1200-W all polarization-maintaining fiber GHz-femtosecond-pulse laser with good beam quality

Hao Xiu; Yiheng Fan; Wei Lin; Wenlong Wang; Molei Hao; Junpeng Wen; Xuewen Chen; Tianxi Wang; Xiaoming Wei; Xiaoming Wei; Zhongmin Yang; Zhongmin Yang; Zhongmin Yang

doi:10.1364/OE.506631

1. Introduction

High-power femtosecond (fs) fiber laser has widespread applications in the fields of fundamental research and industry [1–9]. It features many advantages, such as compact structure, good long-term stability, and high beam quality, which make it an attractive alternative to conventional solid-state lasers. Despite the above advantages, its capability of all fiberizing and scalability of peak power is technically challenging due to the arisen nonlinear effects of optical fibers (particularly in the single-mode operation), such as self-phase modulation (SPM) and stimulated Raman scattering (SRS). To this end, many technologies have been proposed, including the chirped pulse amplification (CPA) technology [10–16] can significantly mitigate the undesired nonlinear pulse distortions [3,17,18] imposed upon the amplified pulse, particularly when in combination with the use of large-mode-area (LMA) fiber [10,19,20], e.g., photonic crystal fiber (PCF) [11,12,21,22], chirally-couple-core (CCC) fiber [23], and tapered fiber [24,25]. In this way, high-power fiber lasers are capable of delivering intense ultrashort pulses, which could be used for micro-nano material processing [26,27], bio-imaging [28,29], extreme ultraviolet (XUV) radiation [30], high harmonic generation (HHG) [31] and so on.

In terms of average power or pulse energy, with the development of LMA fiber fabrication [32,33] and amplification techniques [34], the performance metrics of monolithic fiber lasers have reached a new high. With regard to energy scalability, pulses with energies attaining mJ-scale, i.e., 1.45 [35] and 2.2 mJ [36], were realized by virtue of Yb-doped large-pitch fiber (LPF) – a category of solid-core PCF that possesses effective mode-field diameter (MFD) of over 70 µm [33]. Although this kind of fiber owns unprecedentedly low nonlinearity, it is manifested as a rigid rod and loses a key feature of the conventional fibers – flexibility, which hampers the construction of the all-fiber architecture of the amplifier. In the meantime, the average power was limited to 100∼200 W owing to the onset of transverse mode instability (TMI) [37–45]. For higher average power, step-index Yb-doped fibers (YDF) with core diameter of >20 µm have been widely adopted, which enables single-channel output powers of >800 W and >4000 W for ultrafast and continue-wave lasers, respectively [16,19,46,47]. It is noticed that a lower average power is available for ultrafast lasers compared with continue-wave lasers, which is because the accumulated nonlinear effects caused by the fiber nonlinearity and dispersion, particularly in the higher orders, impose additional restrictions in the power scaling of ultrashort pulses. Such type of gain fiber with double-cladding structure is well compatible with fiber-optic components (e.g., signal-pump combiner), and thus, enables all-fiber format. By far, records of the average powers in non-polarization-maintaining (non-PM) and PM all-fiber configurations are ∼1052 [10] and 612 W [48], respectively. Although single pulse energy therein is limited for smaller MFD in comparison with that of LPF, this type of high-power fiber laser operating at a high repetition rate (hundreds of MHz to GHz) has shown great potential to implement appreciable energy multiplication by means of temporal coherent combination [14,49–51].

In this paper, a high-repetition-rate, kilowatt-class, all PM fiber CPA system at 1.0 µm is theoretically and experimentally investigated, and an average power of 1214 W is achieved at a 1.39-GHz repetition rate by well suppressing the nonlinear effects including SPM and SRS. The pulse width after compression is measured to ∼800 fs, with a compression power efficiency of 73%. The output beam quality factor M² is measured to be <1.1 when the power is up to 1214 W. To the best of our knowledge, it is the highest average power from all PM fiber fs lasers at 1.0 µm. It is worth noting that TMI is not present in this system. The developed fiber laser system is expected to explicitly meet the requests of pulse stacking [49] and GHz burst fs laser ablation [26,52].

2. Theoretical analysis

In this section, we first theoretically explore two types of step-index gain fibers with core diameters of 20 and 30 µm (both are capable of handling kW-class average power [53,54]) primarily from the perspective of transverse modal analysis. Considering the reduction of the nonlinearity accumulation and improvement of beam quality, an all PM fiber scheme of high-repetition-rate, high-power fiber laser at 1.0 µm is designed. The numerical modelling based on the dynamic rate equation and generalized nonlinear Schrödinger equation (GNLSE) is conducted to evaluate the nonlinear phase shift accumulated in the chosen gain fiber with varying pre-chirping GDD.

2.1 Parameters of the gain fiber

Here two typical YDFs with core/cladding diameters of 30/400 and 20/400 µm, respectively, are considered for kW-average-power amplification. Because the energy of GHz-repetition-rate pulse is sub-µJ level, the beam quality becomes a pivotal concern when choosing the gain fibers. In this regard, transverse modal analysis is performed, and the calculated results that cover propagation constants $\delta {\beta _0}$, intermodal dispersions $\delta {\beta _1}$, and modal-resolved overlapping factor ${\varGamma ^{(q )}}$ in the form of

(1)$$\begin{array}{{c}} { {\varGamma ^{(q )}} = \frac{{\mathop \smallint \nolimits_{ - {\alpha _{core}}}^{{\alpha _{core}}} \mathop \smallint \nolimits_{ - {\alpha _{core}}}^{{\alpha _{core}}} {i^{(q )}}({x,y} )dxdy}}{{\mathop \smallint \nolimits_{ - \infty }^\infty \mathop \smallint \nolimits_{ - \infty }^\infty {i^{(q )}}({x,y} )dxdy}},} \end{array}$$

are given in Table 1. Notations of ${\alpha _{core}}$ and ${i^{(q )}}({x,y} )$ represent the radius of core and normalized modal-intensity distribution, respectively [55].

Table 1. Key parameters of the step-index gain fibers

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From the parameters of the two gain fibers, in comparison with the 30/400-µm fiber with 6 eigenmodes (including two pairs of degenerate modes, i.e., LP_11a and LP_11b, LP_21a and LP_21b), the 20/400-µm YDF only support 3 transverse modes, i.e., LP₀₁, LP_11a and LP_11b. The discrepancies of $\{{{\boldsymbol \delta }{{\boldsymbol \beta }_0},{\boldsymbol \delta }{{\boldsymbol \beta }_1}} \}$ and ${{\boldsymbol \varGamma }^{({\boldsymbol q} )}}$ between two fibers respectively imply distinctive actions of nonlinear and gain effects on the mode ratio. More specifically, a larger propagation constant difference $\boldsymbol{\delta}\boldsymbol{\beta}_0^{(1 )}$ of the 20/400-µm YDF can inhibit intermodal four-wave mixing (IM-FWM) more effectively [56], thereby precluding energy exchanges between the fundamental mode and higher-order mode (HOM). Please note that, in the CPA system wherein the pulse is dramatically stretched in time, the effect of intermodal dispersion upon the nonlinear interaction (i.e., IM-FWM and IM-MI [57,58]) is anticipated to be greatly suppressed. In the meantime, the overlapping factor of HOM in 20/400-µm YDF (i.e., 0.8 for LP₁₁) is smaller compared with that of the LP₀₁, indicating that the fundamental mode exhibits advantages in extracting energy from the gain fiber [55].

Based on the discussions above, the employment of 20-µm-core YDF is more suitable for good beam quality. The nonlinearity accumulation must be considered for two reasons: 1) the core diameter is not large enough to circumvent the effects of SPM and SRS; 2) the core-cladding ratio ${{\boldsymbol \alpha }_{\boldsymbol{core}}}/{\boldsymbol{\alpha }_{\boldsymbol{clad}}}$ (${\boldsymbol{\alpha }_{\boldsymbol{clad}}}$ is the cladding radius) renders a considerably small overlapping factor of pump (i.e., 0.005 given below), such that a fairly long length of the YDF (e.g., ∼11 m [16,19]) is demanded. Hence, we theoretically study the nonlinear effects of kW-class amplification.

2.2 Numerical modelling and simulation results

The propagation of the amplified pulse in a gain fiber can be described by the GNLSE in the form of [59]:

(2)$$\begin{aligned} \frac{{\partial A}}{{\partial z}} &= \mathop \smallint \limits_{ - \infty }^\infty \frac{1}{2}g({z,\omega } )\tilde{A}({z,\omega } ){e^{ - i\omega t}}d\omega - i\frac{{{\beta _2}}}{2}\frac{{{\partial ^2}A}}{{\partial {t^2}}} + \frac{{{\beta _3}}}{6}\frac{{{\partial ^3}A}}{{\partial {t^3}}}\\ &{ + i\gamma \left( {1 + \frac{i}{{{\omega_0}}}\frac{\partial }{{\partial t}}} \right)\left( {A({z,t} )\mathop \smallint \limits_{ - \infty }^\infty R({t^{\prime}} ){{|{A({z,t - t^{\prime}} )} |}^2}dt^{\prime}} \right),} \end{aligned}$$

where $A({z,t} )$ and $\tilde{A}({z,\omega } )$ are slowly-evolving field envelope and its Fourier transform, $\delta (t )$ is the Dirac function, and $R(t )$ accounts for the Raman response. The frequency-dependent gain $g(\omega )$ used in Eq. (2) is explicitly written as

(3)$$\begin{array}{{c}} { g({z,{\omega_k}} )= \varGamma [{{\sigma_e}({{\lambda_k}} ){N_2}(z )- {\sigma_a}({{\lambda_k}} ){N_1}(z )} ],} \end{array}$$

and is extracted from steady-state propagation-rate equations given below:

(4a)$$\begin{array}{{c}} {\frac{{\partial {P_p}(z )}}{{\partial z}} = {\varGamma _p}[{{\sigma_e}({{\lambda_p}} ){N_2}(z )- {\sigma_a}({{\lambda_p}} ){N_1}(z )} ]{P_p}(z ), } \end{array}$$

(4b)$$\begin{array}{{c}} {\frac{{\partial {P_s}({z,{\lambda_k}} )}}{{\partial z}} = {\varGamma _s}[{{\sigma_e}({{\lambda_k}} ){N_2}(z )- {\sigma_a}({{\lambda_k}} ){N_1}(z )} ]{P_s}({z,{\lambda_k}} )+ 2{\sigma _e}({{\lambda_k}} ){N_2}(z )\frac{{h{c^2}}}{{\lambda _k^3}}\Delta \lambda ,} \end{array}$$

(4c)$$\begin{array}{c} {\frac{{{\varGamma _p}{\lambda _p}}}{{hc{A_c}}}[{{\sigma_a}({{\lambda_p}} ){N_1}(z )- {\sigma_e}({{\lambda_p}} ){N_2}(z )} ]{P_p}(z )- \frac{{{N_2}(z )}}{{{\tau _{21}}}}}\\ { + \frac{{{\varGamma _s}}}{{hc{A_c}}}\mathop \sum \limits_k {\lambda _k}[{{\sigma_a}({{\lambda_k}} ){N_1}(z )- {\sigma_e}({{\lambda_k}} ){N_2}(z )} ]{P_s}({z,{\lambda_k}} )= 0,} \end{array}$$

(4d)$$\begin{array}{{c}} {{N_1}(z )+ {N_2}(z )= {N_{Yb}},} \end{array}$$

where ${P_p}(z ),{\; }{P_s}({z,{\lambda_k}} )$ represent the pump power and signal power that connects with the Fourier transform of the field envelope in terms of [60]

(5)$$\begin{array}{{c}} {{P_s}({z,{\lambda_k}} )= \frac{{{{|{\tilde{A}({z,{\omega_k}} )} |}^2}}}{{{T_R}{T_{span}}}},} \end{array}$$

where ${T_R},{T_{span}}$ are the time period of the pulse train (i.e., $1/{f_{rep}}$) and the width of the temporal window used in the computation. Definitions and values of the key parameters used in the simulations are provided in Table 2. In the numerical simulation, the fourth-order Runge-Kutta method is applied to solve the ordinary differential equations (4a, b), while the GNLSE is solved by using the enhanced split-step Fourier method [59,61].

Table 2. Key parameters used in the numerical simulation

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Here, a pre-chirped pulse is employed as the initial signal, i.e.,

(6)$$\begin{array}{{c}} {A({0,t} )= {\mathrm{{\cal F}}^{ - 1}}\left( {\mathrm{{\cal F}}\left[ {\sqrt {\frac{{{P_{ave}}}}{{{\tau_0}{f_{rep}}}}} sech\left( {\frac{{1.763t}}{{{\tau_0}}}} \right)} \right]{e^{i{\beta_{PC}}{\omega^2}/2}}} \right).} \end{array}$$

Note that, additional noise with an intensity fraction of ∼0.2% is added to account for the relative intensity noise (RIN) (see the following results in Fig. 4). Then, accumulated nonlinearity is numerically investigated with varying pre-chirping GDD ${\beta _{PC}}$.

As showcased by the calculated B-integral ${\varphi _{NL}}$ in Fig. 1(a), three regimes are identified. In regime I for ${\varphi _{NL}} \ge 10\pi $, the collapse of the optical spectrum is observed [see top panel of Fig. 1(b)] for over-excessive nonlinear phase shift. As it enters regime II that is defined by $3.5\pi \le {\varphi _{NL}} < 10\pi $, the optical spectral collapse can be avoided while SPM-induced spectral broadening still presents, as indicated by the green arrow in Fig. 1(c). The broadened spectrum is accompanied by noise-seeded pedestal-like sidelobes [see in Fig. 1(c)] caused by the optical wave breaking (OWB) phenomenon taking place in the normal-dispersive regime under the situation of ${L_D} \gg {L_{NL}}$ (${L_D}$ and ${L_{NL}}$ are dispersion and nonlinear length, respectively). In the meantime, the Raman-effect-driven redshift component also arises, the energy of which can exchange with that of OWB-mediated sidelobe via FWM [see middle curve in Fig. 1(c)]. Further increasing the pre-chirping GDD allows to access regime III featured by ${\varphi _{NL}} < 3.5\pi $, wherein the optical spectrum is well retained after the high-power amplification [see top panel of Fig. 1(b)]. Simultaneously, parasitic spectral components resulting from OWB + FWM and Raman effect are sufficiently suppressed, such that a signal-to-noise ratio (SNR) of >75 dB is obtained, as shown by the bottom curve in Fig. 1(c). Hence, according to the theoretical guideline, it refers to the pre-chirping GDD range of $|{{\beta_{PC}}} |\ge 37{\; \textrm{p}}{\textrm{s}^2}$.

Fig. 1. Numerical simulations of amplified signals with different pre-chirping group delay dispersions (GDDs). (a) B-integral of the system with varying pre-chirping dispersion. Three regimes I, II, and III are recognized according to different B-integrals. (b) Optical spectra of amplified signals in regimes I and III. (c) Typical optical spectra of amplified signals in regimes II and III under the effects of optical wave breaking (OWB) and four-wave mixing (FWM). Three adopted GDDs (labels 1, 2, 3), i.e., 14 ps², 26 ps² and 40 ps², are also indicated in (a).

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3. Experimental setup

Figure 2 depicts the components of the high-power all PM fiber fs laser system that mainly consists of three sections: a seed laser, five stages of fiber optical amplifiers and a compressor. The seed laser has a Fabry-Pérot (FP) laser cavity configuration and is able to deliver GHz-repetition-rate pulses. To generate stable passively mode-locked pulses, a semiconductor saturable absorber mirror (SESAM), which has a relaxation time of 1 ps and a modulation depth of 5%, is utilized as one of the laser cavity end faces. A dielectric film (DF), which has a transmittance at 976 nm pump band of 60% and a reflection at 1028-1100 nm pump band of 75%, is utilized as the other laser cavity end face. A 7-cm-long high-gain single-mode (SM) Yb-doped single-cladding fiber (YSF) is employed as the gain fiber. At the same time, a 976-nm SM laser diode (SM-LD), which delivers 460-mW power at maximum, is employed via a PM wavelength-division multiplexer (PM-WDM). In order to avoid thermal damage to the SESAM [62], a 1-cm-long passive fiber (PM-980, Nufern) is fusion-spliced between the gain fiber and the SESAM. After passing through the PM-isolator and the optical coupler (OC), the seed laser then enters into the 1^st pre-amplifier. The PM-ISO is employed to improve the stability of the seed laser, which may be damaged by the strong amplified spontaneous emission (ASE) produced by the amplifiers. A small portion of the seed signal is extracted by the OC for performance monitoring.

Fig. 2. Schematic diagram of the experimental setup. A pair of CFBGs is employed for pre-chirping the signal pulse. The total GDD is ∼39.6 ps², which is in accordance with the theoretical guideline. PM: polarization-maintaining; SESAM: semiconductor saturable absorber mirror; YSF: Yb-doped single-mode fiber; DF: dielectric film; PM-YDF: PM Yb-doped double-cladding fiber; PM-WDM: PM wavelength-division multiplexer; OC: optical coupler; SM-LD: single-mode laser diode; PM-ISO: PM isolator; CIRs: circulators; CFBGs: chirped fiber Bragg gratings; MM-LDs: multimode laser diodes; MFA: mode field adaptor; CPS: cladding power stripper; PLMA-YDF: PM large-mode-area Yb-doped double-cladding fiber.

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After the seed laser, there exist four pre-amplifiers and an LMA double-cladding fiber amplifier that boosts the average power to kilowatt-level. The 1^st pre-amplifier consists of a PM-WDM, a 0.6-m-long PM Yb-doped double-cladding fiber (PM-YDF, IXF-DF-PM-6-125, Ixblue) and a PM-ISO. The PM-YDF is pumped by a 976 nm SM-LD, which delivers 460-mW power at maximum, through the PM-WDM. After passing through the PM-ISO, the amplified pulses are temporally stretched by chirped fiber Bragg gratings (CFBGs, each has a GDD of 19.8 ps²), each of which has a 6.5-nm bandwidth in 3 dB and its center wavelength is 1064 nm. It is technically challenging to fabricate CFBG with large dispersion due to the constraints among bandwidth, dispersion, and effective length. For this reason, we utilize a pair of CFBGs with smaller amount of GDD [63]. Here, in accordance with the numerical insight (i.e., $|{{\beta_{PC}}} |\ge 37{\; \textrm{p}}{\textrm{s}^2}$), a pair of CFBGs are cascaded by using two circulators (CIRs) to acquire a total GDD of ∼39.6 ps². After the two CFBGs, the pulses are stretched to about 300 ps, such that the peak power is greatly reduced and excess nonlinear phase shift can be suppressed. The structure of the 2^nd pre-amplifier is almost the same as that of the 1^st pre-amplifier, except that the length of the gain fiber is 0.6 m here. Then the pulses enter into the two double-cladding pre-amplifiers (i.e., 3^rd−4^th pre-amplifiers). A 3-m-long PM Yb-doped double-cladding fiber (PM-YDF, PM-YDF-10/125-M, Nufern) is employed in the 3^rd pre-amplifier, which is pumped by a 976 nm multimode laser diode (MM-LD, BWT), which delivers 27-W power at maximum, via a 1 + 2 signal-pump combiner. The structure of the 4^th pre-amplifier is the same as that of the 3^rd pre-amplifier. Given that the loss of the stretcher is relatively high, the 2^nd pre-amplifier with core pump is additionally employed to compensate for the power loss before the cladding-pumped high-power amplification, resulted in four stages of pre-amplifiers. After passing through a CIR, which is employed to protect the laser system from the back reflection and monitor the backscattered light, the amplified signal is fed into the main amplifier.

Guided by the modal analysis above, the gain fiber of the main amplifier is a 9-m-long 20-µm-core PM large-mode-area Yb-doped double-cladding fiber (PLMA-YDF, PLMA-YDF-20/400-M, Nufern), which has a cladding absorption coefficient of 2 dB/m at 976 nm and numerical apertures of 0.07 and 0.48 for the core and cladding, respectively. The main amplifier is backward pumped by two pump modules (BWT), each of which delivers 800-W power at maximum, which are coupled into the PLMA-YDF via a 1 + 2 signal-pump combiner. Finally, the amplified laser is collimated and compressed by the compressor, which contains a pair of transmission diffraction gratings (1600 line/mm line density and 58° Littrow angle), with a size of 31.4 mm × 24.8 mm and 120 mm × 20 mm, respectively.

4. Result and discussion

The characterization of the 1.0-µm high-repetition-rate seed laser is shown in Fig. 3. The performance of the seed is first converted by a high-speed photodetector (818-BB-51F, Newport), and subsequently analyzed by a 20-GHz real-time oscilloscope (SDA 820Zi-B, Teledyne). The measured optical spectrum shows a central wavelength of 1064 nm and a 4-nm bandwidth in 3 dB, as can be seen in Fig. 3(a). The pulse train over a temporal span of 5 ns is depicted in Fig. 3(b), showing a typical mode-locked state, while a wider span of 50 ns is provided in the inset. The temporal interval of the pulses is 717 ps, corresponding to the 1.39-GHz fundamental repetition rate. As can be seen from Fig. 3(c), at a resolution bandwidth of 100 Hz, the SNR of the radio-frequency (RF) spectrum is 87.98 dB, which identifies the stable performance of mode-locking. As can be observed, consistent with the temporal interval of the pulses, the seed laser has a 1.39-GHz fundamental repetition rate. A wider span of 11 GHz is shown in Fig. 3(d), exhibiting no sidelobes in the fundamental mode-locking, which is free of supermode noise.

Fig. 3. Characterization of the 1.0-µm high-repetition-rate seed. (a) Optical spectrum. (b) Oscilloscopic trace. The inset in the upper right-hand side shows a wider span of 50 ns of the pulse train. (c) Radio-frequency (RF) spectrum measured at a 60-MHz span (at a resolution bandwidth (RBW) of 100 Hz). (d) RF spectrum measured at an 11-GHz span (at an RBW of 10 kHz).

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The average output power of the seed laser is 5 mW with a 76-mW pump power. After passing through the PM-ISO and the OC before the 1^st pre-amplifier, the average power of the pulse signal is decreased to 2 mW. It is then amplified by the 1^st pre-amplifier to 131 mW, with a pump power of 467 mW. After that, the amplified pulses are temporally broadened to 300 ps by the cascaded CFBGs. Due to the insertion loss of the stretcher, the output average power of the pulses is decreased to 5.8 mW. In order to increase the power before entering double-cladding amplifiers (i.e., 3^rd−4^th pre-amplifiers), the 2^nd pre-amplifier boosts the output average power of the pulse signal to 130 mW with a pump power of 386 mW. The amplified pulses then enter into the 3^rd pre-amplifier, wherein the output average power is boosted to 2.9 W with a pump power of 5.3 W. In the 4^th pre-amplifier, an 11.8-W output average power is achieved with a pump power of 17.5 W.

The phase noise and RIN of the high-power high-repetition-rate laser system before and after the stretcher, as well as the 4^th pre-amplifier, are measured by an RF signal analyzer (N9020A, Agilent), as shown in Fig. 4. By comparing the results of phase noise and jitter manifested in Figs. 4(a) and 4(c), we reveal that pulse stretching evidently degrades the phase noise of the signal, while the 4^th pre-amplifier does not. Specifically, before the stretcher, the timing jitter integrated from 100 Hz to 1 MHz is measured to be ∼0.24 ps, while after the stretcher and 4^th pre-amplifier, it is measured to be ∼13.4 ps and ∼15.1 ps. This is because the time stretch additionally converts the fluctuation of the central wavelength of the pulse into the deviation in the temporal position, thereby raising the timing jitter. Based on the increase of PN in the range of 10 kHz to 1 MHz, i.e., up to 439 fs, the wavelength drift is estimated to be 6.6 pm according to the wavelength-time mapping [64]. On the other hand, the RIN mostly sustains before and after the stretcher, while it deteriorates after the 4^th pre-amplifier, particularly in the low-frequency range, as indicated by arrows in Figs. 4(b) and 4(d). Specifically, before the stretcher, the RIN integrated from 10 Hz to 1 MHz is measured to be 0.136%, while after the stretcher and 4^th pre-amplifier, it is measured to be 0.119% and 0.210%. Furthermore, after the stretcher, the RIN in the frequency range from 1 kHz to 100 kHz is reduced, which could be attributed to the filtering effect of CFBGs after partially removing the ASE.

The average output power of the all PM fiber laser and its function of the pump power, as well as the optical spectra at different powers, are shown in Fig. 5. The output power of the main fiber amplifier is monitored by a thermal power sensor (FL1100A-BB-65, Ophir), and the optical spectrum is measured by an optical spectrometer (AQ6370D, Yokogawa). The average power reaches 1214 W with a pump power of 1400 W, corresponding to a slope efficiency of 86.71%. The output power linearly increases with the pump power, and no gain saturation can be observed, as can be seen from Fig. 5(a). There is also good agreement between the experimental data and the simulated one. The optical spectra of the main amplifier at different power levels are depicted in Fig. 5(b), wherein no visible spectral broadening is inspected as the output power reaches up to 1214 W. In consistence with the numerical result in regime III, no Stokes component driven by the Raman effect is observed at the maximum average power in a dynamic range of 40 dB [see the inset of Fig. 5(b)]. We note that the sidelobe of the spectrum at longer wavelength does not originate from OWB but the residual ASE is largely truncated by the band-pass filters that are integrated into each ISO. As no obvious power saturation is observed so far, an even higher output power is expected from the main amplifier by further stretching the signal pulse and increasing the pump power, which however is not available in our laboratory at this moment.

Fig. 4. Noise performance of the fiber laser system, measured after the 1^st pre-amplifier (blue), stretcher (green), and 4^th pre-amplifier (red). (a) Phase noise (PN). (b) Relative intensity noise (RIN). (c) Integrated timing jitter. (d) Integrated RIN.

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Fig. 5. Characterization of the kilowatt-average-power main amplifier. (a) Output power of the main fiber amplifier as a function of the pump power. (b) Optical spectra of the main amplifier at different levels of output power. The inset shows a wider span of 200 nm.

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The main amplifier is placed on a water-cooled plate, and its gain fiber is coiled with a diameter of about 8 cm to suppress the HOMs (i.e., LP_11a and LP_11b). In addition to the benefit of gain extraction with respect to the fundamental mode (LP₀₁), good beam quality characterized by an M² value of <1.1 is obtained at the output power of 1214 W, which confirms that the beam quality is nearly diffraction-limited. After the end cap, the output pulses then enter into the grating-pair compressor with a compression efficiency of ∼73%. As can be seen from Fig. 5(b), the optical spectrum measured at the maximum output power has a 3-dB bandwidth of 3 nm, corresponding to a transform-limited pulse width of 555 fs. However, due to the third-order dispersion, which is uncompensated in the system, the output pulse is only compressed to a duration of 800 fs measured by an autocorrelator (FR-103XL, Femtochrome), which is indicated by the sidelobes of the autocorrelation trace [ Fig. 6(b)]. To access a narrower amplified pulse, two approaches can be considered: 1) applying compensation for higher-order dispersion [48]; 2) exploiting techniques to achieve larger spectral bandwidth of the pulse, e.g., intracavity dispersion management [65–67], pre-chirp managed amplification [22], and gain-managed nonlinear amplification [25,34].

Fig. 6. Beam quality and pulse width measurements of the kilowatt-class high-repetition-rate all PM fiber laser system. (a) Measurement of the beam quality M², measured before the compressor at an output power of 1214 W. Inset: beam profile. (b) Measurement of the autocorrelation trace (blue) and its hyperbolic secant (Sech) fitting (red), measured at the maximum output power.

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5. Conclusion

In conclusion, a high-power all PM fiber fs laser system has been demonstrated, which delivers ultrashort pulses at a 1.39-GHz fundamental repetition rate. This ultrafast all PM fiber laser system can provide an average output power of up to 1214 W at a good beam quality of M²< 1.1. It is shown that this system does not show TMI and obvious nonlinear effects commonly observed in high-power fs fiber laser systems operating at low repetition rates. This kilowatt-class fs fiber laser system is expected to be a promising platform for pulse stacking and industrial applications.

Funding

National Natural Science Foundation of China (12374304, 62235014, 62375087); NSFC Development of National Major Scientific Research Instrument (61927816); Mobility Programme of the Sino-German (M-0296); Introduced Innovative Team Project of Guangdong Pearl River Talents Program (2021ZT09Z109); Natural Science Foundation of Guangdong Province (2021B1515020074).

Disclosures

The authors declare no conflict of interest.

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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Gain fiber	Modes (q)	LP₀₁ (q = 1)	LP₁₁ (q = 2)	LP₂₁ (q = 3)	LP₀₂ (q = 4)
30/400 µm (NA 0.07)	$δ β_{0}^{(q)}$ (mm⁻¹)	0	−1.73	−3.96	−4.67
	$δ β_{1}^{(q)}$ (ps/m)	0	0.65	1.41	1.51
	$Γ^{(q)}$	0.98	0.94	0.89	0.86
20/400 µm (NA 0.065)	$δ β_{0}^{(q)}$ (mm⁻¹)	0	−3.1	/	/
	$δ β_{1}^{(q)}$ (ps/m)	0	0.56	/	/
	$Γ^{(q)}$	0.93	0.8	/	/

Parameters of the fiber amplifier	Value
Length of LMA gain fiber ( $L$ , m)	9
Pump wavelength ( $λ_{p}, n m$ )	976
Signal wavelength ( $λ_{s}, n m$ )	1064
Overlap factor of signal (*Γ_s*)	0.7
Overlap factor of pump (*Γ_p*)	0.005
Upper-state Lifetime $(τ_{21}$ , ms)	0.85
Yb³⁺ Concentration (*N_Yb*, m⁻³)	3.9 × 10²⁵
Absorption Cross Section (*σ_a(λ_p)*, m²)	1.76691 × 10⁻²⁴
Emission Cross Section (*σ_e(λ_p)*, m²)	1.7131 × 10⁻²⁴
Absorption Cross Section (*σ_a(λ_s)*, m²)	6.4 × 10⁻²⁷
Emission Cross Section (*σ_e(λ_s)*, m²)	3.978 × 10⁻²⁵
Core Area (*A_c*, µm²)	314.16
Nonlinear coefficient ( $γ$ , W⁻¹m⁻¹)	3.5 × 10⁻⁴
Second-order dispersion ( $β_{2}$ , ps²/km)	−20
Third-order dispersion ( $β_{3}$ , ps³/km)	0.3
Fractional contribution of the delayed Raman response $f_{R}$	0.18
Phonon frequency ( ${τ_{1}}^{- 1}$ , fs⁻¹)	12.2⁻¹
Bandwidth of the Lorentzian line ( ${τ_{2}}^{- 1}$ , fs⁻¹)	32⁻¹
Parameters of the pulse	Value
Average power ( $P_{a v e}$ , W)	12
Repetition rate ( $f_{r e p}$ , GHz)	1.4
Transform-limited pulse width ( $τ_{0}$ , ps)	0.5
Carrier angular frequency ( $ω_{0}$ , THz)	1770
Pre-chirping GDD ( $β_{P C}$ , ps²)	5∼50
Intensity noise fraction on the input pulse	0.2%

Gain fiber	Modes (q)	LP₀₁ (q = 1)	LP₁₁ (q = 2)	LP₂₁ (q = 3)	LP₀₂ (q = 4)
30/400 µm (NA 0.07)	$δ β_{0}^{(q)}$ (mm⁻¹)	0	−1.73	−3.96	−4.67
	$δ β_{1}^{(q)}$ (ps/m)	0	0.65	1.41	1.51
	$Γ^{(q)}$	0.98	0.94	0.89	0.86
20/400 µm (NA 0.065)	$δ β_{0}^{(q)}$ (mm⁻¹)	0	−3.1	/	/
	$δ β_{1}^{(q)}$ (ps/m)	0	0.56	/	/
	$Γ^{(q)}$	0.93	0.8	/	/

Parameters of the fiber amplifier	Value
Length of LMA gain fiber ( $L$ , m)	9
Pump wavelength ( $λ_{p}, n m$ )	976
Signal wavelength ( $λ_{s}, n m$ )	1064
Overlap factor of signal (*Γ_s*)	0.7
Overlap factor of pump (*Γ_p*)	0.005
Upper-state Lifetime $(τ_{21}$ , ms)	0.85
Yb³⁺ Concentration (*N_Yb*, m⁻³)	3.9 × 10²⁵
Absorption Cross Section (*σ_a(λ_p)*, m²)	1.76691 × 10⁻²⁴
Emission Cross Section (*σ_e(λ_p)*, m²)	1.7131 × 10⁻²⁴
Absorption Cross Section (*σ_a(λ_s)*, m²)	6.4 × 10⁻²⁷
Emission Cross Section (*σ_e(λ_s)*, m²)	3.978 × 10⁻²⁵
Core Area (*A_c*, µm²)	314.16
Nonlinear coefficient ( $γ$ , W⁻¹m⁻¹)	3.5 × 10⁻⁴
Second-order dispersion ( $β_{2}$ , ps²/km)	−20
Third-order dispersion ( $β_{3}$ , ps³/km)	0.3
Fractional contribution of the delayed Raman response $f_{R}$	0.18
Phonon frequency ( ${τ_{1}}^{- 1}$ , fs⁻¹)	12.2⁻¹
Bandwidth of the Lorentzian line ( ${τ_{2}}^{- 1}$ , fs⁻¹)	32⁻¹
Parameters of the pulse	Value
Average power ( $P_{a v e}$ , W)	12
Repetition rate ( $f_{r e p}$ , GHz)	1.4
Transform-limited pulse width ( $τ_{0}$ , ps)	0.5
Carrier angular frequency ( $ω_{0}$ , THz)	1770
Pre-chirping GDD ( $β_{P C}$ , ps²)	5∼50
Intensity noise fraction on the input pulse	0.2%

1200-W all polarization-maintaining fiber GHz-femtosecond-pulse laser with good beam quality

Abstract

1. Introduction

2. Theoretical analysis

2.1 Parameters of the gain fiber

2.2 Numerical modelling and simulation results

3. Experimental setup

4. Result and discussion

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Tables (2)

Equations (9)

Optics Express