higher average power narrow-linewidth output laser with good beam quality in a certain piece of active fiber.

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant No. 11274386) and Natural Science Foundation of Hunan Province, China (Grant No. 14JJ3004).

References and links

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Parameter	Value	Parameter	Value
λ_s	1064.0nm	λ_p	976nm
v_A	5897.4m/s	n_p	1.415
n_{co_s}	1.4511	n_{co_B}	1.4511
F_ao	5.2916 × 10⁴	A_eff	3.5334 × 10⁻¹⁰m²
Г_B	2.0552 × 10⁸	γ_e	0.902
ρ₀	2210kg/m³	n₂	2.6 × 10⁻²⁰m²/W
α_p	2.1dB/km	α_s	15dB/km
Г_p	3.9625 × 10⁻³	Г_s	1
β	1.65dB@976nm	N	7.8189 × 10²⁵/m³
τ	840μs	Ω_B	1.0106 × 10¹¹rad

293 W, GHz narrow-linewidth, polarization maintaining nanosecond fiber amplifier with SBS suppression employing simultaneous phase and intensity modulation

Abstract

1. Introduction

2. Experimental setup

3. SBS theoretical simulation framework

4. Experimental results and analysis

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (12)

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