Ultrashort pulses with high peak power find applications in a very wide range of fields including machining [1], surgery [2], and quantum materials research [3], to name a few. The primary technologies for generating these pulses rely on either solid-state or fiber amplifiers. Solid-state amplifiers typically employ regenerative (and/or multi-pass) amplification [4,5], where a pulse makes multiple passes through an amplifying medium within a cavity with an optical switch. This approach is necessary to achieve large net gain because the single-pass gain through crystals is small (typically $\lesssim 1\;{\rm dB}$). In contrast, fiber amplifiers feature long interaction lengths (${\sim}{\rm m}$ scale) and single-pass amplification with much larger gain (${\sim}20\;{\rm dB}$) [6,7]. Fiber lasers also have a range of well-known practical advantages over solid-state systems, such as their waveguiding and thermal properties. However, it remains difficult to design fiber amplifiers that reach pulse energies typical of solid-state regenerative amplifiers ($\gtrsim 10\;{\unicode{x00B5} \rm J}$) because femtosecond pulses accumulate large nonlinear phase shifts on propagation through small-core fibers over long distances. This limitation has prompted diverse research efforts to mitigate or exploit nonlinear effects in fiber lasers. Among these efforts, the use of multimode fiber in oscillators [8] and amplifiers [9–13] has received attention recently.

Multimode fibers inherently enable higher pulse energies than single-mode fibers due to their larger core areas. Despite this potential, the use of multimode fiber in high-performance ultrafast lasers faces significant challenges. Propagation through multimode fiber distorts the spatial and temporal profiles of a pulse. To address this, researchers have studied techniques and phenomena that aim to control multimode amplification and generate high-quality beams. Examples include multimode amplifiers with adaptive optics [12], and nonlinear phenomena such as Kerr beam cleaning [10,14]. However, these techniques have not yet achieved performance improvements; highly multimode fiber sources are still not capable of generating transform-limited pulses and diffraction-limited beams. Another challenge is the gain behavior of multimode fiber, which differs from that of single-mode fiber. While large-core multimode fiber enables higher gain than single-mode fiber in principle, the spontaneous emission trapped by a fiber scales with the number of guided modes [15,16]. This severely limits the extractable gain for low-average-power seed pulses [17,18]. For these reasons, doped multimode fibers are almost exclusively limited to amplification of nanosecond-scale pulses with highly multimode beams, at average power levels of at least 10 W [19–24].

Regenerative amplification in multimode fiber can address these challenges. Several works have demonstrated regenerative fiber amplifiers capable of very strong amplification of nanosecond pulses (gains of ${\sim}40 - 70\;{\rm dB}$, from ${\sim}1\;{\rm pJ}$ to ${\sim}100\;{\unicode{x00B5} \rm J}$ pulse energies [25–27]), but regenerative amplification of femtosecond pulses remains almost entirely unexplored [28,29]. Conventional wisdom holds that femtosecond fiber sources do not benefit from regenerative amplification, because amplification of femtosecond pulses by these levels of gain in fiber would result in catastrophic nonlinear effects. However, the large mode areas available in multimode fiber should permit scaling to these energy levels. Regenerative amplification may also suppress amplified spontaneous emission (ASE) and enable operation of highly multimode amplifiers with low (${\lt}{10}\;{\rm W}$) average power [30]. Finally, regenerative amplification should provide a previously unexplored mechanism with which to control the spatial and temporal properties of light in a multimode fiber amplifier: optical feedback. Feedback is widely used to control the spatial properties of multimode lasers, such as spatiotemporally mode-locked fiber oscillators [31] and highly multimode solid-state lasers [32,33], but is not available as a degree of control in single-pass amplifiers.

 

Fig. 1. Regenerative amplification in multimode fiber. (a) Schematic of regenerative amplifier cavity. The incoming pulse train enters the cavity through an isolator comprising two polarizing beam splitters (PBS), a half-wave plate (HWP), and a Faraday rotator (FR). Switching through the intracavity PBS is accomplished with a Pockels cell (PC) and quarter-wave plate (QWP). The Yb-doped multimode fiber amplifier (XLMA) is pumped with a 976 nm multimode diode that is free-space-coupled into the fiber via a dichroic mirror (DM). Two lenses on each side of the fiber form 4-f telescopes to image the fiber facets to the cavity mirrors (M), which image the fiber facets back to themselves. Lenses are omitted from the schematic for visual clarity. A spectral filter (SF) on one side of the amplifier prevents CW-lasing at long wavelengths (${\gt}{1055}\;{\rm nm}$) but does not filter the signal. This filter is only necessary due to the limited bandwidth of the PBS used here (1020–1060 nm). (b) Photodiode trace showing the pulse buildup, obtained from a parasitic reflection from the intracavity PBS. (c) Photodiode trace of the output pulse. Inset shows the same for a wider time window.

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Here we report regenerative amplification in a large-core (100 µm diameter) multimode fiber. The amplifier feedback enables robust single-mode operation (${M^2} \le 1.3$) despite the use of fiber that supports over 200 transverse modes. With this amplifier we demonstrate single-stage, high-gain (${\gt}{55}\;{\rm dB}$) chirped-pulse amplification that yields 55 µJ pulses. After compression, the pulse duration is 300 fs. This work is the first demonstration of regenerative amplification of femtosecond pulses in fiber. We discuss how this power-scalable technique will enable a new class of high-performance femtosecond fiber lasers; we expect that this technique can be extended to reach millijoule-scale pulse energies and gigawatt-level peak powers in simple, one-stage amplifier systems.

A schematic of the regenerative fiber amplifier is shown in Fig. 1(a). The linear cavity has similar architecture to typical solid-state regenerative amplifiers [34]. A Pockels cell operating in a quarter-wave configuration switches pulses into and out of the cavity. The repetition rate and number of round trips through the amplifier are controlled by the frequency and duration of the voltage pulses applied to the Pockels cell [an example is shown in Fig. 1(b)]. The amplifier is seeded by 100 pJ pulses from an all-normal-dispersion fiber oscillator [35]. The cavity repetition rate (67 MHz) is larger than that of the incoming pulse train (50 MHz), which allows amplification of a single pulse from the seed pulse train without an additional pulse picker. The output pulse train for 10 kHz operation is shown in Fig. 1(c).

The triple-clad multimode fiber that is the heart of the amplifier has a 100 µm core diameter and step-index profile (Nufern XLMA-YTF-100/400/480). This fiber supports ${\sim}250$ guided modes [36], with a fundamental-mode diameter of 71 µm. The fiber is cut short (35 cm) with angle-cleaved facets (${\sim}{1^ \circ}$) to help suppress reflections, and it is laid in a straight V-groove cut into an aluminum block to minimize linear coupling between modes due to mechanical stresses.

The cavity is designed to support modes that are identical to those of the multimode fiber. This differs from conventional laser cavities where no waveguide is present, and intracavity optics define cavity modes by design. In our amplifier, a 4-f telescope images each fiber facet to a flat cavity end mirror, and vice versa. For perfect alignment and ideal optics, the cavity modes are therefore identical to those of the fiber. However, the cavity modes are not degenerate in any sense, because the gain, loss, and dispersion properties of each mode differ. Differential modal gain is related to mode area and core overlap, while differential modal loss results from small aberrations in the intracavity optics. The steady-state cavity mode—the spatial profile generated by the amplifier in the limit of many round trips—is determined by a competition between these effects [37].

The fundamental mode of the fiber is the lowest-loss and highest-gain cavity mode. This enables fundamental-mode operation of the highly multimode fiber, even if higher-order modes are initially excited. The beam profiles in Fig. 2 demonstrate this behavior. The input seed beam is deliberately aligned off-axis to excite higher-order modes and generate the structured beam shown in Fig. 2(a). After six round trips through the cavity, the output beam profile is noticeably cleaner, consisting of one main lobe off-center from the fiber core [Fig. 2(b)]. After 15 round trips [Fig. (2c)], the beam profile is nearly the pure fundamental mode. Figure 2 shows the results of one initial condition (or equivalently, one seed alignment), but similar behavior occurs for other initial conditions.

 

Fig. 2. Mode-cleaning regenerative amplification. (a)–(c) Output-beam profile of the regenerative amplifier after the indicated numbers of round trips (RTs). For this experiment, the seed pulse is deliberately misaligned from the fundamental mode to excite higher-order modes.

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Fig. 3. Nearly diffraction- and transform-limited 55 µJ pulses from a multimode fiber regenerative amplifier. (a) Spectrum of amplified pulse (black) and seed pulse (blue dashed) normalized to the same background noise floor. (b) Output beam, with centered cross-sections in green. (c) Output pulse measured by frequency-resolved optical gating (FROG). The dotted red line indicates the transform-limited pulse corresponding to the spectrum in (a). Insets show measured and retrieved FROG traces.

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This behavior is a general property of dissipative cavities, and is not unique to this system. Similar behavior is exploited in most laser cavities, where diffraction and dissipation combine to produce the lowest-loss for the fundamental cavity mode [37] (either by resonator design or with deliberate spatial filtering). Simulations indicate that in our system, small and unavoidable aberrations in the intracavity beam increase the loss for higher-order modes and couple higher-order modes to the fundamental mode. While these effects are small in magnitude, they compound over each round trip and are sufficient to generate nearly 100% fundamental-mode content. This is achieved without any direct intracavity spatial filters. Simulations also indicate that the aberrations necessary to achieve this condition are not particular—similar behavior occurs for a variety of small, common aberrations acting alone or together. Additional discussion and numerical simulations that illustrate this behavior are in Supplement 1.

Fundamental-mode operation of large-core multimode fiber should enable laser performance well beyond the limits of ordinary single-mode fibers. We demonstrate this by using this system to amplify chirped pulses [38]. The seed pulses are stretched with a chirped volume Bragg grating (VBG) to ${\sim}200\;{\rm ps}$ before amplification [39]. The same VBG compresses the pulses after amplification, and a standard grating compressor removes the uncompensated chirp accumulated in the oscillator and amplifier. The results of the experiment in Fig. 2 show that fundamental-mode selection is a property of the amplifier cavity, and does not require alignment of the seed pulse to the fundamental mode. Nonetheless, to obtain the best amplifier performance, we deliberately couple the seed pulse to the fundamental mode of the fiber. With this alignment, a nearly pure fundamental mode is maintained for any number of round trips, in contrast to the behavior in Fig. 2.

The performance of the regenerative amplifier operating at 10 kHz and six round trips (12 total trips through the multimode fiber) is summarized in Fig. 3. The amplifier achieves 57 dB gain, amplifying 100 pJ pulses to over 55 µJ. Despite this large gain, the spectral signal-noise contrast is excellent [over 30 dB as shown in Fig. 3(a)]. Without regenerative amplification, the same level of gain would require several single-pass fiber amplifier stages [7]. The regenerative configuration also enables strong amplification of seed pulses with very low average powers (${\sim}1\;{\unicode{x00B5} \rm W}$). The same amplifier operated without regenerative feedback (in a double-pass configuration) provides negligible gain and the output is dominated by ASE (see Supplement 1 for details). We suspect that the single-mode behavior of the cavity helps to effectively filter out ASE that is initially guided by higher-order modes.

The spatiotemporal properties of the amplified pulses are consistent with operation in a single transverse mode. The output beam [Fig. 3(b)] is near-Gaussian in appearance and has high quality ($M_x^2 = 1.3$, $M_y^2 = 1.1$). Higher-order mode content rapidly degrades beam profiles and ${M^2}$ [40]. From the measurements of ${M^2}$, we estimate the fundamental-mode content to be 95%. The compressed pulse [Fig. 3(c)] is close to transform-limited in duration and has a temporal Strehl ratio of 0.74. Evolution in multiple transverse modes would produce pulses with larger deviation from the transform limit owing to modal dispersion. Additional analysis, beam measurements, and multimode evolution experiments are provided in Supplement 1.

The short-pulse performance of the amplifier is limited by nonlinear phase accumulation, and not ASE or gain. Numerical simulations (see Supplement 1) indicate a nonlinear phase of ${\sim}\pi$ for the 55 µJ pulse shown in Fig. 3(c). This matches the experimental trend, as increasing the pulse energy beyond 55 µJ degrades the temporal profile. For this demonstration we operated the amplifier with the minimum number of round trips allowed by our Pockels cell driver (six) in order to limit fiber propagation length and nonlinear phase accumulation. This results in a slope efficiency of 10%. Significantly higher gain and efficiency are available by increasing the number of round trips in the cavity, without deterioration of the ASE contrast or beam profile. We have operated the amplifier with slope efficiencies up to 30% by increasing the number of round trips, but we have not systematically studied the maximum efficiency out of caution for damaging the amplifier components. Detailed numerical modeling and optimization of the gain properties of regenerative fiber amplifiers will be the subject of future study.

Single-mode operation of multimode fiber will underpin peak-intensity scaling of the performance reported here to much higher levels. The fundamental mode area of the fiber used here is already comparable with the mode areas of large rod-type photonic-crystal fibers (PCFs) designed for single-mode operation [41]. The mechanism for single-mode operation demonstrated here—regenerative feedback—does not rely on a special fiber design, so it should be possible to surpass the fundamental-mode diameter of the fiber employed here (71 µm) using this technique with larger-core, standard step-index fibers. We have amplified pulses to 100 µJ pulse energy, limited by the properties of the Pockels cell, without degradation of the beam profile or ASE contrast. The saturation energy of the fiber is ${\sim}1\;{\rm mJ}$, and 10 ns pulses have been amplified to 100 mJ in a similar fiber [24]. It is clear that pulse energies well above 1 mJ will be achievable. The highest peak power obtained from a single-emitter fiber amplifier is 4 GW, in 2.2 mJ and 500 fs pulses [42]. This system has four gain stages including a PCF rod, three acousto-optic modulators, and a spatial light modulator for spectral phase control [42]. Established scaling from the initial results presented above by stretched-pulse duration, mode area, and polarization would allow the regenerative fiber amplifier to generate 2 mJ and ${\sim}300\;{\rm fs} $ pulses, thus duplicating the performance of a highly complex multi-stage system in a single low-cost, small-footprint stage.

Regenerative amplification in multimode fiber will also provide a platform to study ultrafast pulse amplification beyond linear chirped pulse amplification in a single transverse mode. Unlike most solid-state regenerative amplifiers, the single-pass gain in the amplifier here is large enough (${\sim}5\;{\rm dB}$) to comfortably tolerate losses from dissipative, dispersive, or diffractive intracavity optics such as filters [35], stretchers [43], and spatial modulators [12], to name a few. It should be possible to use regenerative feedback with such intracavity components to control pulse evolutions in ways that are impossible in either single-pass amplifiers or mode-locked oscillators. We suspect that fiber regenerative amplifiers will not only realize the extreme limits of well-known nonlinear pulse evolutions [35,44], but enable exploration of new pulse propagation physics.

In conclusion, we have demonstrated a simple, power-scalable approach to single-mode regenerative amplification in highly multimode fiber. Experiments show that regenerative feedback enables unprecedented control over pulse propagation in multimode fiber. Using this feature, we demonstrate a single-stage, high-gain chirped-pulse amplification system. Despite the use of highly multimode fiber, the amplifier generates high-energy, nearly diffraction- and transform-limited pulses. In addition to single-mode operation, regenerative feedback enables high-gain, high-contrast amplification beyond the limits of single-pass amplifiers. This technique unlocks the use of multimode fiber in high-performance femtosecond systems, and we suspect it will enable a new class of high-performance fiber lasers.